Alpha Portland Cement Company v. Reese Reply Brief for Appellant
Public Court Documents
May 2, 1974
Cite this item
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Case Files, McCleskey Legal Records. George Woodward Transcript, 1983. d209d976-5aa7-ef11-8a69-6045bdd6d628. LDF Archives, Thurgood Marshall Institute. https://ldfrecollection.org/archives/archives-search/archives-item/11ff5b19-4a32-4b6d-b661-1cd0bfdd57c6/george-woodward-transcript. Accessed April 30, 2025.
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IN THE UNITED STATES DISTRICT COURT
FOR THE NORTHERN DISTRICT OF GEORGIA
ATLANTA DIVISION
WARREN MCCLESKEY
CIVIL ACTION
NO. C81-2434A
WALTER ZANT
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BEFORE
THE HONORABLE J. OWEN FORRESTER, DISTRICT JUDGE
ATLANTA, GEORGIA
OCTOBER 17, 19583
APPEARANCES OF COUNSEL:
FOR THE PLAINTIFF: JOHN CHARLES BOGER
ROBERT STRCUP
FOR THE DEFENDANT: MARY BETH WESTMORELAND
KIMBERLY C. BRAMLETT
OFFICIAL COURT REPORTER
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NAME PAGE
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GW 9
GW 10
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GW 12
GW 13
INDEX
CF EXHIB ITS
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WOODWORTH ~ DIRECT
(ATLANTA, FULTON COUNTY, GEORGIA; MONDAY, OCTOBER 17, 1983, IN
OPEN COURT.)
THE COURT: EXCUSE ME FOR THE DELAY. IT'S ONE OF THOSE
MONDAY MORNINGS.
I AM DUTY JUDGE AND HAVING BEEN JUDGE FOR TWO YEARS, IT
DOESN'T OFTEN HAPPEN YOU GET A CALL FROM NEW YORK IN THE MIDDLE
OF A DISPUTE. IT ONLY HAPPENS ON MONDAY MORNING WHEN YOU HAVE A
CALENDAR CALL. SO THAT IS WHAT I HAVE BEEN DEALING WITH.
THIS IS THE CONTINUATION OP THE EVIDENTIARY HEARING IN
MECLESKEY VS. ZANT.
AFTER THE LAST HEARINGS I STARTED LOOKING OVER THE DATA
WHICH WAS RECEIVED TRYING TO UNDERSTAND THE REGRESSION ANALYSIS
AND I PICKED UP A COPY OF THE DR. BALDUS' REPORT AND LOOKED AT
IT AND I PICKED UP A COPY OF THE COLUMBIA LAW REVIEW AND LOOKED
AT IT AND I REALIZED I DIDN'T REALLY UNDERSTAND THE INTELLECTUAL
LOGIC AND I USE THOSE TERMS TO DISTINGUISH BETWEEN THE
MATHEMATICAL LOGIC AND THE INTELLECTUAL LOGIC THAT WAS INHERENT
UNDER REGRESSION ANALYSIS.
I COMMUNICATED SOME OF THE QUESTIONS I HAD TO COUNSEL
FOR THE PETITIONER AND I BELIEVE HE HAS ACCURATELY LISTED THEM
IN HIS PREHEARING ORDER HE SUBMITTED AND I SIGNED. THERE MAY BE
QUESTIONS DERIVATIVE OF THOSE BUT THAT I THINK FAIRLY DESCRIBES
THE AREA CF THE COURT'S CONCERN.
WHEN THIS CASE BEGAN, I MADE SCME INQUIRY TO FIRD OUT
WHY THESE STATISTICS WERE DIFFERENT THAN THOSE I PREVIOUSLY
WCODWORTH = DIRECT
HEARD IN MCCORQUODALE AND HCUSE AND 1 WAS TOLD THEY WERE DIFFERENT
RECAUSE ALTHOUGH COMPARABLES CQULD.NOT BE FOUND, YOU COULD KIND
OF DO THE SAME THING BY A REGRESSION ANALYSIS AND WE LISTENED TO
A LOT OF TESTIMONY ABOUT CONTROLLING VARIABLES. AND THAT IS
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WHERE I WOULD LIKE TO START IN TERMS OF WHAT THAT MEANS
LOGICALLY, WHAT 1S BEING DONE, AND YOU MAY GO AHEAD WITH THE
OTHERS AND I WILL PROBABLY ASK QUESTIONS AS WE GO ALCNG.
MR, BOGER, I WILL LET YOU TAKE OVER AT THIS POINT AND
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PUT ON WHATEVER YOU WOULD LIKE TO.
10 MR. BOGER: I WOULD CALL DR. GEORGE WOODWORTH TO THE
11 STAND.
12 THE COURT: DR. WOODWORTH, THIS IS A CONTIRUATION OF
13 THE SAME HEARING, SO CONSIDER YOURSELF AS BEING STILL UNDER
14 OATH.
18 ® ® *
16 GQ EZORGCE WOODWORTH,
17 CALLED AS A WITNESS BY THE PLAINTIFF, BEING
18 FIRST DULY SWORN, TESTIFIED AS FOLLOWS:
19 DIRECT EXAMINATION
3 20 BY MR. BOGER:
4 21 Q. DR. WOODWORTH, AS THE COURT NOTED, YOU REMEMBER WE HAD AN
22 EXTENDED HEARING IN THIS CASE IN AUGUST, DO YOU NOT?
23 A. ¥£8,
24 Q. AND THE COURT HAS, AS IT INDICATED, DIRECTED A FURTHER
25 HEARING TODAY ON SOME OF THE STATISTICAL QUESTIONS THAT AROSE
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WOODWORTH =~ DIRECT
OUT OF THAT BEARING.
HAVE YOU RECEIVED A COPY OF THE PREHEARING ORDER THAT
WAS SIGNED IN THE CASE THAT FRAMES THOSE QUESTIONS?
A. YES, I HAVE,
Q. AND HAVE YOU REFLECTED ON THOSE QUESTIONS AND COME UP WITH
SOME ANSWERS?
A, YES, I BAVE.
Q. LET'S TURN TO THEM ONE BY ONE AND GO THROUGEB THEM AND I WIL]
ASK YOU TEE QUESTIONS AND ASK YOU SOME FOLLOW-UP QUESTIONS ABOUT
THEM AND OBTAIN SOME ANSWERS AND THE COURT SHOULD CERTAINLY FEEL
PRE TO BREAK IN AT ANY TIME IF THERE ARE MATTERS THAT ARE NOT
CLEAR.
THE FIRST QUESTION DR. WOODWORTH IS AS FOLLOWS:
WHAT ARE THE MATHEMATICAL, STATISTICAL, PRACTICAL
EFFECTS OF CONTROLLING FOR VARIABLES OR INCLUDING THOSE
ADDITIONAL VARIABLES IN A REGRESSION EQUATION ESPECIALLY WHERE
THE OUTCOME OF INTEREST IS DYCHOTOMOUS I.E. LIFE SENTENCE OR
DEATH SENTENCE?
TC REALLY DEAL WITH THAT QUESTION I SUGGEST WE START
WITH SOME SUBPARTS AND I WILL ASK YOU SOME QUESTIONS ABOUT THEM
AND GET SOME ANSWERS AND MAYBE COME INTO QUESTION PIECE BY
PIECE.
WHAT DO STATISTICIANS MEAN BY THE TERM "VARIABLES?"
A. A VARIABLE OR VARIABLES ARE ANY CHARACTERISTICS CF AN
CBSERVATION THAT VARY FROM ONE OBSERVATION TO ANOTHER, SUCH AS
WOODWORTH = DIRECT :
1 LIFE OR DEATH SENTENCE OR PRESENCE OR ABSENCE OF ALCOHOL
: CONSUMPTION IMMEDIATELY BEFORE THE CRIME.
3 Q. WHAT DOES IT MEAN TO STUDY THE EFFECT OF ONE VARIABLE WHILE
4 CONTROLLING FOR OTHER VARIABLES?
f 5 A. THE MEANING OF THAT TERM IS TO DETERMINE THE INFLUENCE OF
6 THE ONE VARIABLE IN RAISING THE LEVEL OF THE DEPENDENT VARIABLE
7 WHEN THE OTHER VARIABLES ARE HELD FIXED IN A STATISTICAL SENSE.
8 Q. FOR THE RECORD CLARITY, THE DIFFERENCE BETWEEN DEPENDENT AND
! INDEPENDENT VARIABLE IS WHAT?
10 A. DEPENDENT VARIABLE IS A VARIABLE WHICH REFLECTS THE OUTCOME
11 -- FOR EXAMPLE, DEATH SENTENCE OR NO DEATH SENTENCE IN THE
12 PRESENT EXAMPLE,
3 INDEPENDENT VARIABLE IS ONE WHICH IS THOUGET TO
14 INFLUENCE THAT OUTCOME IN THE SENSE OF CHANGING THE RATE AT
35 WHICH THAT CUTCOME IS IMPOSED.
16 Q. LET'S USE DEATH SENTENCE, LIFE SENTENCE AS THE DEPENDENT
37 VARIABLE AND ALCOHOL USE AS THE INDEPENDENT VARIABLE.
18 WHAT WOULD IT MEAN TO STUDY ALCOHOL USE CONTROLLING FOR
18 THE OTHER VARIABLES?
&. 20 A. IT MEANS IN A GENERAL SENSE TO COMPARE DEATH SENTENCING
~ 21 RATES FOR COMPARABLE GROUPS OF ALCOHOL USING DEFENDANTS AND
22 NON~ALCOHOL USING DEFENDANTS.
23 I HAVE A DIAGRAM WHICH ILLUSTRATES THIS POINT.
24 Q. BEFORE WE GET TO THE DIAGRAM, WHAT IS THE PURPOSE OF SUCH A
25 CONTROL?
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ALL THE OTHER FACTORS?
WOODWORTH - DIRECT
A. THE PURPOSE OF SUCH A CONTROL IS TO DETERMINE THE EFFECTS OF
THE ONE VARIABLE, IN THIS CASE ALCOHOL USE, OVER AND ABOVE THE
EFFECTS OF ALL THE OTHERS -- THE NET OF EFFECTS OF THE OTHER
VARIABLES.
Q. AND IT IS THE EFFECT ON WHAT?
A. ON THE OUTCOME, ON THE DEATH SENTENCING RATE IN THIS CASE.
Q. CAN YOU FRAME THE QUESTION AS POLLOWS: WHAT IS THE EFFECT
OF THE ALCOHOL USE ON THE DEATH SENTENCING RATE INDEPENDENT OF
A. THAT'S ONE WAY IN WHICH IT IS STATED.
Q. NOW ARE THERE ACCEPTED STATISTICAL METHODS FOR CONTROLLING
FOR VARIABLES?
A. YES. THERE IS A CROSS TABULATION METHOD AND THE VARIOUS
FORMS OF REGRESSION.
Q. HOW IS CONTROL ACHIEVED IN A REGRESSION EQUATION?
A. IN REGRESSION IT IS ACHIEVED ALGEBRAICALLY.
QO. IN OTHER WORDS, ONE COMPUTES AN ALGEBRAIC FORMULA OR APPLIES
AN ALGEBRAIC FORMULA TOC DATA IN ORDER TC OBTAIN RESULTS; IS THAT
RIGHT?
A. THAT 18 CORRECT.
Q. CAN YOU GIVE A CONCEPTUAL RATHER THAN AN ALGEBRAIC
EXPLANATION OF HOW REGRESSION -- OR CONTROLS ARE ACHIEVED IN A
REGRESSION MOREL?
A. YES, I CAN IF WE CAN REFER TO GW 9,
MR. BOGER: YOUR HONCR, I HAVE AN EXHIBIT MARKED GW 9
———— —— v—— —— — —
WOODWORTH - DIRECT 3
1 | WHICE CONTINUES THE NUMBERING SYSTEM WE USED DURING THE HEARING}
2 | I WILL GIVE A COPY TO COUNSEL FOR THE STATE AND TWO COPIES FOR
3 | THE COURT, ONE FOR THE COURT INDIVIDUALLY AND ONE FOR THE CLERK|
J 4 | BY MR. BOGER:
5 | Q. LET ME FIRST ASK YOU, DR. WOODWORTH, IF YOU CAN IDENTIFY GW
6 | 9. IS THAT THE DOCUMENT YOU TALKED ABOUT THAT MIGHT ILLUSTRATE
7 | CONCEPTUALLY CONTROL IN A REGRESSION MODEL? |
8 | A. THIS IS THE DOCUMENT I WAS REFERRING TO.
9 | ©. CAN YOU TELL US OVERALL WHAT WE ARE LOOKING AT?
10 | A. WE ARE LOOKING AT TWO GRAPH. THE UPPER GRAPH REFERS TO
11 | DEFENDANTS WHO USED MODERATE TO EXCESSIVE AMOUNT OF ALCOHOL
12 | IMMEDIATELY BEFORE THEIR CRIME, WHEREAS THE LOWER ONE REFERS TO
13 | DEFENDANTS WHO USED LITTLE OR NO ALCOHOL IMMEDIATELY BEFORE
14 | THEIR CRIMES.
15 | 0. LET'S TAKE THE TOP GRAPH FIRST AND CLARIFY FOR THE RECORD
16 | WHAT THE HORIZONTAL AND VERTICAL AXES REPRESENT?
17 | A. THE HORIZONTAL AXIS WHICH IS HERE LABELED AGGRAVATION INDEX
18 | IS IN GENERAL THE PART OF THE REGRESSION MODEL WHICH DOES NOT
19 | INCLUDE THE ALCOHOL USE VARIABLE. IN OTHER WORDS, AS WE GO Pro
if 20 | THE LOW END TO THE HIGH END OF THE MODEL WE ARE ASSOCIATED WITH
: 21 | HIGHER AND HIGHER LEVELS OF AGGRAVATION.
22 | Q. AND THAT REFLECTS THE OTHER VARIABLES APART FROM ALCOHOL
23 | ose?
24 | A. CORRECT. IN THIS CASE TEN OTHER VARIABLES.
35 | 0. LET'S LOCK AT THE VERTICAL AXIS, WHAT DOES THAT REPRESENT?
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WOODWORTH - DIRECT
A. THE VERTICAL AXIS REPRESENTS THE OUTCOME VARIABLE. IN
PARTICULAR IT WOULD REPRESENT THE PROBABILITY OR THE RATE AT
WHICH THE DEATH SENTENCE IS IMPOSED.
0. WHAT DOES ONE POINT ZERO REPRESENT AND WHAT DOES ZERO
REPRESENT?
A. ONE POINT ZERO WOULD REPRESENT HUNDRED PERCENT DEATH
SENTENCING RATE AND ZERO WOULD REPRESENT NO DEATH SENTENCES AT
ALL IN A PARTICULAR CATEGORY OF DEFENDANTS.
THE COURT: LET ME DEFINE FOR YOU WHERE YOU HAVE GOTTEN
AHEAD OF HME.
I DON'T UNDERSTAND AGGRAVATION INDEX. I THOUGHT IF WE
WERE MEASURING ALCOHOL CONSUMPTION, ALCOHOL CONSUMPTION WOULD
APPEAR ON THE HORIZONTAL AXIS?
BY MR, BOGER:
0. DR. WOODWORTH, WHERE DOES SOMETHING APPEAR THAT REFELCTS
ALCOHOL USE ON THIS?
A. THE ALCOHOL USE IS REFLECTED IN THE FACT THAT THE UPPER
GRAPH IS THE ALCOHOL USERS AND THE LOWER GRAPH IS THE NON-USERS,
THE LINE ITSELF REFLECTS THE NET EFFECT OF ALL OTHER VARIABLES.
THE COURT: YOU WERE TALKING ABOUT TEN CTHER VARIABLESY
THE WITNESS: THEY ARE SUMMARIZED IN THIS INDEX.
THE COURT: WHAT INDEX?
THE WITNESS: THE AGGRAVATION INDEX. FOR EXAMPLE, A
GROUP OF DEFENDANTS AT ZERC ON THIS INDEX WOULD BE AT THE --
TEND TO BE AT THE MITIGATING END OF THESE OTHER VARIABLES. THE
— — — — ———
11
WOODWORTH - DIRECT
1 | WAY THIS IS CONSTRUCTED, IF I COULD REFER TO YOUR SECOND
2 | QUESTION IN THE PREHEARING ORDER, QUESTION NUMBER TWO. THE
3 | MODEL IS Y=A+B1X1+B2X2. IF X2 FOR EXAMPLE WERE ALCOHOL USE,
4 | THEN THIS INDEX WOULD BE CONSTRUCTED BY TAKING THE B'S FOR ALL
: 5 | THE OTHER VARIABLES AND IN THIS CASE THERE WOULD BE ELEVEN B'S
6 IN ALL. WE WOULD TAKE TEN OF THEM, USE THOSE REGRESSION
2 | COEFFICIENTS TO COMPUTE WHERE EACH DEFENDANT WAS ALONG THIS
8 | SCALE. |
9 | BY MR. BOGER:
10 | Q. MAYBE I NEED TO BACK UP AND ASK YOU A FEW QUESTIONS TO SET
11 | THIS IN SOME CONTEXT.
12 THESE GRAPH THAT YOU HAVE PREPARED, DO THEY REFLECT
13 | DATA FROM YOUR BALDUS-WOODWORTH STUDY ABOUT WHICH WE HAD MUCH
14 | TESTIMONY EARLIER THIS SUMMER?
15 | A. NO. THE DATA SET HERE FROM THE STANFORD LAW REVIEW PAPER
16 | THAT PROFESSOR BALDUS AND I WROTE EARLIER. THEY REFER TO STATE
17 | OF CALIFORNIA. THERE ARE 210 CASES REPRESENTED HERE.
18 THE COURT: FOR THE PURPOSE OF THIS CASE, THIS IS
19 PURELY HYPOTHETICAL?
20 THE WITNESS: CORRECT.
. 21 BY MR. BOGER:
22 0. AND YOU HAVE TESTIFIED THERE ARE A TOTAL OF ELEVEN VARIABLES
23 IN THE REGRESSION HODEL?
24 A. THAT IS CORRECT.
25 Q. AND ONE OF THOSE ELEVEN VARIABLES IS ALCOHOL USE?
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WOODWORTH - DIRECT
A. RIGHT.
Q. I UNDERSTAND YOUR TESTIMONY WAS ALSO TEAT THE AGGRAVATION
INDEX IS COMPUTED BY EXCLUDING ALCOHOL USE AND LOOKING AT THE
OTHER TEN VARIABLES IN GIVING NUMBERS OR ASSIGNING WEIGHTS TO
THEM; IS THAT CORRECT?
A. TBAT IS CORRECT.
AS YOU POINT OUT, MR. BOGER, THIS IS A CONCEPTUAL
EXPLANATION OF BOW THE COMPUTATION PROCEEDS. THIS IS NOT THE
ACTUAL ALGEBRAIC COMPUTATION. THIS DIAGRAM BEGS THE QUESTION
HOW COULD ONE HAVE THE AGGRAVATION INDEX WITHOUT HAVING THE
REGRESSION COEFFICIENTS TO BEGIN WITH? THAT IS A POINT I WILL
GET TO SHORTLY.
WHAT I INTEND TO DEMONSTRATE WITH THIS DIAGRAM IS HOW
ONE WOULD CALCULATE THE B VALUE FOR ALCOHOL, THEN ONE WOULD USE
THIS SAME PROCEDURE TO GET THE B VALUES FOR EACH OF THE OTHER
VARIABLES IN TURN. THE AGGRAVATION INDEX IS SIMPLY THE, WHAT
THE MODEL WOULD PREDICT ABSENT THE ALCOHOL VARIABLE,
MR. BOGER: I THINK, YOUR HONOR, WHEN I WENT THROUGH
THIS WITH DR. WOOLWORTH, I HAD SOME OF THE SAME DIFFICULTIES
THAT YOU MAY BE EXPERIENCING. IN ASKING HIM I DON'T UNDERSTAND
HOW WE GOT TO WHERE WE GOT AND HIS RESPONSE TO ME WAS IF YOU LET
ME GO A LITTLE FURTHER YOU MAY BE ABLE TO LOOK BACK AND SEE HOW
WE TOOK TREAT STEP.
THE COURT: I WILL TAKE A STEP OF FAITH WITH YOU, MR.
J
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WOODWORTH - DIRECT 32
3 MR. BOGER: I ASSURE YOU YOU WILL HAVE A CHANCE TO COME
2 BACK AND ASK THE KIND OF QUESTIONS I ASKED AT LENGTH.
3 BY MR. BOGER:
4 Q. IF WE HAVE GOT A VERTICAL AXIS THAT IS THE PREDICTION OF THE
4 5 DEATH SENTENCING RATE AND WE HAVE THE HORIZONTAL AXIS THAT IS
6 THE AGGRAVATION INDEX, WHAT DO THE DOTS REPRESENT IN THE GRAPH
7 AT THE TOP?
8 A. THE DOTS REPRESENT THE DEATH SENTENCING OBSERVED -- ACTUAL
9 DEATH SENTENCING RATES FOR DEFENDANTS WHO ARE SIMILAR IN TERMS
10 OF WHAT WE WOULD PREDICT -- WHAT WE WOULD PREDICT THEM TO BE
11 USING THE OTHER VARIABLES. IN OTHER WORDS, THESE ARE IN EFFECT
13 SIMILAR DEFENDANTS WITH RESPECT TO THE OTHER TEN VARIABLES.
13 0. LET'S LOOK AT AN EXAMPLE OF THAT IF YOU WOULD. POINT TO ONE
14 OF THE DOTS AND SHOW US WHAT IT MEANS.
35 A. FOR EXAMPLE, AT POINT FOUR ON THE UPPER GRAPH, THERE ARE A
16 NUMBER OF DEFENDANTS WHO HAVE AN AGGRAVATION LEVEL OF
37 APPROXIMATELY POINT FOUR. IN OTHER WORDS, FOR WHOM -- ON
18 EXAMINATION OF ALL THE OTHER VARIABLES WE WOULD PREDICT THE
b 5 DEATH SENTENCING RATE TO BE ABOUT POINT FOUR. NOW THESE
: 20 DEFENDANTS -- THERE WERE A CERTAIN NUMBER OF DEATHS AMONG THESE
i 21 DEFENDANTS AND A CERTAIN NUMBER OF LIFES. TEE DOT THERE
22 REPRESENTS THE PERCENTAGE OR FRACTION OF THE DEATH WHICH LOOKS
23 LIKE ABCUT POINT FOUR NINE PERHAPS. SO AMONG THAT PARTICULAR
24 GROUP OF DEFENDANTS, THERE WERE ABOUT FORTY-NINE PERCENT DEATH
25 SENTENCES AND ABOUT FIFTY-ONE PERCENT LIFE SENTENCES.
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WOODWORTH - DIRECT
THE COURT: HOW DID YOU DETERMINE THEY WERE SIMILAR?
THE WITNESS: I DETERMINED THEY WERE SIMILAR BX
MATCHING THEM WITH RESPECT TO WHAT ALL THE OTHER VARIABLES SAID
ABOUT THAT CASE.
BY MR. BOGER:
OQ. YOU SAID ABOUT THAT CASE. IN OTHER WORDS, YOU MATCHED IT
ALONG THE HORIZONTAL AXIS BY AGGRAVATION SCORES, IF YOU WOULD?
A. THAT IS CORRECT.
THE COURT: IF WHAT YOU DID IS WHAT YOU SAY, THEN YOU
WOULD HAVE FOUND SOME NUMBER OF CASES AND OF COURSE AS I
UNDERSTAND IT THIS DOESN'T CONTROL FOR THE NUMBER OF CASES, BUT
YOU WOULD HAVE FOUND SOME NUMBER OF CASES WHERE THE
CIRCUMSTANCES AS TO THE OTHER TEN FACTORS WERE IDENTICAL.
THE WITNESS: NOT IDENTICAL.
THE COURT: HOW IDENTICAL WERE THEY?
THE WITNESS: THEY NEED NOT BE FACTUALLY SIMILAR. THEY
ARE IDENTICAL IN TERMS OF THE -- IN TERMS OF PREDICTED DEATH
SENTENCING RATE, THEY ARE CLOSELY SIMILAR IN TERMS OF THE DEATH
SENTENCING RATES WE PREDICT FCR THESE CASES USING ALL THE OTHER
VARIABLES. THE INDEX IS CALCULATED BY A SCORING METHOD AS YOU
RECALL.
IF -—- POR EACH VARIABLE A REGRESSION COEFFICIENT IS
CALCULATED. FOR EXAMPLE A REGRESSION COEFFICIENT FCR RESISTING
ARREST IS POINT TWO FOUR ZERO. IF A CASE HAD RESISTED ARREST
THEN HE WOULD RECEIVE POINT TWO FOUR ZERO POINTS TOWARD HIS
— —— p— —— —— —
WOODWORTH ~ DIRECT je
1 TOTAL INDEX OR IF ANOTHER CASE HAD NOT RESISTED ARREST, THEN HE
2 WOULD NOT HAVE RECEIVED THE POINT TWO FOUR ZERO POINTS TOWARD
3 HIS AGGRAVATION SCORE. SO WE TAKE EACH CASE AND WE LOCK AT THE
4 FACTS OF THE CASE AND ASSIGN A SCORE, OR RATHER ASSIGN -- LOOK
5 UP RATHER THE REGRESSION COEFFICIENT FOR THAT PARTICULAR FACT
6 AND WE TOTAL UP THE REGRESSION COEFFICIENTS FOR THE FACTS THAT
7 ARE PRESENT.
8 IT'S SORT OF LIRE THESE QUIZZES YOU SEE IN THE
9 MAGAZ INES LIKE YOUR MARRIAGE I.Q. WHERE THEY ASK YOU A SERIES OF
10 QUESTIONS AND IF YOU SIT DOWN FCR HALF HOUR AFTER DIKNER AND
il TALK TO YOUR WIFE, THEN THAT IS WORTH FIVE POINTS BUT IF YOU
32 ARGUE WITH HER EVERY MORNING YOU LOSE TWO POINTS. WHAT YOU DO,
pic] YOU SCORE YOURSELF AND YOU MIGHT GET FIVE POINTS PLUS THREE
14 POINTS, WHEREAS SOMEBODY ELSE MIGHT GET THREE POINTS BUT NOT THE
15 FIVE POINTS.
16 THE REGRESSION COEFFICIENTS HERE REPRESENT THE POINTS
7 YOU GET AWARDED SO TO SPEAK, THAT A DEFENDANT GETS AWARDED FOR
18 POSSESSING A CERTAIN CHARACTERISTIC. IN THIS PICK EXAMPLE, ¥OU
15 GET AWARDED TWENTY-TWO PERCENTAGE POINTS FOR CONTEMPORANEOUS
: 20 FELONY AND TWENTY PERCENTAGE POINTS FOR HAVING A CRIMINAL RECORD
2 21 AND SO ON. ALL OF THESE POINTS ARE ADDED UP; ONCE THEY ARE
22 ADDED UP THAT PLACES THE CASE ALONG THE HORIZONTAL AXIS,
23 SO THE CASES NEED sor $c FACTUALLY SIMILAR BUT THEY DO
24 HAVE SIMILAR POINT TOTAL. ONE CASE MIGHT HAVE A PRICR CRIMINAL
25 ~ RECORD. THAT WOULD BE WORTH TWENTY POINTS, BUT NOT HAVE A
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WOODWORTH = DIRECT
CONTEMPORANEOUS FELONY, WHEREAS ANOTHER CASE MIGHT HAVE A
CONTEMPORANEOUS FELONY WORTH TWENTY TWO POINTS AND NO CRIMINAL
RECORD —
THE COURT: LET'S TAKE THE PLOT OVER ZERO AND REFERRING
TO THE ZERO ON THE HORIZONTAL AXIS, DOES THAT REPRESENT ONE
CASE?
THE WITNESS: NO. THAT DOT WOULD REPRESENT -- IF I CAN
CONSULT MY COMPUTER OUTPUT. OVER ZERO THAT DOT WOULD REPRESENT
IN THIS CASE TEN CASES. EACH DOT WOULD REPRESENT A VARYING
NUMBER OF CASES. IT'S A NUMBER OF CASES THAT HAPPEN TO FALL AT
THAT POSITION.
THE COURT: IN OTHER WORDS YOU TOOK -- IT'S LIKE THE
CHICKEN AND THE EGG. YOU TOOK ALL OF THE CASES THAT HAD A ZERO
AGGRAVATION INDEX.
THE WITNESS: OR CLOSE TO IT.
THE COURT: PLUS OR MINUS WHAT?
THE WITNESS: APPROXIMATELY POINT ONE IN THIS CASE
BECAUSE WE HAD SUCH A SMALL DATA SET.
THE COURT: PLUS OR MINUS POINT ONE.
THE WITNESS: ROUGHLY, YES, SIR.
THE COURT: AND THEN YOU OBSERVED THE PROBABILITY OR
THE PERCENTAGE OF THE CASES WHEREIN THE DEATH PENALTY WAS
IMPOSED AND THAT GAVE YOU THE ELEVATION ON THE -- WHICH IS X AND
Y? I CAN'T REMEMBER.
THE WITNESS: Y IS VERTICAL.
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WOODWORTH ~ DIRECT
THE COURT: SO THAT GAVE YOU THE ELEVATION ON THE Y
AXIS?
THE WITNESS: YES.
THE COURT: AND IT SEEMS YOU NEXT WENT OUT TO SOME
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PLACE AT ABOUT POINT TWO. NOW LET ME ASK YOU FIRST OF ALL HOW
6 |. YOU GOT THE VALUE POINT TWO? HOW DID YOU GET THE VALUE OF POINT
7 | TWO ON THE X AXIS?
8 THE WITNESS: ARE YOU ASKING HOW A PARTICULAR DEFENDANT
9 | WOULD HAVE ARRIVED AT THAT POINT ON THE AXIS?
10 THE COURT: I AM SO FAR AT THE POINT WHERE YOU STARTED
11 | OFF WITH A ZERO AND YOU OBSERVED ALL OF THOSE WITHIN THE DATA
12 | BASE THAT EAD A ZERO ON THE AGGRAVATION INDEX AND TREN YOU MADE
13 AN OBSERVATION ABOUT THE DEATH SENTENCING RATE AND YOU PLOTTED
14 THAT?
18 THE WITNESS: RIGHT.
16 THE COURT: YOU MOVE OUT SOME ON THE X AXIS?
17 THE WITNESS: YES, SIR.
18 THE COURT: HOW DID YOU DETERMINE HCW FAR OUT TO MOVE?
is THE WITNESS: POR THE SARE OF ILLUSTRATION HERE, I
2 20 PICKED EQUAL NUMBERS OF CASES. SO I HAVE TWO HUNDRED TEN SO
! 21 THAT DIVIDES NEATLY INTO SEVEN CATEGORIES. SO I TOOK THE FIRST
22 ~~ 1 TOOK THE FIRST ONE-SEVENTH OF THE DATA FOR THE FIRST POINT
23 AND THE NEXT ONE-SEVENTH AND SO ON.
24 THE COURT: SO YOUR SECOND POINT THEN IS THE AVERAGE
25 AGGRAVATION VALUE OF THE NEXT HIGHEST ONE-SEVENTH?
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WOODWORTH - DIRECT
THE WITNESS: YES, THAT IS CORRECT.
THE COURT: AND THE DEATH PENALTY RATE GOES DOWN
MODESTLY THERE?
THE WITNESS: MODESTLY.
THE COURT: IF I UNDERSTAND YOU CORRECTLY, THE CASES
WHICH WOULD BE ONE-SEVENTH OF 210 WOULD NOT NECESSARILY HAVE THE
SAME ACTUAL FACTORS PRESENT, BUT THEY WOULD HAVE FACTORS WITH
THE SAME, ROUGHLY, POINT VALUE?
THE WITNESS: CORRECT.
THE COURT: WHAT I WANT TO KNOW IS WHERE YOU GOT THE
POINT VALUE, IT SEEMS CLEAR TO ME ~-- I SAY IT SEEMS CLEAR. IT
SEEMS CLEAR TO ME IF YOU ARE PLOTTING THE DEATH PENALTY RATE YOU
COULDN'T USE THE DEATH PENALTY RATE AS YOUR AGGRAVATION INDEX,
BUT THAT SEEMS LIKE YOU MAY BE DOING THAT?
THE WITNESS: IT'S NOT ACTUALLY THE DEATH PENALTY RATE
THAT DETERMINES THE INDEX. IT'S THE REGRESSION COEFFICIENTS FOR
ALL THE OTHER VARIABLES THAT DETERMINE THE INDEX.
THE COURT: EXPLAIN THAT TO ME.
THE WITNESS: THIS IS WHERE WE GET INTO THE CHICKEN AND
THE EGG PROBLEM, WHAT I AM ILLUSTRATING HERE IS IN CONCEPT HOW
THE COEFFICIENTS ARE OBTAINED YET I AM ASSUMING THAT I ALREADY
KNOW THEM IN ORDER TO DRAW THE HORIZONTAL AXIS.
THE COURT: TELL ME HOW YOU CAME ABOUT SCORING THE
AGGRAVATION LEVEL FOR YOUR -- ACTUALLY IT IS YOUR TBIRD PLCT
POINT GOING OUT THE X AXIS?
WOODWORTH - DIRECT je
1 THE WITNESS: HOW I SCORED THE CASES THAT FOLLOWED
2 THERE?
3 THE COURT: HOW DID YOU COME UP WITH A NUMBER THAT
4 YIELDED POINT ONE FIVE OR THEREABOUTS ON THE X AXIS? HOW DID
5 YOU GET THAT POINT? '
6 THE WITNESS: ONCE AGAIN AT THE THIRD POINT THERE WERE
7 ~- IF 1 READ THIS CORRECTLY ELEVEN CASES AT THE THIRD POINT AND
8 OF THOSE ONE RECEIVED THE DEATH PENALTY WHICH WOULD BE A RATE OF
o POINT ZERO NINE.
10 THE COURT: THAT IS ON THE Y AXIS?
11 THE WITNESS: YES. VERTICALLY POINT ZERO NINE.
12 THE COURT: WHAT I WANT TO KNOW IS HOW YOU GOT YOUR
13 VALUE ON THE X AXIS?
14 THE WITNESS: THAT WOULD BE THE AVERAGE POINT VALUE FOR
15 THOSE ELEVEN CASES, THOSE ELEVEN NEARBY CASES.
16 THE COURT: AVERAGE POINT VALUE OF WHAT?
37 THE WITNESS: OF THE PACTS OF THE CASE EXCLUDING
18 ALCOHOL USE.
19 THE COURT: WHERE DID YOU GET THE POINT VALUE?
:» 20 THE WITNESS: 1 AM COMING TO THAT. WHAT I AM GIVING
: 21 HERE IS CONCEPTUAL. YOU HAVE TO IMAGINE THAT MUSE OF STATISTICS
22 HAS GIVEN ME ALL THE REGRESSION COEFFICIENTS BUT ONE, NAMELY THY
23 ONE FOR ALCOHOL AND I AM TRYING TO GET IT. THEN I WILL COME
24 ALONG LATER AND EXPLAIN HOW WE CYCLE THROUGH THIS PROCESS TO GET
25 ALL THE OTHERS. SO WHAT WE ARE DOING WE ARE PRETENDING HERE IS
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WOODWORTH - DIRECT
THAT SOMEHOW 1 HAVE BEEN GIVEN ALL THE OTHER POINT VALUES EXCEPT
ALCOHOL. SO GIVEN ALL THOSE OTHERS I CAN POSITION A CASE ON THY
HORIZONTAL AXIS BY ADDING UP ITS POINT SCORE.
BY MR. BOGER:
Q. WHAT THEN DOES THE DIAGONAL LINE REPRESENT ONCE WE HAVE
PLOTTED THE CASES ALONG THE X AND Y AXIS ON THE TOP GRAPH?
A. THE DIAGONAL LINES ARE WHAT ARE REFERRED TO AS LEAST SQUARES
REGRESSION LINES. THESE ARE BEST FITS THROUGH THOSE POINT
CLOUDS. |
Q. HOW IS THAT DIAGONAL LINE EXPRESSED IN TERMS CF YOUR OVERALL
REGRESSION EQUATION IF YOU WOULD OR IS IT AND DOES IT RECEIVE A
NUMBER OF SOME SORT?
A. NOT FOR THE PURPOSE OF THIS ILLUSTRATION, NO.
Q. LET'S GO TO THE BOTTOM GRAPH AND WHAT DO YOU HAVE REFLECTED
THERE?
A. THE BOTTOM GRAPH IS CONSTRUCTED IN A MANNER SIMILAR TO THE
TOP ONE EXCEPT THIS ONE IS USING CASES WITH LITTLE OR NO AMOUNTS
OF ALCOHOL.
EPFECT TO THE DOTS IN THE TOP ONE?
A. CORRECT.
Q. AND WE HAVE A LINE THAT IS DRAWN DIAGONALLY THERE, WHAT DOE§
THAT REFLECT?
A. THAT IS THE LEAST SQUARES LINE THAT REPRESENTS THE GENERAL
TREND OF THE DEATH SENTENCING RATES GETTING HIGHER AS THE POINT
21
WOODWORTH - DIRECT
VALUE FOR EACH CASE BECOMES HIGHER.
THE COURT: GOING ALONG WITH YOUR ASSUMPTION ABOUT YOUR
1
2
3 MUSE FOR THE MOMENT. WHAT DO THESE TELL ME ABOUT ALCOHOL?
4 THE WITNESS: WHAT THEY TELL YOU ABOUT ALCOHOL IS
5 ILLUSTRATED IN GW 10, THE NEXT FIGURE THAT I PREPARED.
5) BY MR. BOGER:
7 Q. LET ME INTRODUCE IT AND HAVE IT PREMARKED GW 10. I HAVE TWO
8 COPIES FOR THE CCURT AND A COPY FOR COUNSEL.
9 THE COURT: THIS IS TOTALLY WITHOUT ALCOHOL. I THINK [
0 KNOW WHAT GW 10 IS. YOU PRODUCED AN ADDITIONAL FACTOR.
11 THE WITNESS: THE HORIZONTAL AXIS IS WITHOUT ALCOHOL.
12 BY MR. BOGER:
13 Q. NOW YOU HAVE GOTTEN -- IN GW 9, AS I UNDERSTAND IT, ONE LIN] | 3
)
14 THAT REPRESENTS DEFENDANTS WITH MODERATE EXCESSIVE USE ARD
15 ANOTHER LINE REPRESENTS LIGHT KO ALCOHOL USE. WHAT DOES GW 10
16 DO?
17 THE COURT: WAIT A MINUTE.
18 IS LIGET TO MODERATE OR LIGHT TO NO OR MODERATE TO
19 EXCESSIVE ONE OF THE TEN FACTORS IN THE AGGRAVATION INDEX?
fe 20 THE WITNESS: NO. IT'S THE FACTOR WE HAVE IN FOCUS.
21 IT'S THE ONE WE WERE NOT GIVEN REGRESSION COEFFICIENT FOR AND WX
22 ARE NOW TRYING TO GET IT.
23 BY MR. BOGER:
24 Q. WHAT DOES GW 10 SHOW US?
25 A. THE REDRAWING OF THESE TWO LINES ON THE SAME GRAPH.
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WOODWORTH ~ DIRECT
Q. WHAT DOES THE SOLID LINE REPRESENT AND WHAT DOES THE DOTTED
LINE REPRESENT?
A. THE SOLID LINE WOULD BE THE LOWER GRAPH FROM THE PREVIOUS
PAGE AND THE DOTTED LINE WCULD BE THE UPPER GRAPH.
Q. YOU SAY PREVIOUS PAGE, YOU MEAN GW 97
A. GW. 9, EXCUSE ME. HERE WE CAN CLEARLY SEE THE EFFECTS OF
ALCOHOL IN THAT THE REGRESSION LINE FOR LOW ALCOHOL DEFENDANTS
IS ABOUT SIXTEEN PERCENTAGE POINTS ABOVE THE CORRESPONDING LINE
FOR THE HIGH ALCOHOL USERS.
Q. WHAT DOES THAT REFLECT WITH RESPECT TO THE Y AXIS OR THE
DEATH SENTENCING RATE?
A. THE VERTICAL AXIS IS -- CALIBRATED IS THE DEATH SENTENCING
RATE, THAT MEANS IF THE VERTICAL SEPARATION BETWEEN THOSE TWO
LINES IS POINT ONE SIX THEN THAT MEANS THAT THE AVERAGE
SEPARATION =~ THAT THE AVERAGE DIFFERENCE BETWEEN THE LOW
ALCOHOL AND HIGH ALCOHOL DEFENDANTS IS ABOUT SIXTEEN PERCENTAGE
PCINTS.
Q. AND THAT'S THE DIFFERENCE IN THE DEATH SENTENCING RATE?
A. THAT IS AN OVERALL DIFFERENCE IN DEATH SENTENCING RATES,
YES.
Q. WHAT DOES ONE AGAIN CONCEPTUALLY SPEAKING DO WITH THAT
DIFFERENCE?
A. THAT DIFFERENCE IS THE REGRESSION COEFFICIENT FOR ALCOHOL.
Q. WHAT DOES IT REFLECT?
A. IT REFLECTS THE AVERAGE EFFECTS OF ALCOHOL FOR CASES WHICH
—— — — p——— —— —
WOODWORTH - DIRECT i
1 ARE SIMILAR IN THE SENSE OF HAVING A SIMILAR -- A CLOSELY
2 MATCHING POINT VALUE ON THE OTHER VARIABLES, -=
3 OQ. AND USING THE LANGUAGE OF CONTROL AND CONTROLLING FOR
4 VARIABLES, WHAT DOES GW 10 REFLECT?
5 A. GW 10 VERTICAL SEPARATION IS THE EFFECT OF ALCOHOL
6 CONTROLLING IN THE REGRESSION SENSE FOR THE OTHER VARIABLES.
7 OQ. NOW THE COURT HAS QUICKLY PICKED UP ON THE FACT YOU
8 CONSTRUCTED AN AGGRAVATION INDEX THAT HAS POINT VALUES ASSIGNED
9 TO THE OTHER TEN VARIABLES ==
10 THE COURT: I HAVE ANOTHER PROBLEM BEFORE YOU GO BACK
11 TO THAT. DID YOU DO SOMETHING THAT IS INTELLECTUALLY SIMILAR TQ
12 CROSS TABULATION TO GET THE CASES THAT YOU USED IN THE TOP AND
13 BOTTOM TABLE ON NINE? IN OTHER WORDS, DID YOU MAKE YOUR
14 AGGRAVATION AND DEATH PENALTY SENENCING RATE OBSERVATIONS OH A
15 DICHOTOMOUS GROUP OF DATA?
16 THE WITNESS: YES. I DID DO A CROSS TABULATION. THAT
17 IS WHAT I HAVE BEEN REFERRING TO. THE COMPUTER OUTPUT -- I HAVE
18 GROUPED THE EFFECTS OF ALL VARIABLES INTO SEVEN CATEGORIES AS
19 YOU CAN SEE FROM THE SEVEN DOTS ACROSS THE PAGE AND THEN I CROSS
' 20 TABULATED THOSE SEVEN CATEGORIES AGAINST ALCOHCL USE, SO I HAVE
21 A TWO BY SEVEN CROSS TABULATION WHERE EACH BOX IN THE CROSS
22 TABULATION WILL HAVE THE DEATH SENTENCING RATES.
23 THE COURT: YOU MAY HAVE ANSWERED MY QUESTION BUT I
24 DIDN'T UNDERSTAND IT. YOU SAID YOU HAVE TWO HUNDRED TEN CASES
2% INVOLVED IN THE TOP CHART. ARE THOSE CASES YOU HAVE SELECTED
——— —— —— ——— —— ——— ————— —— — —— —— — — — ——. ——— ——— —
WOODWORTH - DIRECT 2
1 FOR STUDY ON ACCOUNT OF THEIR HAVING MODERATE TO EXCESSIVE
2 ALCOHOL PRESENT?
3 THE WITNESS: YES, SIR.
4 THE COURT: YOU ARE STUDYING THOSE TWO HUNDRED TEN
5 WHICH YOU HAVE PICKED OUT OF A GREATER SAMPLE BECAUSE THEY HAVE
6 IN COMMON MODERATE TO EXCESSIVE ALCOHOL IMMEDIATELY BEFORE
7 CRIME?
8 THE WITNESS: TWO HUNDRED TEN IS THE TOTAL OF BCTH
9 ALCOHOL AND NON-ALCOHOL USERS. UNDER ALCCHOL WE HAVE --
10 THE COURT: WHAT I AM TRYING TO FIND OUT IS ON THE TOP
il CHART ARE YOU STUDYING ONLY THOSE THAT HAVE MODERATE TO
12 EXCESSIVE?
13 THE WITNESS: THAT IS CORRECT.
14 THE COURT: SO YOU HAVE DONE ORE SORT AND THEN STUDIED
15 THE SUBGROUPS?
16 THE WITNESS: EXACTLY.
17 THE COURT: OKAY. I HAVE THAT POINT NOW.
18 BY MR, BOGER:
19 Q. I SHOULD HAVE CLARIFIED THAT. SO THE TWO HUNDRED TEN TOTAL
> 20 CAN BE FOUND WITHIN THE TOP AND BOTTOM GRAPH BUT THE TWC HUNDRED
21 TEN ARE NOT REFLECTED IN EITHER OF THE TWO IN GW 97?
22 A. THERE ARE I THINK SEVENTY-THREE IN THE TOP OKE AND THE REST
23 ARE IN THE BOTTOM ONE.
24 Q. AND WITH RESPECT TO THE 73 IN THE TOP YOU PERFORMED THE SAME
a5 ANALYSIS ON THE OTHERS ~~ WITH RESPECT TO THE OTHER TEN
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WOODWORTH - DIRECT
VARIABLES THAT YOU PERFORMED ON THE BOTTOM ON THE RESIDUAL GROUP
OF TWO HUNDRED TEN LESS SEVENTY-THREE; IS THAT CORRECT?
A. 1 APPLIED THE GRAPH IN THE SAME MANNER. I USED THE SAME
POINT VALUES FOR THE UPPER AND THE LOWER GRAPH FOR ALL THE OTHER
VARIABLES.
Q. SO WHEN WE LOOK AT GW 10 AND WE SEE THESE TWO LINES, THESE
LINES ARE NOW REFLECTIVE OF ALL OF THE CASES IN THE STANFORD
STUDY THAT YOU USED IN THE HYPOTHETICAL?
A. RIGHT THE UPPER LINE REFLECTS THOSE SEVENTY-ODD CASES THAT
HAD LOW ALCOHOL USE AND THE LOWER LINE REFLECTS THE REMAINDER,
ABOUT ONE HUNDRED FORTY THAT HAD HIGH ALCOHOL USE.
Q. WITH RESPECT TO BOTH LOW ALCOHOL GROUP AND HIGH ALCCHOL
GROUP YOU HAVE TAKEN INTO ACCOUNT THE OTHER TEN FACTORS?
A. IN THE SENSE OF SORTING CASES ACCORDING TO THEIR PCINT
VALUE.
Q. AND YOU DERIVED SOME SCORE BY THE VERTICAL DIFFERENCE ON THE
Y AXIS BETWEEN THE TWO?
A. VERTICAL DIFFERENCE THEN BECOMES THE POINT VALUE FOR THE
ALCOHOL USE VARIABLE. ALCOHOL THEN IS WORTH POINT ONE SIX
POINTS IN THE REGRESSION EQUATION. IT REGRESSION COEFFICIENT IS
POINT ONE SIX.
Q. HAVE YOU AT THAT PCINT COMPLETED YOUR ANALYSIS ~- THE OTHER
WAY I ASKED THE QUESTION, THE COURT HAS NOTED THAT YOU DEVELOPED
AN AGGRAVATION INDEX THROUGH YOUR MUSE AND YET YOU HAVE NOT
EXPLAINED TO US HOW YOU GOT THE VALUES, HOW DOES ONE
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WOODWORTH ~ DIRECT
CONCEPTUALLY AGAIN SPEAKING DEVELOP THE VALUES FOR THE OTHER TE} po
e)
VARIABLES?
A. CONCEPTUALLY -- ALGEBRAICALLY ALL REGRESSION COEFFICIENTS
ARE ESTIMATED SIMULTANEOUSLY. THERE IS A FORMULA. WE REFER TO
IT AS THE SWEEP OPERATOR, WHICH SIMULTANEOUSLY CALCULATES ALL OF
THESE REGRESSION COEFFICIENTS AND ALGEBRAICALLY AND INCIDENTALLY
THE FORMULA IN EFFECT DOES NOT GROUP CASES. I DID THIS GROUPING
FOR THE SAKE OF CLARITY IN THE ILLUSTRATION.
Q. SO EACH CASE 1S TREATED SEPARATELY WHERE IT FALLS ON THE
HORIZONTAL AND VERTICAL AXIS?
A. CORRECT.
THE COURT: WAIT. EACH CASE IS CONSIDERED SEPARATELY?
THE WITNESS: THE ACTUAL ALGEBRAIC FORMULA DOES NOT
REQUIRE THE GROUPING IN ORDER TO DRAW THE STRAIGHT LINES. I AM
NOT CAPABLE OF MENTALLY DRAWING A STRAIGHT LINE THROUGH RAW
DATA. I HAD TO GROUP IT FOR MY PURPOSES, BUT THE ALGEBRAIC
PORMULA DOESN'T HAVE TO GO THROUGH THIS STEP. SO WE DON'T HAVE
THIS QUESTION OF HOW I PORMED THE GROUPS WHEN WE DO THE ALGEBRA,
IT 1S, SIMPLY IS NOT DONE.
THE COURT: THEN HOW DO YOU GET A COEFFICIENT FOR ANY
GIVEN AGGRAVATING FACTOR? |
THE WITNESS: BY A PROCESS WHICH IS INTELLECTUALLY
EQUIVALENT TO THIS. THE NUMBER ACTUALLY PRODUCED BY THE
COMPUTER DIFFERS FROM THE ONE I GOT THIS WAY BY -- IN THE THIRD
WOODWORTH - DIRECT
1 JUST -- IN ORDER FOR ME TO GIVE A CONCEPTUAL DISPLAY I HAD TO GO
2 THROUGH THIS GROUPING STEP,
3 THE COURT: I UNDERSTAND WHAT YOU DID ON NINE AND TEN
4 BUT I STILL DON'T UNDERSTAND HOW YOU GOT THE COEFFICIENTS FOR
5 THE OTHER TEN. ARE WE THERE YET WHERE--
6 MR. BOGER: I BAVE ONE MORE QUESTION TO CLARIFY THE
7 LAST POINT, THEN WE WILL GET THERE.
8 BY MR. BOGER:
9 Q. IF IN FACT YOU HAD NOT GROUPED BUT DONE IT CONCEPTUALLY THE
10 WAY THE ALGEBRA IS DONE, YOU WOULD HAVE HAD HOW MANY POINTS ON
5 4 GW 9 ON THE GRAPH?
12 A. TWO HUNDRED TEN.
33 0. SEVENTY-THREE AT THE TOP AND THE REMAINDER AT THE BOTTOM?
14 A. YES.
is THE COURT: HOW DO YOU GET A PLOT POINT ON A DEATH
16 SENTENCING RATE WHEN YOU HAVE TWO HUNDRED TEN DISCRETE
17 VARIABLES?
i8 THE WITNESS: IT IS DONE ALGEBRAICALLY.
13 THE COURT: THAT IS WHERE I BROKE DOWN.
. 20 ‘BY MR. BOGER:
% 23 Q. LET ME ASK A QUESTION, DR. WOODWORTH, YOU DID NOT TESTIFY
22 DID YOU THERE WERE TWO HUNDRED TEN VARIABLES, THERE ARE TWO
23 HUNDRED AND TEN=-
24 A. CASES.
25 Q. AND WE ARE LOOKING AT HCW MANY VARIABLES?
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WCODWORTH =~ DIRECT
THE COURT: I MAY HAVE USED THE THE WRONG TERM OF ART
BUT WHEN YOU ARE TRYING TO ASCERTAIN -- IF THIS MODEL IS
REPRESENTATIVE OF THE THOUGHT PRCCESS AT ALL, IF YOU ARE TRYING
TO ASCERTAIN THE EFFECT IT HAS, THEN YOU HAVE CASE ONE VARIABLE
ONE AND YOU HAVE A PLOT AND YOU CAN'T PLOT IT ON A DEATH
SENTENCING RATE CHART BECAUSE IT EITHER GOT IT OR IT DIDN'T GET
ITs
THE WITNESS: THAT IS CORRECT. HOWEVER, ALGEBRAIC
METHOD IS ABLE IN EFFECT TO PLOT THE VARIABLES SIMULTANECUS =--
PLOT THE CASES SIMULTANEOUSLY ON ALL VARIABLES.
THE COURT: THAT INTELLECTUAL PROCESS IS WHAT I SEEK TQ
TRY TO LEARN.
THE WITNESS: LET ME TRY TO GIVE YOU SOME CONCEPTUAL
NOTION OF HOW THIS WORKS. THIS METHOD THAT I ALLUDED TO WHICH
WE CALL THE SWEEP OPERATOR, S-W-E-E-P PROCEEDS IN THE FOLLOWING
WAY.
IT WILL START OUT WITH A SINGLE VARIABLE ON THE
HORIZONTAL AXIS, PERHAPS NUMBER OF VICTIMS, AND PRODUCE PLOTS
LIKE THIS. FROM THAT PLOT IT WILL DEVELOP COEFFICIENT FOR THE
VARIABLE, LET'S SAY ALCOHOL USE. SO KOW IT HAS A REGRESSION
COEFFICIENT FOR ALCOHOL USE.
THEN IT COMBINES THAT WITH THE REGRESSION COEFFICIENT
FOR NUMBER OF VICTIMS. NOW IT HAS TWO REGRESSION COEFFICIENTS.
IT THEN CALCULATES THE AGGRAVATION INDEX USING THOSE TWO
COEFFICIENTS AND USES A THIRD VARIABLE, PERHAPS PRESENCE OR
WOODWORTH - DIRECT i
1 ABSENCE OF A MITIGATING CIRCUMSTANCE, AND CALCULATES THE
2 REGRESSION COEFFICIENT FOR MITIGATING CIRCUMSTANCE. NOW IT HAS
3 THREE REGRESSION COEFFICIENTS.
4 IT TARES THESE THREE REGRESSION COEFFICIENTS AND
4 3 CALCULATES THE AGGRAVATION INDEX FOR EACH CASE AND THEN SPREADS
6 THE CASES OUT ON YET ANOTHER VARIABLE. POSSIBLY WHY IT IS
v REFERRED TO AS THE SWEEP OPERATOR ALTHOUGH I HAVE NOT LOCKED
8 INTO THE HISTORY OF IT IS BECAUSE IN EFFECT AT EACH STAGE IT
9 SWEEPS THE CASES OUT ON AN AXIS IN TERMS OF THEIR POINT VALUE
10 AND GRADUALLY IN A STAGE-WIDE PROCESS COMPUTES EACH REGRESSION
11 COEFFICIENT. IT IS SORT OF A BOOT STRAP PROCESS.
12 ONE WAY OF CONCEPTUALIZING IT IS TO IMAGINE YOU START
13 WITH A -- SOME INITIAL GUESSES. YOU DON'T HAVE THE MUSE S50 YOU
14 JUST START WITH SOME GUESSES OF THE REGRESSION COEFFICIENT AND
15 GO THROUGH THIS EXERCISE FOR EACH VARIABLE IN TURN AND THAT WILL
16 GIVE YOU A BETTER SET OF REGRESSION COEFFICIENTS.
17 USE THE BETTER SET OF REGRESSION COEFFICIENTS TO SPREAD
18 OUT THE VARIABLES ON THIS AGGRAVATION INDEX FOR EACH VARIABLE IN
19 TURM AND GET A YET EVEN BETTER SET OF REGRESSION COEFFICIENTS.
. 20 THIS IS, AS I SAID, A CONCEPTUAL WAY OF GETTING AROUND
21 THE PROBLEM OF NOT HAVING A MUSE. I HAVE TO SAY THAT THE ACTUAL
22 ALGEBRAIC CONPUTATION THAT WE GO TO THAT IS EMBODIED IN THIS
23 SWEEP OPERATOR IS SOMETHING THAT TAKES ME A BETTER PART OF A
24 SEMESTER TO TEACH WHEN I TEACH THIS MATERIAL,
25 I CAN SIMPLY SAY THAT THE -- THAT THE ALGEBRAIC PROCESS
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WOCDWORTH - DIRECT
THAT GETS ALL THE COEFFICIENTS SIMULTANEOUSLY IS INTELLECTUALLY
EQUIVALENT TO WHAT I HAVE LAID CUT HERE IN THESE GRAPH.
BY MR. BOGER:
GC. THE COURT, DR. WOODWORTH, BROUGHT UP THE QUESTION CF
DICHOTOMOUS OUTCOMES.
CAN YOU EMPLOY REGRESSION ANALYSIS WHERE THE OUTCOMES
DICHOTOMOUS AS IN LIFE SENTENCE OR DEATH SENTENCE? IN OTHER
WORDS WHERE YOU HAVE DICHOTOMOUS VARIABLES CAN A REGRESSION
ANALYSIS STILL WORK AND CONTROL FOR OTHER VARIABLES?
A. OH, YES. THERE IS NO PROBLEM WHATEVER IN CONTROLLING FOR A
DICHOTOMOUS INDEPENDENT VARIABLE AND THAT IN FACT IS WHAT I
DEMONSTRATED HERE IN GW 9 AND 10,
Q. LET'S LOOK AT GW 10 FOR A SECOND. YOU ACTUALLY HAVE ON THE
Y AXIS IN THE REAL WORLD ONLY TWO OUTCOMES THAT ARE POSSIBLE.
YOU HAVE DEATH WHICH I TAKE IT IS ONE ALONG THE Y AXIS AND LIFE
WHICH IS ZERO ALONG THE Y AXIS; IS THAT CORRECT?
A, THAT IS IF WE WERE PLOTTING THE INDIVIDUAL TWO HUNDRED TEN
CASES RATHER THAN THEIR AVERAGES, YES.
Q. AND YET YOU HAVE A LINE THAT REFLECTS AT THE POINT FOR LEVEI
OF AGGRAVATION ALONG THE X AXIS SOMETHING IF THE LOW ALCOHOL
USER IS CLOSE TO FIFTY-EIGHT OR POINT FIVE EIGHT, YET NO
INDIVIDUAL CASE IS AT POINT FIVE EIGHT, HOW CAN THAT POINT BE
MEANINGFUL?
A. THE POINTS ALONG THE DIAGONAL LINES REPRESENT AVERAGE DEATH
SENTENCING RATES FOR GROUPS OF DEFENDANTS, IN GENERAL THIS IS
—_ pr—— {—— — —— TY — W—
3
WOODWORTH - DIRECT
WHAT A REGRESSION MODEL REPRESENTS. AGAIN IF WE CAN REFER TO
QUESTION NUMBER TWO WHICH SAYS Y=A+B1X1+B2X2+U, TEE PART OF THE
MODEL INVOLVING A'S, B'S AND X'S IS A MODEL FOR THE AVERAGE
VALUE OF THE DEPENDENT VARIABLE, IT IS NOT A MODEL FOR
1
2
3
4
if 5 INDIVIDUAL OUTCOMES.
6 Q. CAN YOU GIVE ME AN EXAMPLE OF A DICHOTOMOUS OUTCOME
7 SITUATION THAT CAN BE AVERAGED THAT WAY?
8 A.. THE TEXTBOOK EXAMPLE OF A DICHOTOMOUS OUTCOME IS TOSSING A
9 COIN. IF YOU SAY HEADS IS ONE AND TAILS IS ZERO AND YOU TOSS A
10 COIN TEN TIMES AND GET FIVE HEADS, THEN THE DATA WOULD BE ONE,
11 ONE, ONE, ONE, ONE. YOU WOULD HAVE FIVE CONES AND FIVE ZEROS IN
12 YOUR DATA SET. NOW THOSE ARE THE VALUES OF Y. THOSE ARE THE
33 VALUES OF THE DEPENDENT VARIABLES THAT YOU OBSERVE IN THOSE TEN
14 CASES, TEN TOSSES.
35 BUT IF YOU AVERAGE THOSE THAT MEANS TO ADD ALL OF THESE |
5
|
16 NUMBERS UP AND DIVIDE BY TEN, BY THE NUMBER OF TOSSES, WELL, YOU
17 ADD UP FIVE ONES AND FIVE ZEROS AND YOU GET FIVE. YOU DIVIDE
18 | THAT BY TEN AND YOU GET POINT FIVE OR FIFTY PERCENT. IN OTHER
19 | WORDS IT IS THAT AVERAGE THAT IS BEING MODELED BUT BY THE A + B
20 PART OF THE MODEL. WE ARE MODELING RATES THAN INDIVIDUAL
gi 21 OUTCOMES .
22 | OQ. SO IN YOUR EXAMPLE THERE IS NO CASE INVOLVING A COIN TOSS
23 WITH A POINT FIVE, SO TO SPEAK?
24 A. NO.
25 Q. BUT IF THE COIN EITHER LANDS ON ITS HEAD OR ITS TAIL, EITHER
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WOODWORTH -~ DIRECT
ONE OR ZERO, SOME I GUESS LAND UP ON THE RIDGE THERE, BUT--
A. NO INDIVIDUAL COIN TOSS IS GOING TO PRODUCE ANYTHING OTHER
THAN A ZERO OR ONE. YET POINT FIVE IS A CORRECT MODEL FOR THE
COIN. IT COMES UP HEADS HALF THE TIME AND TAILS HALF THE TIME.
NOT ALL DICHOTOMOUS VARIABLES -~- NOT ALL DICHOTOMOUS OUTCOMES
OCCUR AT A FIFTY PERCENT RATE. THAT IS THE POINT OF THE
REGRESSION MODEL. THAT GIVES US A MODEL FOR HOW THE RATES
CHANGE AS THE FACTS OF THE CASE CHANGE.
THE COURT: SUPPOSE YOU TAKE -- TELL ME WHAT YOUR TEN
AGGRAVATING VARIABLES ARE SO I CAN PICK ONE,
THE WITNESS: THEY ARE NOT ALL AGGRAVATING. NUMBER OF
VICTIMS, CONTEMPORANEOUS FELCNY, ALCOHOL WHICH IS MITIGATING,
CRIMINAL RECORD, WHETHER OR NOT--
THE COURT: LET ME TAKE TWO -- CONTEMPORANEOUS FELONY
AND NUMBER OF VICTIMS. I AM SUPPOSING AND I BELIEVE CORRECTLY
THAT CONTEMPORANEOUS FELONY OCCURS FAIRLY OFTEN?
THE WITNESS: YES.
THE COURT: AND MULTIPLE VICTIM CASES CCCUR FAIRLY
INFREQUENTLY?
THE WITNESS: YES.
THE COURT: WOULD THE RATE AT WHICH THE AGGRAVATING
CIRCUMSTANCE OCCURS CHANGE THE SLOPE OF THE LINE?
THE WITNESS: NO. THAT WOULD NOT CHANGE THE SLOPE.
THE COURT: ACTUALLY I DON'T MEAN THE SLOPE, I MEAN
THE reve
Tv WOODWORTH =~ DIRECT 3
1 THE WITNESS: THE HEIGHT OR INTERCEPT. NO. THE
2 RATE OF OCCURRENCE OF THE INDEPENDENT VARIABLE HAS NO
3 EFFECT ON THAT. THE INTERCEPT WOULD REFLECT THE SORT OF OVERALL
; 4 RATE OF THE DEPENDENT VARIABLE AND NOT THE RATE OF THE
; 5 INDEPENDENT VARIABLE OCCURRING. °
6 THE COURT: WHICH IS THE DEPENDENT?
7 THE WITNESS: THAT IS THE Y, THE DEATH SENTENCE IS THE
8 DEPENDENT. SO -- ONE COULD HAVE -~ ONE COULD HAVE AN EXTREMELY
9 RARE -- COMPARATIVELY RARE AGGRAVATING CIRCUMSTANCE WHICH
10 ELEVATES THE DEATH SENTENCING RATE BY THE SAME AMOUNT AS A
11 COMPARATIVELY COMMON AGGRAVATING CIRCUMSTANCE. IN GENERAL HOW
12 OFTEN THE CIRCUMSTANCE OCCURS DOES NOT AFFECT THE -- THERE IS NO
13 THE INTELLECTUAL REASON FOR IT TO AFFECT THE DEATH SENTENCING
14 RATE. THERE MAY BE SYSTEMATIC REASONS, BUT THAT IS A DIFFERENT
15 ISSUE.
16 BY MR. BOGER:
17 Q. WOULD IT AFFECT THE COEFFICIENT THAT YOU GET FOR THAT
18 VARIABLE?
19 A, ND, IT DOESN'T.
20 Q. IN OTHER WORDS, JUST THE SLOPE OF THE LINE THAT IS YOU
. 21 QUESTION, ISN'T IT, JUDGE.
22 THE COURT: I THINK THAT IS MY QUESTION. WHAT I WANT
23 TO KNOW AS IT TOUCHES MULTICOLINEARITY BUT THAT IS NOT THE ONLY
24 THING. IF SOME AGGRAVATING CIRCUMSTANCE OCCURRED AN AWFUL LOT
25 OF TIMES OR SOME MITIGATING CIRCUMSTANCE OCCURRED AN AWFUL LOT
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WOODWORTH = DIRECT
OF TIMES, IN YOUR STUDY USING THIS EQUATION IT WOULD NOT MAKE
ANY EFFECT AT ALL ON THE DEATH SENTENCING RATE OR THE LINE IT
FITS OR THE COEFFICIENTS OR ANYTHING ELSE. IF IT OCCURS =--
GOING BACK TO THE VISUAL DATA, IF WHATEVER OCCURRED, IF THERE
WAS ONLY ONE CASE AT THE ONE POINT ZERO LEVEL ON GW 9, IT WOULD
APPEAR THERE?
THE WITNESS: YES.
THE COURT: THAT PLOT POINT?
THE WITNESS: YES.
THE COURT: AND IF THERE WERE ONLY ONE CASE AT THE
MINUS POINT TWO LEVEL THAT PLOT WOULD NEVERTHELESS APPEAR THERE;
THE WITNESS: NO. ONE HAS TO HAVE A FAIR NUMBER OF
CASES AT EACH POINT TO GET A STABLE ESTIMATE OF ARRAY AND I TRY
TO KEEP IT ABOVE TEN CASES AT EACH POINT. BUT THE DIFFERENCE
BETWEEN HAVING TEN CASES AT A POINT AND HAVING ONE HUNDRED CASES
AT A POINT WILL NOT CHANGE THE RATE. IF YOU TOSS A COIN TEN
TIMES YOU WILL GET FIFTY PERCENT HEADS. IF YOU TOSS IT ONE
HUNDRED TIMES YOU GET FIFTY PERCENT HEADS.
THE COURT: IN SQUARING THESE NUMBERS THAT RATE
DIFFERENCE DOESN'T COME INTO EFFECT.
TEE WITNESS: SQUARING?
THE COURT: THE LEAST SQUARES -- SQUARE IT TO GET
POSITIVE VALUES.
THE WITNESS: WHAT IS SQUARED IS THE DIFFERENCE BETWEED
THE DOT AND THE LINE.
}
WOODWORTH - DIRECT 32
1 THE COURT: I UNDERSTAND.
2 THE WITNESS: THAT IS TO GET RID OF THE NEGATIVE
3 VALUES.
4 THE COURT: IT IS THAT WHICH IS IMPLICIT IN THE WORD
* 5 "SQUARE" THAT YOU MULTIPLY THAT VALUE TIMES ITSELF?
6 THE WITNESS: THAT DEVIATION TIMES ITSELF.
7 THE COURT: IF YOU HAD THEN A LOT OF CASES OUT AT POINT
8 EIGHT AND POINT ONE OR THE POINT EIGHT AND ONE ZERO AND ONLY A
9 FEW AT THE ZERO AND POINT TWO, YOU STILL WOULD HAVE A SLOPE THAT
10 LOCKS LIKE A PORTY-FIVE DEGREE ANGLE, ALTHOUGH THAT DOESN'T
bit 9 NECESSARILY PREDICT THE DEATH SENTENCING RATE FOR THE
12 POPULATION?
33 THE WITNESS: IF THE ONLY DATA YOU HAD WERE A POINT
14 EIGHT AND ONE POINT ZERO YOU CAN SAY THE SLOPE WOULD CHANGE
15 SLIGHTLY BUT NOT A GREAT DEAL AND IT WOULDN'T BE SAFE TO TRY TO
16 EXTRAPOLATE THAT LINE DOWN TO THE REST OF THE POPULATION.
17 THE COURT: I THINK I AGREE WITH THAT BUT I WANT TO
18 KNOW HOW WE HAVE AVOIDED DOING THAT?
19 THE WITNESS: BECAUSE WE HAVE A SPREAD OF DATA OVER THE
20 WHOLE RANGE. IF WE DIDN'T HAVE A SPREAD OF DATA, THEN THAT
21 WOULD BE REFLECTED IN THE PRECISION WITH WHICH WE CAN ESTIMATE
22 THE SLOPE.
23 THE COURT: GOING BACK TO PETITIONER'S DB 87. YOU HAVE
24 THAT IN FRONT OF YOU, MR. STROUP?
25 MR. STROUP: YES, YOUR HONOR.
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WOODWORTH - DIRECT
THE COURT: 1S THAT THE ONE WHERE YOU TAKE AN AWFUL LOT
OF VARIABLES AND THEN YOU FIGURE YOUR COEFFICIENTS BASED ON
THOSE THAT ARE STATISTICALLY SIGNIFICANT AT THE POINT ONE ZERO
LEVEL?
THE WITNESS: THIS IS LOGISTIC REGRESSION, YOUR HONOR.
CORRESPONDING ONE FOR LINEAR REGRESSION--
THE COURT: WOULD BE 967?
THE WITNESS: YES. DB 96 GIVES REGRESSION
COEFFICIENTS. |
THE COURT: IS THAT ONE WHERE YOU START OUT WITH A
WHOLE LOT OF THEM AND THEN YOU NARROW IT DOWN TO THOSE THAT ARE
STATISTICALLY SIGNIFICANT AT THE POINT ONE ZERO LEVEL?
THE WITNESS: THERE ARE FIGURES IN WHICH WE DO THAT,
YES.
THE COURT: AREN'T THOSE THE FIGURES?
THE WITNESS: WE ARE STILL LOOKING AT LOGISTIC FOR SOME
REASON.
THE COURT: SOMEWHERE IN THAT SERIES, I THOUGHT IT WAS
97 BUT I MAYBE WRONG.
THE WITNESS: YES, DB 95.
THE COURT: HOW DO I KNOW -- WHAT IS THERE ABOUT THAT
EXHIBIT THAT TELLS ME THAT THE RATE AT WHICH A VARIABLE OCCURRED
OR DID NOT OCCUR HAS NO EFFECT ON THE COEFFICIENT REPORTED IN
THAT?
THE WITNESS: I DON'T THINK THERE IS ANYTHING IN THAT
-
A—— p—— — —— —— ——— — — —
WOODWORTH - DIRECT ¥
1 PARTICULAR TABLE THAT CONVEYS THAT INFORMATION, IT IS A
2 THEORETICAL RESULT WHICH SAYS THAT THE DISTRIBUTION OF THE X
3 VARIABLE, THE INDEPENDENT VARIABLES, DOES NOT AFFECT THE
4 REGRESSION COEFFICIENTS,
5 WHAT IT DOES APFECT IS THE PRECISION WITH WHICH WE ARE
6 ABLE TO ESTIMATE THOSE COEFFICIENTS. SO ONE WOULD EXPECT IN YOUR
7 HYPOTHETICAL IF THERE ARE ONLY CASES AT POINT EIGHT AND ONE
8 POINT ZERO, WE WOULD GET APPROXIMATELY THE SAME SLOPE AS YOU CAR
9 EASILY SEE, BUT THE SLOPE WOULD BE LESS PRECISE IN THE SENSE OF
10 STANDARD DEVIATION.
5) IT'S LIKE TRYING TO HOLD A LONG STICK IN TWO HANDS. IF
12 YOU SUPPORT A LONG STICK WITH YOUR HANDS CLOSE TOGETHER, IT
13 WOBBLES, BUT IF YOU SUPPORT IT AT GREAT DISTANCES, THEN IT IS
14 MORE STABLE. NEVERTHELESS THE SLOPE OF THIS STICK IS THE SANE
15 AS THE SLOPE OF THIS LINE AND IS THE SAME EVEN IF WE REMOVE THE
16 POINTS AT THE LOWER END.
17 NOW, THERE IS NO FREE LUNCH IN STATISTICS IF YOU DO
18 HAVE ONE OF THESE EXTREME DISTRIBUTIONS OF THE DEPENDENT
19 VARIABLE, THEN IT IS GOING TO BE REFLECTED IN A LARGE STANDARD
20 DEVIATION OF THE REGRESSION COEFFICIENT ITSELF. WE WILL GET
s 21 APPROXIMATELY THE SAME ESTIMATE FOR THE COEFFICIENT BUT THE PLUS
22 OR MINUS SURROUNDING THE ESTIMATE WILL BE LARGER. IN DB S55
23 REGRESSION COEFFICIENT -- THE STANDARD ERRORS THEMSELVES ARE NOT
24 QUOTED, BUT IF ONE COULD REFER TO ONE OF MY -- THIS IS GW 4,
25 TABLE ONE, THE FIGURES IN PARENTHESIS THAT ARE MARKED SE, OR
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WOODWORTH - DIRECT
STANDARD ERROR, INDICATE THE PLUS OR MINUS STATISTICAL ERROR IN
THE ESTIMATE OF A REGRESSION COEFFICIENT.
NOW, THE WAY IN WHICH THE DISTRIBUTION OF THE X VALUES,
THEIR ARRANGEMENT, HOW ABUNDANT THEY ARE AT EACH LEVEL IN THE
SCALE, THE WAY THAT AFPECTS THE REGRESSION COEFFICIENT IS
THROUGH THAT STANDARD ERROR, THROUGH THAT PLUS OR MINUS
PRECISION. AND THIS IS A THEORETICAL RESULT.
THE WAY TO GET IT TO SHOW UP IN PRACTICE WOULD BE TO
ARTIFICIALLY PRUNE THE DATA SET TO ALTER THE ABUNDANCE OF ONE
PARTICULAR AGGRAVATING CIRCUMSTANCE AND OBSERVE WHAT THAT DOES
TO THE REGRESSION COEFFICIENTS. BUT THAT WOULD BE A THEORETICAL
EXERCISE. IT WOULDN'T HAVE ANY BEARING ON THE ANALYSIS OF THE
DATA AS CBTAINED.
BY MR. BOGER:
Q. LET ME GET BACK TO THE SOMETHING ON GW 9 WHICH I THINK MAY
BE IN LINE, I HOPE IT MIGHT BE WITH THE COURT'S QUESTION,
BECAUSE THE QUESTION MIGHT BE COMING IN A SLIGHTLY DIFFERENT
DIRECTION. LET'S LOOK AT GW 9. DOES ANYTHING ON THAT TOP GRAPH
REFLECT THE INCIDENCE OF CASES AT EACH LEVEL OF AGGRAVATION, THE
NUMBER OF CASES AT EACH LEVEL OF AGGRAVATION. |
THE COURT: I UNDERSTAND HIS TESTIMONY THERE IT DOES
BECAUSE BE BAS PARCED IT INTO SEVEN DISCRETE THINGS, BUT MY
QUESTION TO HIM ON 95 HAS HE OR HASN'T HE AND I DON'T UNDERSTAND
WHETHER HE HAS OR HASN'T,
BY MR. BOGER:
WERE SOMEWHAT DIFFERENT LIKE POINT TEN CR POINT ONE FIVE?
WOODWORTH - DIRECT
Q. LET ME ASK A SECOND QUESTION. IF IN FACT THE INCIDENCE OF
CASES IN THIS UNIVERSE WERE DIFFERENT, THE NUMBERS AT EACH
PARTICULAR LEVEL OF AGGRAVATION, WOULD THE LINE, SLOPE OF THE
LINE CHANGE?
A. IF FOR EXAMPLE I HAD GROUPED THE CASES IN A SLIGHTLY
DIFFERENT WAY THE SLOPE WOULD CHANGE VERY LITTLE BECAUSE IN FACT
I TRIED THAT. :
IF THIS HAD BEEN A DIFFERENT UNIVERSE, ONE IN WHICH
THERE WERE MORE HIGHLY AGGRAVATED CASES, THEN THE SLOPE WOULD
NOT CHANGE, YOU SEE BECAUSE THE HEIGHT OF THESE, THE VERTICAL
HEIGHTS OF THESE POINTS ON THE GRAPH IS A PERCENTAGE.
NOW PERCENTAGE DOES NOT DEPEND UPON HOW MANY CASES YOU
HAVE GOT, AS I MENTIONED EARLIER. IF YOU TOSS A COIN ONE
HUNDRED TIMES YOU'RE GOING TO GET THE SAME PERCENTAGE OF HEADS
IP YOU TOSS IT FIFTY TIMES OR TEN TIMES. AGAIN IF WE HAD THIRT]
CASES AT LEVEL ONE POINT ZERO INSTEAD OF TEN CASES UP THERE AND
WE ASSUMED THAT THE THIRTY CASES CAME FROM THE SAME UNIVERSE,
THEN WE WOULD EXPECT TO GET THE SAME RATE OF DEATH SENTENCING.
Q. THAT IS WHERE I WANT TO ASK THE FOLLOW-UP QUESTION. WHAT Wi
ASSUME THAT THE OVERALL DEATH SENTENCING RATE, IN OTHER WORDS,
THERE WERE A LOT OF LOW AGGRAVATION CASES AND A FEWER NUMBER OF
HIGHER AGGRAVATION CASES AND THAT THE CVERALL DEATH SENTENCING
RATE WAS ONLY LIKE POINT ZERO FIVE, WOULD IT MAKE ANY DIFFERENCE
IN THE SLOPE OF THE LINE, IF THE OVERALL DEATH SENTENCING RATE
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WOODWORTH - DIRECT
DOES THIS KIND OF GRAPH REFLECT THOSE SORTS OF
DIFFERENCE IN THE OVERALL DEATH SENTENCING RATES OR 1S IT
AFFECTED BY THE OVERALL DEATH SENTENCING RATES?
A. WELL YES, BUT —- YES. THE DEATH SENTENCING RATE IS HOW HIGH
THE POINT IS ON THE GRAPH.
THE COURT: LET ME ASK YOU IF CONCEPTUALLY I CAN DO
THIS, |
IN A TEN VARIABLE MODEL WITHOUT PARSING THE DATA INTO
SEVENTHS FOR SOME PURPOSE, COULD I CONCEIVE OF WHAT YOU ARE
DOING IS TAKING FACTOR NUMBER ONE AND RUNNING A PERCENT OF THE
DEATH PENALTY RATE, WHICH IS A PERCENT OF ALL OF THE CASES THAT
HAVE THAT FACTOR IN COMMON AKD THAT IS ONE PLOT POINT AND THEN
TAKE POINT TWO, AND YOU RUN THE DEATH PENALTY RATE OF ALL OF TH
CASES THAT HAVE THAT INCOME AND THEN FACTOR THREE AND THE DEATH
PENALTY RATE FOR ALL OF THE CASES THAT HAVE THAT IN COMMON. IS
THAT WHAT YOU'RE DOING? |
THE WITNESS: NOT EXACTLY, NO. THE FIRST ROUND WOULD
BE -- WOULD GIVE YOU A GRAPH OF TWO POINTS ON THE HORIZONTAL
WOULD BE CASES WITHOUT THAT FACT AND CASES WITH IT. SO YOU HAVE
TWO DEATH SENTENCING RATES.
THE COURT: GOING ALONG WITH YOUR IDEA YOU'RE DOING
PERCENTAGES, IF I TOOK CONCURRENCE OF ANOTHER FELONY AND I TOOK
MY DATA AND I DID A PERCENT, WHAT PERCENT OF CASES WHERE YOU
HAVE CONCURRENCE OF ANOTHER FELONY YOU HAVE THE DEATH PENALTY
RATE -- WELL, JUST ARBITRARILY POINT SIX.
— — —— —— —— ———
WOODWORTH = DIRECT i
1 THE WITNESS: RIGHT.
2 THE COURT: SO THAT IS ONE POINT AND THEN I GO TO
3 MULTIPLE VICTIMS AND I SAY WELL I HAVE TWENTY CASES AND FIVE OF
4 THEM HAVE MULTIPLE VICTIMS AND THE DEATH PENALTY -- TWENTY HAD
3 MULTIPLE VICTIMS AND FIVE GOT DEATH PENALTY RATE, SO THE DEATH
6 PENALTY RATE IS WHAT, POINT TWO AND THAT BECOMES THE
7 COEFFICIENT. 1s THAT WHAT YOU ARE DOING CONCEPTUALLY?
8 TRE WITNESS: NO. FOR EXAMPLE SOME OF THOSE CASES THAT
9 HAVE == 1 HAVE FORGETTEN WHAT YOUR TWO VARIABLES WERE.
10 THE COURT: I WAS USING THE NUMBER OF VICTIMS AND
33 CONTEMPORANEOUS FELONY.
12 THE WITNESS: SOME OF THOSE MULTIPLE VICTIM CASES MIGHT
13 ALSO HAVE A CONCURRENT FELONY. YOU ACTUALLY HAVE THREE
14 CATEGORIES. THOSE WITH BOTH, THOSE WITH FELONY, THOSE WITH
15 MULTIPLE VICTIMS AND ACTUALLY A FOURTH CATEGORY, THOSE WITH
16 NONE. SO YOU ACTUALLY HAVE FOUR POINTS ALONG YOUR GRAPH, FOUR
17 DIFFERENT GROUPS THAT WOULD BE INVOLVED THERE AND NOT JUST TWO.
18 THE COURT: WELL, WHETHER IT'S TWO OR FOUR, YOU THEN
13 ARE PLOTTING THE DEATH PENALTY RATE FOR THOSE FOUR GROUPS BASED
20 UPON PERCENTAGE WITHIN EACH GROUP THAT GOT THE DEATH PENALTY?
. 21 THE WITNESS: THAT IS CONCEPTUALLY WHAT WE ARE DOING IN
22 GW 9, WHERE WE POSITION THE GROUPS ON THE HORIZONTAL AXIS
23 DEPENDS ON THE POINT VALUE THEY GET FOR HAVING THOSE
24 CHARACTERISTICS.
25 THE COURT: THE CONSTRUCTION OF DB 95, WHAT IS THE ZX
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WOODWORTH - DIRECT
AXIS? IS IT AN AGGRAVATION INDEX LIKE THIS?
THE WITNESS: DB 95 WAS DONE ARITHMETICALLY, HOWEVER,
CONCEPTUALLY, YES, THE HORIZONTAL AXIS -- WHAT YOU HAVE TO
IMAGINE IS THAT WE HAVE GONE THROUGH THIS EXERCISE FOR EACH
VARIABLE IN TURN AND NOT JUST FOR THE ALCOHOL USE BUT FOR EACH
OF THE VARIABLES IN THE EQUATION AND PLOTTED OUT THE CASES
ACCORDING TO THE AGGRAVATION INDEX, DRAWN CUR STRAIGHT LINES ANI
SEEN HOW FAR THEY ARE SEPARATED VERTICALLY FOR EACH VARIABLE.
SO IN THAT CASE THE HORIZONTAL AXIS IS SLIGHTLY DIFFERENT FOR
EACH PLOT, FOR =-- IF WE ARE TRYING TO GET THE REGRESSION
COEFFICIENT FOR ALCOHOL USE, THEN THE HORIZONTAL AXIS WILL NOT
INCLUDE ALCOHOL USE WHEREAS IF WE ARE TRYING TO GET THE
REGRESSION COEFFICIENT FOR MULTIPLE VICTIMS, THEN HORIZONTAL
AXIS WOULD INCLUDE ALCOHOL USE AND WOULD NOT INCLUDE MULTIPLE
VICTIMS.
THE COURT: IP YOU DO IT STEPWISE AND YOU COME UP WITH
THE DEATH RATE OF THE FIRST FACTOR, THE COEFFICIENT?
THE WITNESS: THE DIFFERENCE IN DEATH RATES.
THE COURT: AND THAT'S THE COEFFICIENT PER FACTOR ONE?
THE WITNESS: RIGHT.
THE COURT: AND THEN YOU SOLVE FOR FACTOR TWO?
THE WITNESS: SPREADING OUT THE CASES ON FACTOR CHE.
THE COURT: HOW DO YOU SPREAD THEM OUT? CONCEPTUALLY
WHAT DO YOU MEAN BY THAT?
THE WITNESS: COMPUTE THE POINT VALUE FOR EACH CASE.
WOODWORTH - DIRECT #2
1 | NOW YOU ONLY HAVE ONE FACTOR TO BASE THE POINTS ON. THEY ARE,
2 | EITHER BAVE MULTIPLE VICTIMS OR THEY DON'T. SO YOU ARE ONLY
3 | GOING TO HAVE TWO GROUPS OF CASES, THOSE WITHOUT AND THOSE WITH,
4 | THEN WE WILL DRAW THESE TWO GRAPH FOR SOME OTHER VARIABLE,
5 | ALCOHOL USE, SAY. |
6 THE COURT: BUT THE POINT IS YOU HAVE TWO PLOTS AT THAT
7 | POINT ON YOUR GRAPH; IS THAT CORRECT?
8 THE WITNESS: TWO POINTS ON EACH OF TWO GRAPH.
9 THE COURT: THOSE THAT DO AND THOSE THAT DON'T?
10 THE WITNESS: RIGHT.
11 THE COURT: WE KNOW THE VARIATION BETWEEN THOSE TWO
12 | RATES, THOSE THAT DO AND THOSE THAT DON'T ARE CONTROLLED BY A
13 | BUNCH OF THINGS BESIDE THAT ONE VARIABLE?
14 THE WITNESS: RIGHT.
15 THE COURT: YOU HAVE NOT REALLY SOLVED FOR THAT
16 | VARIABLE?
17 THE WITNESS: NOT YET. BUT WHEN WE GET TO THE END WE
18 | CAN GO BACK. AT THE END WE HAVE TEN REGRESSION COEFFICIENTS.
19 | NOW THE EARLIER ONES ARE NOT GOING TO BE VERY GOOD, BUT WE COULD
50 | RECYCLE BACK AND RECOMPUTE THOSE EARLIER ONES USING ALL OF THE
. 21 | REGRESSION COEFFICIENTS THAT WE HAVE SO FAR CALCULATED AND THAT
22 | WOULD GIVE US AN IMPROVEMENT.
23 SO CONCEPUTALLY WE CAN KEEP GRINDING THIS CRANK AND
24 | KEEP RECYCLING THROUGH AND KEEP IMPROVING THE REGRESSION
25 | COCFFICIENTS EVERY TIME WE GO AROUND AND ULTIMATELY WE WILL
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WOODWORTH —~ DIRECT
ARRIVE AT THE CONES IN DB 95.
BY MR. BOGER:
Q. SO THE CONCEPUTAL EXPLANATION FOR THE REGRESSION
COEFFICIENTS THAT ARE OBTAINED ALGEBRAICALLY IS AN INFINITE
SERIES OF RECALCULATION OF COEFFICIENTS FOR EACH OF THE
VARIABLES MODIFYING THE SUCCESSIVE VARIABLES AS WE OBTAIN MORE
INFORMATION?
A. THAT IS CORRECT. THE KEY TO THIS IS POSITIONING THE CASES
ON AGGRAVATION INDEX AND THE KEY TO THAT IS HAVING POINT VALUES
TO ASSIGN TO THE VARIABLES.
NOW WE COULD COME UP WITH -- WE CAN START WITH SOME
SORT OF POINT VALUES AND MIGHT START WITH THE SET OBTAINED BY
THIS STEPWISE PROCESS THAT YOU OUTLINED, YOUR HONOR, AND HAVING
GOTTEN THOSE, WE KNOW THEY ARE NOT QUITE RIGHT SO WE GO BACK
AGAIN TO SQUARE ONE WHERE WE ARE DEALING WITH MULTIPLE VICTI!NS
AND NOW INSTEAD OF JUST USING MULTIPLE VICTIMS NOW WE ARE GOING
TO SPREAD THE CASES OUT ON THE AGGRAVATION INDEX THAT WE CAN GET
FROM THE REGRESSION COEFFICIENT AND RECOMPUTE THE REGRESSION
COEFFICIENT FOR MULTIPLE VICTIMS AND NOW IT WILL BE MUCH CLOSER
TO THE VALUE THAT IS GIVEN BY DB 85 AND WE KEEP DOING IT FOR
EACH VARIABLE IN TURN.
THE COURT: HOW DC YOU RECOMPUTE?
THE WITNESS: AS IN GW 9 AND GW 10. IMAGINE WE HAVE
GONE THROUGH THIS STEPWISE PROCESS THROUGH ELEVEN VARIABLES, SO
AT THE END WE HAVE A LIST OF REGRESSION COEFFICIENTS ADMITTEDLY
J
— — — — — —
WOODWORTH =~ DIRECT ae
: NOT PERFECT ESTIMATES, BUT ESTIMATES.
2 SO NOW WE HAVE A POINT VALUE FOR EVERY VARIABLE AND NOW
3 WE GO BACK AND TAKE THE TEN VARIABLES EXCLUDING MULTIPLE
4 VICTIMS, WE GOT POINT VALUES FOR ALL OF THE VARIABLES SO WE CAN
5 NOW CALCULATE THE POINT VALUE FOR EACH INDIVIDUAL CASE, THAT
6 WILL ENABLE US TO DRAW A GRAPH LIKE GW 9 WHERE THE VARIABLE IN
7 QUESTION IS MULTIPLE VICTIMS AND WE DRAW A GRAPH LIKE GW 10
8 WHERE THE UPPER CURVE REFERS TO MULTIPLE VICTIMS AND THE LOWER
. CURVE REFERS TO NO MULTIPLE VICTIMS, ZERO OR ONE VICTIM, AND
10 FROM THAT SEPARATION WE GET AN ESTIMATION OF THE REGRESSION
11 COEFFICIENT FOR MULTIPLE VICTIMS WHICH WE NOW PUT IN OUR LIST oF
12 REGRESSION COEFFICIENT.
13 NOW WE TURN OUR ATTENTION TO THE NEXT VARIABLE WHICH
14 MIGHT BE THE PRESENCE OF A FELONY, CONTEMPORANEOUS FELONY. NOW
15 WE HAVE REGRESSION COEFFICIENTS FOR EVERY VARIABLE. THE
16 REGRESSION COEFFICIENT FOR MULTIPLE VICTIMS WHICH WE JUST
17 FINISHED RECOMPUTING ALIA GW 10 AND ALL THE OTHER REGRESSIONS
18 COEFFICIENTS WHICH WE COMPUTED BY STEPWISE, WE USED THE POINT
19 VALUES GIVEN BY THE REGRESSION COEFFICIENTS TO SPREAD OUT THE
20 CASES NOW ON AN INDEX OF AGGRAVATION THAT DOES RCT INVOLVE
21 PRESENCE OR ABSENCE OF A FELONY CIRCUMSTANCE AND THEN AS AGAIN
22 IN GW 10 WE WILL GET THE VERTICAL SEPARATION DUE TO PRESENCE OR
23 ABSENCE OF A FPELONY CIRCUMSTANCE, THAT WILL BE CUR IMPROVED
24 REGRESSION COEFFICIENT FOR FELONY CIRCUMSTANCE AND SO ON. AT
25 EACH STAGE OF THIS PROCESS WE ARE IMPROVING THESE REGRESSION
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WOODWORTH - DIRECT
COEFFICIENTS.
NOW THIS IS =-- EVERYTHING I HAVE SAID IS CONCEPTUAL.
IT IS AN INTELLECTUAL WAY OF UNDERSTANDING WHAT IS GOING ON.
THE ACTUAL COMPUTING FORMULA DOES NOT HAVE TO DO THIS IKFINITE
RECYCLING TO GET THE BEST VALUES OF THE REGRESSION COEFFICIENT.
WHAT THE ACTUAL PROCESS DOES IS SIMULTANEOUSLY ESTIMATE ALL
REGRESSION COEFFICIENTS.
THE COURT: LET'S TAKE A TEN MINUTES BREAK.
* * *%
(RECESS.)
* ®
GEORGE WOODWORTH, RESUMED
DIRECT EXAMINATION CONTINUED
BY MR. BOGER:
0. DR. WOODWORTH, DURING THE RECESS, I HAVE ASKED YOU IF YOU
WOULD TO SET PORTH TWO FIGURES WHICH MIGHT REFLECT DIFFERENT
KINDS OF MEASUREMENTS ONE COULD MAKE IN A SITUATION INVOLVING
NUMBER OF VICTIMS, MULTIPLE VICTIMS VS. ONE VICTIM OR NO
VICTIMS.
HAVE YOU COMPLETED SUCH A DIAGRAM FOR US?
A. YES, 1 BAVE.
Q. LET ME ASK YOU IF YOU CAN IDENTIFY THE LARGE CHART THAT HAS
BEEN PLACED BEFORE THE COURT HERE, WHICH WITH THE COURT'S
PERMISSION I WILL MARK GW ll FOR IDENTIFICATION. CAN YOU
IDENTIFY THAT?
—— — — —, — —— — — —
47
WOODWORTH - DIRECT
1 A. THIS IS THE CHART I JUST PREPARED, IT SHOWS A HYPOTHETICAL
2 IN WHICH THERE ARE TWENTY MULTIPLE VICTIMS CASES, EIGHTEEN CF
3 WHICH RECEIVED THE DEATH PENALTY AND ONE HUNDRED NON-MULTIPLE
4 VICTIM CASES, TEN OF WHICH RECEIVED THE DEATH PENALTY.
5 Q. THERE ARE TWO GRAPH APPARENTLY REPRESENTED IN GW 11. LET'S
6 LOOK AT THE TOP ONE AND I WILL ASK YOU WHAT THAT REPRESENTS.
7 A. THE TOP ORE SHOWS A GRAPH OF A NUMBER OF DEATHS AGAINST
8 NUMBER OF VICTIMS.
9 Q. IN OTHER WORDS, THE VERTICAL AXIS IS WHAT?
10 A. NUMBER OF DEATHS.
31 Q. HORIZONTAL AXIS?
2 A. REPRESENT THE DUMMY VARIABLE FOR MULTIPLE VICTIMS. AT ONE
13 END IT IS ZERO OR ONE VICTIM AND AT THE OTHER END IT IS MULTIPLE
14 VICTIMS.
15 Q. WHAT DO THE TWO POINTS REPRESENT PLOTTED ON THAT GRAPH?
16 A. THE POINTS IN THIS GRAPH REPRESENT THE NUMBER OF DEATH
37 SENTENCES THAT WERE BROUGHT IN THESE CASES. SO WE SEE THAT
18 THERE WERE TEN DEATH SENTENCES IN THE NON-MULTIPLE VICTIM CAGES
1% AND EIGHTEEN DEATH SENTENCES IN THE MULTIPLE VICTIM AND I HAVE
20 CONNECTED THESE WITH A STRAIGHT LINE.
21 Q. THAT IS THE DOTTED STRAIGH LINE, IF YOU WOULD?
22 A. YES.
23 Q. NOW WOULD THE SLOPE OF THAT LINE VARY DEPENDING UPON THE
24 NUMBER OF CASES THAT HAD MULTIPLE VICTIMS CR THE NUMBER THAT HAD
25 SINGLE OR FEWER VICTIMS?
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WOODWORTH - DIRECT
A. YES. BECAUSE THE VERTICAL AXIS IS THE NUMBER OF DEATHS AND
THEREFORE THE HEIGHT OF THE POINT WOULD DEPEND ON HOW MANY CASES
THERE WERE. IF WE HAD FEWER NON-MULTIPLE VICTIM CASES THEN WE
WOULD HAVE FEWER DEATH SENTENCES AND THAT POINT WOULD GO DOWN.
Q. IN THIS HYPOTHETICAL WE HAVE CONSTRUCTED LET'S LCOK AT A
LOWER OF THE TWO GRAPH, WHAT DOES THAT REPRESENT?
A. THAT REPRESENTS THE RATES AT WHICH THE DEATH SENTENCES ARE
BROUGHT IN THESE TWO GROUPS OF CASES AND HERE WE SEE THAT TEN
PERCENT OF THE NON-MULTIPLE VICTIM CASES RECEIVE DEATH. THAT IS
REFLECTED BY THE DECIMAL FRACTION POINT ONE ON THE VERTICAL AXIS
WHEREAS NINETY PERCENT OF THE NON-MULTIPLE VICTIM CASES RECEIVE
THE DEATH PENALTY WHICH WOULD BE REFLECTED BY DECIMAL FRACTION
OF POINT NINE oN THE VERTICAL AXIS. THIS VERTICAL AXIS WOULD BR
LABELED DEATH SENTENCING RATE, JUST AS IN GW 9 AND 10.
Q. WOULD THE SLOPE OF THAT LINE VARY DEPENDENT UPON THE NUMBER
OF MULTIPLE VICTIM CASES OR OF SINGLE OR NO VICTIM CASES?
A. NO, THIS ONE SHOWS RATES, A RATE DOES NOT CHANGE WHEN YOU
INCREASE THE NUMBER OF OBSERVATIONS AS IN -- IF FOR EXAMPLE WE
HAD FIFTY NON-MULTIPLE VICTIM CASES, THEN WE WOULD EXPECT TO
HAVE FIVE DEATHS. SO THE NUMBER OF DEATHS WOULD GO DOWN, BUT
THE RATE OF DEATH WOULD NOT GO DOWN. IT WOULD BE THE SAME,
THEREFORE THE SLOPE WHICH REFLECTS THE CHANGE IN THE DEATH
SENTENCING RATE WOULD STAY THE SAME,
Q. NOW WHICH OF THE TWO GRAPH REFLECTS THE KIND OF CALCULATION
THAT IS USED TO CREATE A REGRESSION COEFFICIENT?
— — —— — — —
WOODWORTH ~- DIRECT 82
1 A. THE LOWER GRAPH IS THE TYPE THAT 1S USED TO CALCULATE
2 REGRESSION COEFFICIENT. IN THIS CASE THE RISE IN THE GRAPH
3 BEING THE SLOPE WOULD REPRESENT THE REGRESSION COEFFICIENT IN
4 THE SIMPLE REGRESSION THAT CONTAINS ONLY THE MULTIPLE VICTIM
5 VARIABLE.
6 Q. SO IT IS YOUR TESTIMONY BASED ON THESE TWO HYPOTHETICAL
7 GRAPH THAT THE REGRESSION COEFFICIENT IS NOT AFFECTED BY THE
8 NUMBER OF CASES AT THE DIFFERENT OUTCOME POINTS?
9 A. NO.
10 THE COURT: AS I UNDERSTAND IT YOU'RE NOT REALLY DOING
11 THAT IN YOUR MULTIPLE VARIABLE REGRESSIONS. WOULD THAT ALSO BE
12 TRUE OF THE EQUATION YOU USE THAT IT WCULD NOT MAKE ANY
13 DIFFERENCE ON THE RATE AS TO WHETHER ONE OF THE FACTORS YOU HAVE
14 ON THE Y AXIS OCCURRED OFTEN COR SELDOM?
15 THE WITNESS: THAT IS CORRECT. IT WOULD NOT AFFECT --
16 THE USE OF RATES MEANS THAT THE NUMBER OF CASES POSSESSING A,
17 CERTAIN CHARACTERISTICS WOULD NOT -- THERE IS NO INTELLECTUAL
18 REASON FCR IT TO CHANGE THE SLOPE.
19 THE COURT: WHAT -- WOULD YOU VENTURE AN EDUCATED GUESS
20 AS TO WHAT THE STATISTICAL SIGNIFICANCE MEASURE WOULD BE ON THE
’ 33 BOTTOM GRAPH?
22 THE WITNESS: WELL, LET'S SEE, THE STANDARD ERROR FOR
23 THE MULTIPLE VICTIM CASES WOULD BE ABLE POINT TWO AND MAY I
24 APPROACH THE GRAPH?
25 THE COURT: UH-HUH.
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WOODWORTH - DIRECT
THE WITNESS: SO IF WE HAD TO PUT ERROR BARS AROUND
EACH POINT HERE JUST TO SEE THE APPARENT CALCULATION WE WOULD
SAY THE STANDARD ERROR IS ABOUT POINT TWO AND STANDARD ERROR
DOWN HERE IS ABOUT POINT THREE, SO, IF WE LOCK AT THE
DIFFERENCE HERE BETWEEN THESE TWO POINTS, THAT DIFFERENCE 1S
QUITE LARGE COMPARED TO THE STANDARD ERRORS, SO I WOULD GUESS
THAT TO BE SIGNIFICANT WELL UNDER THE ONE PERCENT LEVEL.
THE COURT: MY QUESTION TO YOU IS HAVING CREATED THE
MODEL, WHICH IS STATISTICALLY SIGNIFICANT IN PREDICTING DEATH
RATES, BUT WE KNOW THERE ARE MANY MANY OTHER FACTORS BESIDE THE
NUMBER OF VICTIMS WHICH GO INTO THE CALCULATION OF THE DEATH
PENALTY, HOW CAN I RELY ON THAT?
IN OTHER WORDS YOU SET ME UP A MODEL THAT IS
STATISTICALLY SIGNIFICANT AND TELL ME WHEN THE DEATH PENALTY
RATE IS GOING TO BE IMPOSED AND AT WHAT RATE AND YET I KNOW THA]
MODEL DOES NOT REFLECT REALITY.
THE WITNESS: BECAUSE IT DOES NOT HAVE ENOUGH
INDEPENDENT VARIABLES IN IT.
THE COURT: HOW MANY IS ENOUGH?
THE WITNESS: WHEN ONE CAN FIND NO FURTHER MEANINGFUL
VARIABLES THAT PRODUCE A SIGNIFICANT IMPROVEMENT IN THE FIT OF
THE MODEL.
BY MR, BOGER:
Q. DR. WOODWORTH, THIS GETS YOU BACK TO THE QUESTION OF
CONTROL. IT APPEARS TO ME AT LEAST THAT ONE CAN CONTROL
— — — —_—— ——
53
WOODWORTH - DIRECT
1 SUCCESSIVELY FOR AN INCREASING NUMBER OF ADDITIONAL INDEPENDENT
2 VARIABLES; IS THAT CORRECT?
A. THAT IS CORRECT. 3
4 Q. AND IF ONE CONTROLS FOR MORE INDEPENDENT VARIABLES THAT ARE
5 [5
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RELEVANT OR DEEMED RELEVANT TO THE QUESTION AT HAND, THE OUTCOMI
6 VARIABLE OF INTEREST, ONE CAN ARRIVE AT DIFFERENT LEVELS OF
7 CERTAINTY WITH RESPECT TO THE MEANINGFULNESS OR ACCURACY OF THE
8 CALCULATIONS ONE HAS DEVELOPED? IS THAT APPROPRIATE?
2 A. IF I CAN REFER BACK TO THE COURT'S QUESTION ABOUT HOW CAN
10 THIS REGRESSION BE RELIED UPON AND OF COURSE WE ARE NOT TALKING
1} ABOUT THIS SIMPLE HYPOTHETICAL BUT A GENERAL ONE.
12 THE COURT: IF WE WERE COMPARING THAT WITH ALCOHOL, FOR
13 EXAMPLE, THEN WE HAVE TWO, AND I WOULD ASSUME THAT THE ONES ON 3
14 AND 10 ARE STATISTICALLY SIGNIFICANT AND WE STILL END UP WITH
15 SOMETHING THAT HAS STATISTICAL SIGNIFICANCE THAT WE KNOW IN
16 REALITY DOES NOT MIRROR THE WORLD, DON'T WE?
17 THE WITNESS: IN WHAT SENSE DOES YOUR HONOR MEAN IT
18 | DOESN'T MIRROR THE WORLD?
19 THE COURT: WE KNOW TO USE THE EQUATION THAT THE AUTHOR a
4
20 OF THE ARTICLE IN THE COLUMBIA LAW REVIEW ARTICLE PUT FORWARD
1 23 THERE IS A REAL BIG "U" OUT THERE.
22 THE WITNESS: IT DOES MIRROR THE WORLD IN THE POLLOWING
23 SENSE. THE ®"U"™ TERM IN THE EQUATION THAT YOU ARE REFERRING TO
24 REFLECTS UNIQUE -- "U" PROBABLY STANDS FOR UNIQUE —- REFLECTS
25 ALL OF THOSE UNIQUE CHARACTERISTICS OF EACE INDIVIDUAL CASE THAT
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WOODWORTH - DIRECT
DO NOT OPERATE ON A SYSTEM-WIDE BASIS.
THE REGRESSION MODEL REFLECTS THE REALITY IN THE SENSE
THAT THE FACT THAT EACH CASE HAS UNIQUE ELEMENTS IS A FACT OF
THE WORLD. THE MODEL DOES MODEL THE REAL WORLD IN THE FOLLOWING
SENSE.
IT SAYS WITH RESPECT TO THESE ELEVEN VARIABLES WE CAN
FIND GROUPS OF CASES WHICH ARE SIMILAR IN TERMS OF THE DEATH
RATES AND WE CAN PREDICT WHAT THOSE DEATH RATES ARE. WITHIN
EACH OF THOSE CLASSES OF CASES, OF SIMILAR CASES, THERE ARE
UNIQUE INFLUENCES AS WELL. WE DON'T KNOW WHAT THOSE UNIQUE
INFLUENCES ARE, BUT WE KNOW THEY DON'T OPERATE SYSTEM-WIDE
BECAUSE --
THE COURT: HOW DO YOU KNOW THAT?
THE WITNESS: BECAUSE WE HAVE EXAMINED A LARGE NUMBER
OF VARIABLES, CANDIDATE VARIABLES THAT MIGHT HAVE SYSTENM-WIDE
OPERATION AND WE CAN'T FIND ANY WHEN GRAPHED AS IN GW 10 WILL
PRODUCE A SYSTEMATIC DIFFERENCE IN THE DEATH SENTENCING RATES
OVERALL CASES. THAT IS WHAT IT MEANS TO HAVE ACHIEVED
STATISTICAL CONTROL. THAT MEANS WE CANNOT FIND ANY MORE
VARIABLES WHICH WILL CAUSE THE DEATH RATES TO SEPARATE, WHEN WE
PLOT THEM SEPARATELY~~-
THE COURT: IN WHICH CHART DID YOU REACH THAT POINT?
MR. BOGER: YOUR HONOR, I BELIEVE AND, IT WAS
APPROPRIATE TO TURN TO ME, WE DID NOT OFFER DR. WCODWORTH AS THEY
EXPERT ON THE CRIMINAL JUSTICE STATISTICS AREA. I BELIEVE THERE
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53
WOODWORTH - DIRECT
WAS TESTIMONY BY PROFESSOR BALDUS THAT HE EMPLOYED IN EFFECT A
MULTITUDE OF APPROACHES.
THE COURT: I HAVE THAT POINT. THE PROBLEM I HAVE GOT
IS THE PROBLEM I AM TRYING TO ILLUSTRATE HERE. AND I MAYBE
OVERSTATING THE CASE. HE MAY TAKE A MODEL WITH EIGHT VARIABLES
AND HE MAY TAKE A MODEL WITH TWO HUNDRED VARIABLES AND HE IS
TELLING ME THE EIGHT VARIABLE MODEL IS STATISTICALLY SIGNIFICANT
ACCORDING TO THE SIGMA VALUE OR THE S VALUE, WHATEVER THE --
MR. BOGER: P VALUE.
THE COURT: WHEN EVERYBODY IN THE COURTROOM KNOWS THAT
EIGHT VARIABLE MODEL DOES NOT REALLY TAKE INTO ACCOUNT THOSE
THINGS WE KNOW.
IT LOOKED TO ME LIKE IN THINKING ABCUT IT SOME, YOU
NEED TO NOT ONLY AS A LEGAL MATTER BUT AS A STATISTICAL MATTER -
STATISTICAL TO FOLLOW WHAT DR. WOODWORTH JUST SAID -- TO SAY
WHICH MODEL IT IS THAT YOU HAVE ADJUSTED FOR EVERY VARIABLE YOU
THINK IN A LEGAL SENSE OR IN AN INTELLECTUAL SENSE MAY HAVE SOME
EFFECT ON IT AND WHERE THERE IS =-- AND SHOW ME THERE IS NOT ANY
DIFFERENCE. I SUBMIT IF YOU TOOK TEN AND ADDED ELEVEN, THERE I$
A DIFFERENCE. SO THEREFORE WE KNOW THAT THE TEN AND ELEVEN
VARIABLE -- WE KNOW THE TEN VARIABLE MODEL DOES KOT EXPLAIN
THINGS. WE KNOW THAT. SO I CANNOT RELY ON THE TEN VARIABLE
MODEL BECAUSE WE KNOW THERE IS AN ELEVENTH VARIABLE THAT WILL
GIVE US DISPARITY IN THE DEATH RATE SENTENCING.
MR, BOGER: I THINK PROFESSOR BALDUS' TESTIMONY
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WOODWORTH - DIRECT
REFLECTED BY DR. WOODWORTH IS THAT WHAT ONE DOES IS GO LOOKING
FOR VARIABLES THAT MAKE A DIFFERENCE AND IF YOU INCLUDE AS
PROFESSOR BALDUS DID IN A NUMBER OF HIS CHARTS OR TABLES, MODELS
THAT INCLUDE ALL OF THE VARIABLES THAT HE HAD COLLECTED DATA ON
IN THEIR REDUCED FORM, TWO HUNDRED THIRTY PLUS, AND YOU DON'T
FIND ANYTHING WHICH SHAKES THE DEATH SENTENCING RATES BASED UPON
RACE WHICH OF COURSE WAS THE MATTER OF INTEREST BEFORE THE
COURT, THEN IT BECOMES APPROPRIATE TO COME BACK TO MODELS == THE
MODEL THAT PROFESSOR BALDUS I THINK LIKED BEST WAS THE
THIRTY-NINE VARIABLE MODEL AND I BELIEVE DR. BERFORD ALSO
REFLECTED THAT MODELS WITH TWO HUNDRED THIRTY PLUS VARIABLES MAY
HELP FLESH OUT ONES THAT MIGHT MAKE RACE GO AWAY BUT IF IN FACT
THEY DON'T EAVE THAT EFFECT THAT FOR PURPOSES OF STATISTICAL
ANALYSIS MODELS WITH FEWER VARIABLES ARE PREFERABLE NOT BECAUSE
THEY PERFECTLY MIRROR REALITY BUT BECAUSE THEY ARE AN ACCEPTABLE
COMPROMISE BETWEEN MODELS THAT HAVE VARIABLES THAT ARE IMPORTANT
WITH AVOIDING THE MULTI-COLINEARITY PROBLEMS THAT APPARENTLY
ARISE WHEN YOU GET TWO HUNDRED PLUS FACTORS IN THE SAME MODEL.
THE COURT: YOU HAPPEN TO REMEMBER OFFHAND THE EXHIBIT
NUMBER FOR THIRTY~NINE?
MR. BOGER: THERE ARE AT LEAST FIVE OR SIX TABLES IN
WHICH I THINK THERE ARE REPORTED FIGURES WITH TWO HUNDRED THIRTY
PLUS. :
THE COURT: HE SAID HE SEEMED TO LIKE THE THIRTY-NIKE
VARIABLE MODEL. DO YOU HAPPEN TO REMEMBER THE EXHIBIT NUMBER
WOODWORTH = DIRECT 2
1 FOR THE THIRTY-NINE VARIABLE MODEL?
2 MR. BOGER: I THINK HE USED THE THIRTY-NINE VARIABLE
3 MODEL IN A NUMBER OF THEM, DR. WOODWORTH USED THEM IN THE
4 DIAGNOSTIC TEST HE RAN, I BELIEVE; IS THAT CORRECT?
5 : THE WITNESS: THE THIRTY-NINE VARIABLE MODEL IS ONE WE
6 REFERRED TO AS THE MID-RANGE MODEL.
7 THE COURT: THAT'S THE ONE YOU TESTIFIED AT LENGTH
8 ABOUT; IS THAT RIGHT?
9 THE WITNESS: YES, THAT'S RIGHT.
10 THE COURT: WITH THE R FACTORS?
31 THE WITNESS: WITH THE LARGE CHARTS.
12 THE COURT: THOSE ARE THE ONES THAT YOU COMPUTED THE R
13 VALUES ON?
14 THE WITNESS: YES, AMONG OTHERS. THE THIRTY-NINE
15 VARIABLE MODEL AS MR. BOGER SAYS IS A COMPROMISE BETWEEN A MODEL
16 WHICH HAS LARGE NUMBERS OF VERY MINOR VARIABLES IN IT AND A
37 MODEL WHICH CONTAINS AN IRRATIONAL SET OF VARIABLES INFORMED BY
18 ~ PROFESSOR BALDUS' KNOWLEDGE OF THE CHART AND SENTENCING SYSTEM.
19 THE THIRTY-NINE VARIABLE MODEL LIKE ANY MODEL WE DON'T CLAIM IS
20 A PERFECT MIRROR OF REALITY. ON THE OTHER HAND, IT IS CLOSE
2) ENOUGH.
22 THE WAY WE DEMONSTRATE IT IS CLOSE ENOUGH 1S THAT WITH
23 RESPECT TO THE KEY COEFFICIENT, NAMELY, THAT OF THE RACE, ADDING
24 MORE VARIABLES TO THE MODEL DOES NOT CHANGE THAT PARTICULAR
25 COEFFICIENT WHICH IS TO SAY THAT THE OTHER EFFECTS THAT ARE
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WOODWORTH - DIRECT
PRESENT IN THE MODEL ARE SMALL AND ARE NOT RELATED -- DO NOT
EXPLAIN AWAY THE RACE EFFECT,
THERE ARE PLENTY OF EXAMPLES IN SCIENCE IN WHICH A
SIMPLIFICATION OF REALITY IS STILL INTELLECTUALLY USEFUL IF THE
SIMPLIFICATION DOES NOT DO VIOLENCE TO REALITY AND DISTORT IT.
THE COURT: I AGREE WITH WHAT YOU SAID. I AM NOT
TROUBLED BY THAT NOTION. WHAT DOES TROUBLE ME SOME, YOU VERY
GRACEFULLY POINTED OUT TO ME THAT YOU COULD NOT IN A SHORT
PERICD OF TIME EXPLAIN TO ME WHAT YOU DID ALGEBRAICIALLY AND
THAT MAY BE TRUE AND I WILL LEAVE THAT TO YOUR COUNSEL AS TO
WHETHER IT IS NECESSARY OR NOT.
BUT IF I AM TO UNDERSTAND THIS WHOLE THING BASED ON THE
CHARTING SORT OF THING, IT SEEMS TO ME THAT I AM TROUBLED BY THE
FACT THAT A GIVEN VARIABLE WHICH MAY BE AWFULLY IMPORTANT, COULD
BE WEIGHED IN AGAINST A LOT OF VARIABLES WHICH ARE NOT IMPORTANT
AND BY THE TIME YOU SQUARE THEM AND A WHOLE BUNCH OF OTHER
VARIABLES, THE ONE VARIABLE THAT IS MORE EQUAL THAN THE REST OF
THE VARIABLES GETS SWALLOWED UP IN IT.
THE WITNESS: THAT IS TRUE. FOR EXAMPLE IF WE HAD FIVE
DIFFERENT WAYS, FIVE DIFFERENT VARIABLES WHICH REFLECTED ON
PRIOR CRIMINAL RECORD, THEY MIGHT FIGHT WITH EACH OTHER FOR
ENTRY INTO THE REGRESSION EQUATION. BUT PROFESSOR BALDUS DID
NOT EMPLOY STEPWISE REGRESSION IN CASES WHERE THERE WAS COMMON
INFORMATION IN SEVERAL VARIABLES. THERE WAS AN ATTEMPT TO,
EITHER TO FORM A COMPOSITE OF THOSE, ON LEGAL AND SOCIOLOGICAL
WOODWORTH - DIRECT i
1 | PRINCIPLES OR TO TAKE A REPRESENTATIVE, SO TO SPEAK, FLAGSHIP
2 | VARIABLE FROM THAT SET AND TO USE IT AS A PROXY FOR THE REST.
3 THE COURT: JUST ASSUMING THAT IS FINE, IF YOU HAVE GOT
4 | A VARIABLE THAT IS PROHIBITIVE ONE WAY OR THE OTHER OR DAMN NEAR
S | PROHIBITIVE, YOU KNOW, IF THIS OCCURS IN A CASE YOU HAVE A DEATH
6 | PENALTY RATE OF POINT ZERO ZERO ONE OR IF IT APPEARS IN A CASE
7 | YOU HAVE A POINT NINE NINE NINE DEATH PENALTY PACTOR AND IF YOU
8 | THROW THAT IN WITH THIRTY-EIGHT OTHERS, THEN THAT LINE SLOPE IS
9 | GOING TO BE -- THE OTHER, THIRTY-EIGHT EVEN THOUGH THEY ARE
10 | INTELLECTUALLY DEFENSABLE ARE GOING TO SO CHANGE THE SLOPE OF
11 | THE LINE THAT GOING BACK TO YOUR IDEA OF SIMPLICITY, WE LOSE THE
12 | DRIVE OF THE ONE THAT IS REALLY MORE IMPORTANT THAN ANY OF THE
13 | OTHERS, DON'T WE?
14 THE WITNESS: IT DEPENDS UPON WHETHER THAT VARIABLE
15 | OCCURS OFTEN ENOUGH TO BE SAID TO BE SYSTEMATIC. IF IT OCCURRED
16 | IN ONLY ONE OR TWO CASES, THEN IT'S HARD TO SAY WHETHER IT WAS
17 | JUST A COINCIDENCE THAT THOSE TWO CASES WHERE IT OCCURRED GOT
18 | DEATH AND OTHERS DID NOT.
19 BUT IF THAT PARTICULAR CIRCUMSTANCE OCCURRED A
20 | SUBSTANTIAL NUMBER OF TIMES, MAYBE TWENTY, AND EVERY TIME IT
21 | OCCURRED WE GOT THE DEATH SENTENCE, THEN IT WILL PROBABLY COME
22 | INTO THE REGRESSION EQUATION AND PROBABLY COME IN WITH A
23 | SUBSTANTIAL REGRESSION COEFFICIENT AND THE EFFECT OF IT IN GW 9,
24 | FOR INSTANCE, THE EFFECT OF HAVING SUCH A VARIABLE, ONE THAT IS
25 | PROHIBITIVE OR DETERMINATIVE, IF IT IS DETERMINATIVE IT WOULD
— ————— ——| — — — —— — ———— ——— —— —— — —— ————
58
WOODWORTH - DIRECT
TEND TO -- ANY CASE THAT HAS THAT CHARACTERISTIC WOULD BE
SITTING AT THE HIGH END OF THIS SCALE BY VIRTUE OF THAT VARIABLE
HAVING A LARGE POINT COUNT.
THE COURT: I UNDERSTAND THAT, BUT IF WE GO THROUGH,
AND I AM BACK TC THE KIND OF MINDLESS LINE FITTING SORT OF A
NOTION, AND I AM LOOKING AT GW 9 AND YOU HAVE FOUR PLOT POINTS
THAT NEVER REACH THE POINT TWO DEATH PENALTY RATE, AND THEN YOU
GET TWO ON UP HERE. SUPPOSE WE MOVED THESE NEXT TWO, I AM GOING
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10 STAY UNDER THE POINT TWO LEVEL AND WE HAVE ONE UP HERE AT ALMOST
11 THE POINT ONE ZERO LEVEL. I DON'T KNOW WHAT THAT 1S. IT MAY BE
3% POINT NINE, OR POINT NINE FIVE OR SOMETHING LIKE THAT. THAT'S
13 GOING TO HAVE THE TENDENCEY TO SHIFT THAT LINE THIS WAY, ISN'T
14 IT?
15 THE WITNESS: IT'S GOING TO SHIFT IT.
16 THE COURT: IT'S GOING TO DEPRESS THE SLOPE?
17 THE WITNESS: YES. IF THAT OCCURRED IT WOULD SUGGEST
18 | THAT THE USE OF THE LINEAR MODEL ITSELF WAS NOT VALID. THIS
19 | GOES INTO THE HEADING OF THE DIGANOSTIC TEST I WENT THROUGH THAT
20 | I DISCUSSED IN GW 4.
21 TO CALL IT LINEAR REGRESSION AS IT DOES IN THE CAPTION
22 | MEANS THAT A LINE WORKS, A LINE IS A GOOD DESCRIPTOR OF THESE
23 | RATES. SO IN YOUR HYPOTHETICAL A LINE WOULD NOT BE A GOOD
24 | DESCRIPTOR AND THAT WOULD SHOW UP=-
25 THE COURT: I DON'T MEAN TO BE DISCOURTEOUS BUT IF I
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SYSTEM AND THERE ARE RACIAL DISPARITIES THAT ARE NOT AFFECTED B)
59
WOODWORTH - DIRECT
CAN'T SEE THE BLACK BOX HOW DO I KNOW THAT IS NOT HAPPENING
INSIDE THE BLACK BOX? HOW DO I KNOW THAT IS NCT HAPPENING IN
THE THIRTY-NINE VARIABLE MODEL?
THE WITNESS: IT IS HAPPENING TO AN EXTENT. WE DID
DIAGNOSTICS ON IT TO DETERMINE IF THERE WERE ANY OF THESE
INTERACTIONS INVOLVED. THESE ARE REFERRED TO AS INTERACTIONS,
WHAT YOU HAVE DESCRIBED, AND NON-LINEARITIES. WE DID FIND SOME)
AND I DID IN GW 4 DO SOME MORE REFINED FITS THAT TOOK THESE INTO
ACCOUNT WHICH DID NOT CHANGE THE FACT OF RACE OF VICTIM EFFECT
STILL REMAINED SIGNIFICANT, ALTHOUGH YOUR HONOR RECALLS THAT THE
MAGNITUDE OF THE EFFECT THEN DEPENDED UPON THE LEVEL OF
AGGRAVATION IN THE MORE REFINED MODELING.
MR. BOGER: YOUR HONOR, IF I COULD INTERJECT A LEGAL
POINT, WE DO NOT CONTEND OR SUBMIT THAT OUR BURDEN OF PROOF IN
THIS CASE IS NECESSARILY TO SHOW EXACTLY HOW THE DEATH
SENTENCING SYSTEM WORKS IN GEORGIA,
WE CONTEND OUR BURDEN OF PROOF IS TO DEMONSTRATE THAT
RACIAL FACTORS ARE A REAL FACTOR OR A PERSISTENT FACTOR IN THAT
THESE OTHER VARIABLES THAT HAVE BEEN LOOKED Bs
TO THAT EXTENT THE REASON IT SEEMS TO BE APPROPRIATE TC
BRING THAT POINT UP HERE, ONCE WE HAVE SHOWN THERE ARE RACIAL
FACTORS AND ONCE WE HAVE ACCOUNTED FOR OTHER POSSIBLE VARIABLES
THAT COULD WASH THOSE FACTORS OUT AND THEY DON'T WASH THEM OUT
EVEN WHEN THESE DIAGNOSTIC TESTS ARE PERFORMED TO ACCOUNT FOR
3
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WOODWORTH - DIRECT
OTHER POSSIBLE FACTORS THAT MAY BE MASKING A LACK OF RACIAL
EFFECT, WE SUBMIT OUR BURDEN IS SATISFIED AND I AM NOT EXACTLY
SURE IF I AM ON STATISTICALLY SOUND GROUND, BUT I AM NOT SURE
THAT THE QUESTIONS YOUR HONOR IS POSING ABOUT THE OVERALL
VALIDITY OF THE MODEL AND WHETHER THERE ARE OTHER STATISTICAL
FACTORS -- STATISTICAL FACTORS THAT MAY COME INTO ACCOUNT TO
MODIFY THE ACCURACY OF THE MODEL ARE FINALLY RELEVANT TO THE
QUESTION OF WHETHER ANY OF THOSE FACTORS AFFECT RACE.
IF THE RACIAL COEFFICIENTS WE SUBMIT REMAIN SIGNIFICANT
AND UNAFFECTED THEN THE PACT THAT THE MODEL, THE PERFECT MODEL,
THE LAWYERS! MODEL, THE JUDGE'S MODEL MIGET CONTAIN OTHER
VARIABLES IN ITS OVERALL PREDICTIVE TASK IS SOMEWHAT BESIDE THE
POINT.
AS LONG AS WE KNOW THAT NO MATTER WHICH MODEL WE USE,
RACE REMAINS, OUR CONTENTION IS THAT THE BURDEN OF PROOF IS MET,
DOESN'T MEAN THAT THE OTHER QUESTIONS ARE IRRELEVANT ALTOGETHER
BECAUSE ONE HAS TO FIRST ASK ONESELF THROUGH THE USE OF THESE
VARIOUS MODELS IF INDEED OTHER FACTORS SURFACE.
IF FOR EXAMPLE ONE COULD SHOW THAT THE RACE OF VICTIM
EFFECTS DISAPPEARED ALTOGETHER WHEN THE REALLY IMPORTANT FACTORS
COME INTO PLAY, THOSE THAT YOU WORRY MIGHT BE SUBMERGED, THER
ONE MIGHT BE ABLE TO SAY SEE THERE ARE REALLY NO RACIAL EFFECTS.
ALL YOU HAVE IS THE SUBMERSION INTO THE WHOLE POOL OF TWO
HUNDRED THIRTY VARIABLES CF THE ONES I THINK REALLY MAKE THE
DIFFERENCE.
61
WOODWORTH ~ DIRECT
1 WHEN YOU HOLD THOSE FACTORS CONSTANT AND LOOK AT THE
2 RACIAL -- NOT HOLD THEM CONSTANT, WHEN YOU LOOR AT THE RACIAL
3 OUTCOMES WITH THOSE FACTORS IN MIND AND RACE OF THE VICTIM AND
4 RACE OF DEFENDANT DISPARITIES PERSIST, THEN I GUESS OUR
5 SUBMISSION IS WE HAVE PROVEN OUR CASE; AND SO NO ULTIMATE °*
6 JUDGMENT IS NECESSARY ON THE PART OF THE PETITIONER ABOUT WHICH
7 FIVE OR TEN OR FIFTEEN OR TWENTY FACTORS ARE REALLY THE MOST
8 IMPORTANT IN THE SYSTEM. PROFESSOR BALDUS HAS GONE A LONG WAY
9 TOWARD =
10 THE COURT: I DON'T KNOW THAT YOU HAVE AN OBLIGATION of
: PROVING WHICH FACTORS ARE MOST SIGNIFICANT BUT UNTIL YOU DO, YOU
12 MAY NOT CONVINCE ME YOU HAVE PROVED ANYTHING AT ALL.
13 IN OTHER WORDS I HAVE IN TERMS OF LOOKING AT A PRIMA
14 FACIE CASE SORT OF NOTION, I HAVE TO BELIEVE THAT YOU HAVE
35 PROVED IT. SIMPLY SAID TODAY WHAT YOU ARE ASKING ME TO DO IS TO
16 MARE A LEAP OF PAITH. MATHEMATICS AS I UNDERSTAND IT IS REALLY
17 NOTHING MORE THAN SYMBOLIC EXPRESSION OF LOGIC. LAWYERS DEAL IN
18 LOGIC BUT WE DON'T UNDERSTAND THE SYMBOLS PERHAPS THAT THEY DO.
19 1 HAVE A THRESHOLD CONCERN ABOUT WHETHER REGRESSION
20 | ANALYSIS IS APPLICABLE TO THIS ASPIRY AND THAT IS NOT A GREAT
; 21 | CONCERN OF MINE BUT IT IS A CONCERN. I HAVE TO PUT THAT TO REST
22 IN MY OWN MIND. 7
23 THE GREATER CONCERN I HAVE BECAUSE YOU AND I HAVE HAVE
24 | BEEN DOWN THIS ROAD BEFORE IS THAT YOU HAVE GOT TO ULTIMATELY
25 DEMONSTRATE THAT LIKES ARE TREATED UNEQUALLY. TO DO THAT WITH
WOODWORTH - DIRECT
1 | STATISTICS YOU MUST DO SO, AND I USE IT IN THE BROAD SENSE OF
2 | THE WORD, A STATISTICALLY RELIABLE WAY AND I DON'T MEAN P VALUES
3 HERE. :
4 I HAVE GREAT CONCERN OR RESPECT FOR THE KNOWLEDGE AND
S | LEARNING OF PROFESSOR BALDUS AND PROFESSOR WOODWORTH BUT I AM
6 | NOT WILLING TO ACCEPT ANYBODY'S DISCUSSION OF LOGIC WITHOUT
7 | UNDERSTANDING THE LOGIC. I AM NOT WILLING TO SAY THAT YOU HAVE
8 | DEMONSTRATED SOMETHING STATISTICALLY UNTIL I BELIEVE YOU HAVE
9 | DEMONSTRATED SOMETHING STATISTICALLY.
10 I DON'T KNOW IF I AM CONVEYING THE IDEA EXCEPT IT HAS
11 | TO DO WITH THE DEGREE OF TRUSTWORTHINESS THAT 1 WOULD PLACE ON
12 | YOUR PRIMA FACIE CASE. AS I HAVE PERHAPS INARTFULLY POINTED OUT
13 | A MINUTE AGO, WE HAVE SEVERAL MODELS HERE BEFORE US THAT EXPLAIN
14 | THE DEATH PENALTY IMPOSITION IN A STATISTICALLY SIGNIFICANT WAY
15 | AND THAT MIGHT END THE INQUIRY.
16 WE NOW KNOW THAT -- JUST IN DEALING WITH THESE
17 HYPOTHETICALS =- THAT IT IS STATISTICALLY SIGNIFICANT AS TO THE
18 | NUMBER OF VICTIMS IMPOSED AND THAT EXPLAINS THE DEATH PENALTY
19 | AND WE ALL KNOW THAT IS NOT IT, SO WE ADD ANOTHER ONE.
20 WELL, WE GET UP TO TEN OR ELEVEN AND WE STILL FIND OUT
21 | THERE ARE MORE AND I AM LOOKING AT EXHIBITS GW 9 AND TEN. I DID
22 | NOT UNDERSTAND THAT YOU EVER GOT TO ONE WHERE YOU SAID WE ADDED
23 | ANOTHER ONE WHERE WE LOOKED AT THE INTELLECTUAL POSSIBILITIES
24 | OTHER THAN RACE AND WE ADDED ANOTHER ONE AND IT DID NOT MAKE ANY
25 | EFFECT.
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WOODWORTH - DIRECT
MR. BOGER: I THINK PROFESSOR BALDUS' TESTIMONY WILL
REFLECT HIS TWO HUNDRED THIRTY PLUS VARIABLE MODEL REFLECTED
EVERY VARIABLE IN HIS JUDGMENT SUPPLEMENTED BY HIS READING,
SUPPLEMENTED BY STATISTICAL METHODS TO FLESH OUT POSSIBLE
SIGNIFICANT VARIABLES, REFLECTED EVERYTHING THAT CAME TO HIS
MIND AND THE MIND OF HIS COLLEAGUES THAT MIGHT BE REFLECTED OR
MIGHT BE INFLUENTIAL ON DEATH SENTENCING OUTCOME. WE HAVE HEARD
NOTHING FROM THE STATE THAT SUGGESTED OTHER VARIABLES THAT,
GOSH, YOU SHOULD HAVE TRIED THIS OR YOU SHOULD HAVE TRIED THAT.
THERE WERE NO ADDITIONAL CANDIDATES AND SO I THINK PROFESSOR
BALDUS' TESTIMONY, AND I WOULDN'T WANT TO MISSTATE IT, WAS THAT
IN HIS BEST PROFESSIONAL JUDGMENT THE TWO HUNDRED THIRTY
VARIABLE MODEL LEFT NO STONE UNTURNED BECAUSE IT HAD SOME
STATISTICAL DISADVANTAGES AS AN OPERATING MODEL. WHILE HE USED
IT IN A NUMBER OF INSTANCES AND DR. WOODWORTH PERFORMED SOME
DIAGNOSTICS TO CHECK IT, THEY WENT BACK AND USED OTHER MODELS AS
WELL.
THE COURT: FUNDAMENTALLY, WHAT I AM TRYING TO SAY, I
DON'T UNDERSTAND THE REGRESSION ANALYSIS WELL ENOUGH TO BE
CONVINCED IT DEMONSTRATES THAT EQUALS ARE TREATED UNEQUALLY AS /
REFERENCE TO ANY FACTOR.
MR. BOGER: LET ME ASK DR. WOODWORTH A COUPLE OF
QUESTIONS.
THE COURT: I DON'T MEAN TO SAY I DON'T THINK THE
TECHNIQUE IS CAPABLE OF IT. THE DEPTH OF MY UNDERSTANDING TO
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WCODWORTH - DIRECT
THE EXTENT THAT IT IS BROADENED BY GW 9 MAKES MY CONCERNS
GREATER INSTEAD OF LESS IN THAT IF I UNDERSTAND IT THIS APPROACH
IS INCAPABLE OF LOOKING AT THE TOTAL CASE AGAINST THE TOTAL CASE
AND IF I AM IN ERROR, PLEASE CLEAR HE UP.
MR, BOGER: I AM NOT SURE WHAT YOUR HONOR MEANS BY THE
TOTAL CASE?
THE COURT: PROFESSOR WOODWORTH TESTIFIED A MOMENT AGO
THAT HE PRESUMED THE LETTER "U®" IN THE EQUATION QUOTED BY FISHER
AND FINKELSTEIN IN 80 COLUMBIA LAW REVIEW, NUMBER 4 MEANT
UNIQUENESS. I DON'T KNOW IF IT MEANS UNIQUENESS OR UNKNOWN, BUT
WHICHEVER ONE IT IS, WHAT I AM LEFT TO UNDERSTAND AS RESULT OF
GW 9 AND WHAT I UNDERSTAND BEFORE IS THAT WE ARE NOT COMPARIRG
THE LIKE CASES TO GET THESE FITS. WE ARE LOOKING AT THE EFFECT
OF THE DISCRETE VARIABLES AND SPREADING THEM OUT.
MR. BOGER: I THINK THAT PRCBABLY DEPENDS, YOUR HONOR,
ON WHAT ONE MEANS BY LIKE CASES. MY UNDERSTANDING IS ONE TAKES
CASES THAT ARE SUBSTANTIALLY SIMILAR BUT FOR THE VARIABLE YOU'RE
LOOKING AT AT THAT MCMMENT.
THE COURT: I START WITH YOU THERE.
MR. BOGER: AND LOOKS AT DISPARITIES BASED ON THE
PRESENCE OR ABSENCE OF THAT VARIABLE AND THAT THEN BECOMES A
MEASURE ONE PUTS INTO THE OVERALL ANALYSIS.
WHEN ONE IS LCOKING AT LITERALLY HUNDREDS CF FACTORS AT
A TIME AND EVEN IN THIS MODEL ELEVEN FACTORS AT A TIME, ONE IS
NOT DOING THE SAME KIND OF ANALYSIS AS CROSS TABULATION WHERE
65
WOODWORTH =~ DIRECT
1 YOU FINALLY DO WIND UP WITH CELLS THAT ARE IDENTICAL WITH
2 RESPECT TO ABSENCE OR THE PRESENCE OF EACH OF THE VARIABLES BUT
FOR THE VARIABLE OF INTEREST, BECAUSE THE CELLS WOULD BE EMPTY.
BUT MY UNDERSTANDING OF DR. WOODWORTH'S TESTIMONY BOTH
THIS SUMMER AND ON TODAY'S OCCASION IS THAT REGRESSION ANALYSIS
3
4
..
6 IS AN ACCEPTED STATISTICAL ALTERNATIVE TO THAT PROCEDURE OF
7 CROSS TABULATION THAT SIMPLY CANNCT BE PERFORMED IF YOU HAVE FP
8 ENOUGH DATA IN YOUR UNIVERSE OR FEW ENOUGH OBSERVATIONS IN YOUR
9 UNIVERSE. BUT IT IS THE STATISTICALLY EQUIVALENT CALCULATION TO
10 A COMPARISON OF LIKE CASES.
th I WAS GOING TO ASK A COUPLE OF QUESTIONS TO REFLECT
12 WHERE WE HOPE TO COME OUT WHETHER OR NOT WE HAVE COME OUT THERE
13 OR NOT AND THEN MAYBE ADDRESS THE ®"U® TERM TO SEE IF THAT
14 QUESTION CAN FACTOR INTO THE COURT'S UNDERSTANDING OR MY
15 UNDERSTANDING.
16 THE COURT: WE HAVE SOME OTHER THINGS TO DO. I PUT OFF
17 THE CRIMINAL CASE BECAUSE WE ARE NOT MAKING THE KIND OF PROGRESS
18 WE NEED TO MAKE. I TRIED TO SUGGEST IN THE MODEL I DESIGNED AND
19 OBVIOUSLY I DIDN'T DO WELL BECAUSE I DIDN'T EVEN PREDICT HALF OF
20 THE DEATH PENALTIES THAT CAME OUT WHICH I GUESS IS A SUGGESTION
21 OF THE DIFFICULTY THERE IS IN TRYING TO MODEL THE SYSTEM.
22 THE CONCERN I BAVE IF I UNDERSTAND THIS THING IS THAT =~
23 GW 9 -- IS THAT WITHOUT REFERENCE TO WHAT THEY WERE OR WHAT MIX
24 THAT OCCURRED, HE ASSIGNED SOME POINT VALUE AT THE FIRST PLOT ON
25 THE AGGRAVATION SCALE, AND THEN WITHOUT REFERENCE TO THE MIX OF
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WOODWORTH - DIRECT
VARIABLES HE ASSIGNS ANOTHER POINT VALUE AND HENCE ON OUT UNTIL |
HE HAS GOT A SEVEN PLOT.
FOR EXAMPLE I DON'T KNOW WHAT THE VARIABLES ARE AND I
DON'T KNOW THAT IT MATTERS BUT I WOULD BE WILLING TO BET YOU I
COULD FIND AN AGGRAVATING OR MITIGATING FACTOR WHICH WOULD -- IF
PRESENT IN EVERYONE OF THE CASES THAT OTHERWISE ARE OUT PAST
POINT EIGHT WOULD DROP THAT DEATH PENALTY RATE TO ZERO OR
APPROACHING ZERO AND IF THAT IS TRUE, THEN THAT SYSTEM IS NOT
GOING TO HELP.
WHAT I AM TRYING TO DEAL WITH, MR. BOGER, IS THE
PRACTICALITY OF HOW A JURY REACTS AND HOW A PROSECUTOR REACTS.
sinh MR. BOGER: THE QUESTION WE THINK WE HAVE TO ADDRESS
AND WHICH WE HOPE WE HAVE ANSWERED, (IF YOU LOOK AT THE AGGREGATE
OF CASES AND NOT ANY INDIVIDUAL CASES, IF THERE ARE HUNDREDS OF
CASES YOU CAN FIND THAT ARE LIKE THE ONE WITH THE AGGRAVATING
FACTOR THAT YOU MENTIONED AND THERE IS A DROP TO TEN PERCENT
DEATH SENTENCING RATE IN THE BLACK VICTIM CASES BUT A DROP ONLY
TO TWENTY PERCENT DEATH SENTENCING RATES IN BLACK VICTIM CASES,
THAT RACIAL DISPARITY REMAINS EVEN WHEN ONE LOOKS AT THIS VERY
STRONG POWERFUL AGGRAVATING FACTOR.
IF WE HAVE SHOWN THAT, IF WE HAVE SHOWN WHILE THIS
OTHER AGGRAVATING FACTOR IS SIGNIFICANT AND PLAYS INTO THE CASE,
BUT WHEN YOU LOOK AT THE AGGREVATE OF CASES THERE IS A
DIFFERENTIAL DEATH SENTENCING RATE BASED ON RACE, I BELIEVE WE
HAVE PROVED OUR CASE AT THAT POINT.
——————— Se ———. ——— J—— Ap——. ——, SO
WOODWORTH - DIRECT ot
1 THE COURT: THAT MAKES THE ASSUMPTION =- I WOULD AGREE
2 | WITH YOU ABSOLUTELY. IF EVERYTHING ABOUT THOSE TWO CASES WERE
3 | THE SAME AND YOU INTRODUCED THE ONE FACTOR AND IT DROPPED TO THE
4 | POINT TWO ON ONE AND POINT ONE ON THE OTHER THEN AT LEAST ON A
5 | SYSTEM-WIDE BASIS YOU WOULD HAVE MADE A SUBSTANTIAL STEP DOWN
6 | THE ROAD. BUT IF I UNDERSTAND WHAT THE GOOD DOCTOR IS TELLING
7 | MB, HE IS NOT COMPARING LIKE CASES, HE IS COMPARING CASES WITH
8 | LIKE VALUES?
9 MR. BOGER: MY UNDERSTANDING OF HIS TESTIMONY IS THAT
10 | BECAUSE CASES COME IN SUCH VARIED PACKAGES, A LITTLE BIT OF THE
11 | AGGRAVATING CIRCUMSTANCE AND NONE OF AGGRAVATING CIRCUMSTANCE
12 | THREE ET CERTERA, THAT ONE CANNOT FIND LARGE NUMBERS OF CASES
| 13 | THAT ARE EXACT REPLICAS EXCEPT FOR THE ONE FACTOR OF INTEREST
14 | SUCH AS RACE.
15 BUT THAT MULTIPLE REGRESSION, THE WHOLE POINT OF
16 | CONTROL WHICH, OF COURSE, IS YOUR HONOR'S FIRST QUESTION, AND WE
17 | ARE REALLY FOCUSING ON THAT FIRST QUESTION, IS THAT IT PERMITS
18 | ONE TO DEAL WITH A MULTITUDE OF CASES WITH A MULTITUDE OF
19 | VARIABLES AS IF WE COULD CONTROL FOR OR MAKE SIMILAR ALL OF THE
20 | CASES BUT FOR THE VARIABLES OF THE INTEREST.
21 THE COURT: THAT IS WHY I AM TRYING TO UNDERSTAND, THE
22 | LOGIC OF IT, AND I AM TRYING TO UNDERSTAND THE LOGIC OF IT AS IT
23 | WOULD APPLY TO SOMETHING THAT I KNOW A LITTLE BIT ABOUT ALTHOUGH
24 | NOT A LOT AND THAT IS WHAT MAKES PROSECUTORS MAKE DECISIONS AND
25 | WHAT MAKES JURORS MAKE DECISIONS.
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WOODWORTH - DIRECT
THE ONE THING THAT I DO NOT UNDERSTAND THAT GW 9 DOES
1S TAKE INTO CONSIDERATION INTERRELATIONSHIPS OF AGGRAVATING AND
MITIGATING FACTORS AND I DON'T KNOW HOW ELSE TO SAY IT. I THINK
MAYBE IT IS POSSIBLE BUT I DON'T KNOW HOW TO DO IT, BUT I AM
CONCERNED THAT IS NOT OCCURRING.
MR, BOGER: I SEE WHERE -- FRANKLY WHERE THE FOCUS OF
SOME ADDITIONAL QUESTIONING SHOULD BE BASED ON THAT QUESTION YOU
JUST ASKED ME, AT LEAST I HOPE I DO. I THINK WE CAN HAVE SOME
OF THAT FOR THE COURT,
THE COURT: IT IS SOME TIMES EASIER FOR ME TO BE DIRECT
RATHER THAN IT IS TO BE COURTEOUS. BUT THE MERE LUMPING OF ONE-4
SEVENTH OF THE TOTAL WHO ALL HAPPEN TO HAVE A POINT TWO FOUR
VALUE IS A MINDLESS EXERCISE AND I DON'T MEAN TO BE INSULTING
THE WITNESS.
BUT YOU UNDERSTAND IN THE DISCRETE STUDY OF CHOICES, Ii
YOU LUMP ALL CASES THAT HAPPEN TO HAVE A POINT TWO FOUR DEATH
RATE OR THEREABOUT, YOU HAVE THROWN IN A LOT OF FACTORS THAT MAY
PLAY STRONGER OR WEAKER OR MAY HAVE GREATER OR LESSER =-- YOU
KNOW IF YOU THROW IN A CASE THAT HAS A POINT TWO FIVE -- I DON'1
KNOW IF YOU THROW IN FACTORS OR CASES, BUT IF YOU THROW IN A
CASE THAT HAS A POINT TWO FOUR IS IT BECAUSE IT WAS
SUBSTANTIALLY AGGRAVATED AND MITIGATED AND THAT IS A FAIRLY LOW
DEATH RATE? OR IS IT BECAUSE IT WAS MILDLY AGGRAVATED OR WAS 17
BECAUSE IT WAS NOT AT ALL MITIGATED. THAT DOESN'T TELL ME
ANYTHING ABOUT WHAT IS HAPPENING IN THAT CASE. IT IS EVERYBODY
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WOODWCRTH ~- DIRECT 2
1 THAT HAPPENED TO HAVE THE SAME NUMBER BY A LUCK OF THE DRAW ENDS
2 UP IN A PLOT POINT AND THAT ENDS UP AFFECTING THE SHAPE OF THE
3 LINE. I AM JUST TROUBLED BY THAT.
4 YOU HAVE TO UNDERSTAND THAT WHAT I AM LOOKING AT 1IS
5 FINKELSTEIN WHICH SAYS YOU DO IT ON A CASE BY CASE BASIS AND THE
6 PROBLEM I HAD BEFORE IN MCCORQUODALE WHICH IS IT DOSEN'T MODEL
7 REALITY AND THE ONE CASE I REFERRED TO YOU ABOUT WHEN I HAD SEEN
8 THE ELEVENTYH CIRCUIT ONLY IN A HEADNOTE REFER TO MULTIPLE
9 REGRESSION ANALYSIS, THE PROPONENT OF THE ANALYSIS LOST BECAUSE
10 IT DIDN'T MODEL REALITY.
11 AND I THINK THE FINDER OF THE FACT ON AN ISSUE SUCH AS
12 THIS HAS TO BE CONVINCED THAT IT MODELS THE SYSTEM BEFORE HE IS
33 WILLING TO MAKE SOME CHOICES -- MAKE SOME DECISIONS ABOUT THE
14 SYSTEM AND TO THAT EXTENT I HAVE TO UNDERSTAND THAT YOU REALLY
is ARE CONTROLLING FOR THOSE THINGS THAT MIGHT HAVE MADE THE JURY.
16 MAKE A CHOICE THAT ARE LEGITIMATE IN WHAT I CALL MINDLESS
17 LUMPING TOGETHER, AND THAT IS A HARD TERM BUT I THINK YOU
18 UNDERSTAND WHAT I MEAN. THE NONDISCRETIONARY LUMPING TOGETHER
19 OF EVERYTHING THAT JUST HAPPENS TO HAVE THE SAME VALUE IS NOT IN
. 20 MY MIND SHOWING COMPARABLES AND THAT IS THE FUNDAMENTAL CONCERN,
: 21 LET ME MENTION -- YOU HAVE TOLD ME ABOUT SOME THINGS I
22 WANTED TO KNOW. FROM READING THE ARTICLE I DID READ, I GATHER
23 THAT IN PACT -- DID WE USE DUMMY VARIABLES IN THIS CASE?
24 MR. BOGER: THAT IS CORRECT. DR. WOODWORTH COULD
25 ASSURE ME OF THAT.
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WOODWORTH - DIRECT
THE COURT: I UNDERSTAND WHAT WE DO WHEN WE USE A DUMMY
VARIABLE IS NOT TO COMPUTE TWO SEPARATE COEFFICIENTS AND
SUBTRACT THEM OR DRAW TWO SEPARATE LINES AND MEASURE THE
DIFFERENCE, BUT TO PUT A VARIABLE IN THE A + Bl, B SUB ONE, X
SUB ONE, PLUS B SUB TWO, X SUB TWO EQUATION, I DON'T KNOW WHAT
IT MEANS BUT I WOULD LIKE TO UNDERSTAND IT.
MR. BOGER: WE WILL ADDRESS THAT. I THINK THE ANSWER
TO THAT IS QUITE QUICK. |
THE COURT: AND OBVIOUSLY UNDERLYING SOME OF THIS, TOO,
GOES BACK TO SOMETHING PROFESSOR WOODWORTH SAID A WHILE AGO AND
WHAT DR. KATZ TESTIFIED TO THE OTHER DAY. THAT IS, YOU DON'T
ALWAYS HAVE TO USE THE EXACT VARIABLE OR EVERYTHING THAT WOULD
MAKE UP THE VARIABLE AS LONG AS YOU BAVE A SURROGATE OR A
FLAGSHIP OR WHAT WAS THE OTHER TERM YOU USED?
THE WITNESS: PROXY.
THE COURT: IF I UNDERSTAND, I HAVE NOT READ THE
STATE'S BRIEF, I AM NOT SURE WHETHER IT IS IN. I HAVE NOT READ
YOUR BRIEF BUT IF I SUSPECT WHAT MS. WESTMORELAND IS GOING TO
ARGUE, IT IS THAT WHEN YOU THROW IN AGGRAVATING FACTORS, THEY
ACT AS A PROXY FOR RACE, BECAUSE SHE HAS DEMONSTRATED WITH SOME
FORCE, I HAVE NOT DECIDED HOW MUCH BUT WITH SOME, THERE IS A
CORRELATION BETWEEN AGGRAVATION AND MITIGATION AND THE RACE OF
THE VICTIM. AND IN TERMS OF LOOKING AT YOUR MODELS, I HAVE TO
KEEP THAT SORT OF NOTION IN MIND. SO THAT OBVIOUSLY IS IN THE
BACKGROUND OF MY MIND IN ASKING SOME OF THESE QUESTIONS, AS 1
71
WOODWORTH - DIRECT
HAVE SAID, I HAVE EXCUSED THE CRIMINAL CASE SO LET'S TAKE A FULL
HOUR FOR LUNCH AND BE BACK AT TWO.
® RR *
(RECESS.)
® & %
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WOODWORTH - DIRECT
AFTERNOON SESSION
2:00 P, M.
GEORGE WOODWORTH, RESUMED
DIRECT EXAMINATION CONTINUED
BY MR. BOGER:
Q. DR, WOCDWARD, WOULD YOU=-
THE COURT: MR. BOGER, I AM NOT SURE IF THIS WAS
COVERED OR NOT. I WANT TO MAKE SURE I I UNDERSTAND ONE POINT.
DR. ON YOUR 9, AS I UNDERSTAND WHAT YOU DID TC GET YOUR
PLOT POINTS, YOU SCORED A CASE WHICH I WOULD SUPPOSE MEANS
ADDING UP THE POSITIVE AND NEGATIVE COEFFICIENTS?
THE WITNESS: RIGHT,
THE COURT: AND GETTING THE RESULTANT?
THE WITNESS: RIGHT.
THE COURT: AND THAT INDICATES THE POSITION ON THE
AGGRAVATION INDEX?
THE WITNESS: THAT IS CORRECT.
BY. MR. BOGER: |
Q. ALL RIGHT. DR. WOODWORTH, THE COURT INDICATED BEFORE LUNCH
THERE MIGHT BE SOME FACTORS THAT WOULD RENDER A DEATH SENTENCE
IN A CASE VIRTUALLY CERTAIN OR OTHER FACTORS THAT MIGHT RENDER 4
DEATH SENTENCE EXTREMELY UNLIKELY AT THE POINT OF BEING ALMOST
NON-EXISTENCE.
HOW WOULD SUCH FACTORS MANIFEST THEMSELVES IN A
WOODWORTH - DIRECT a
1 REGRESSION EQUATION OR IN AN ANALYSIS?
2 A. THEY WOULD MANIFEST THEMSELVES QUITE STIKINGLY SUCH AS GW 9}
3 IF I COULD DEMONSTRATE THIS.
i Q. WOULD YOU NEED THE ASSISTANCE OF THE BLACKBOARD?
5 A. YES.
6 MR. BOGER: YOUR HONOR, MAY THE WITNESS APPROACH IT?
7 THE COURT: ORAY.
- 8 MR. BOGER: THANK YOU.
9 BY MR. BOGER:
10 Q. LET ME MARK THIS PIECE OF PAPER GW 12 FOR IDENTIFICATION.
11 A. FOR THE SAKE OF ILLUSTRATION SUPPOSE THERE IS A BYPOTHETICAL
12 FACTOR WHICH MARES THE DEATH SENTENCING VIRTUALLY IMPOSSIBLE.
13 NOW IN GW 9, WE WOULD DRAW TWO FIGURES, THE HORIZONTAL AXIS AS
14 USUAL WOULD BE THE SUM OF THE SCORES, THE POINT VALUE OF THE
15 CASE ON ALL THE OTHER FACTORS IN THE CASE OTHER THAN THE ONE IN
16 FOCUS.
17 NOW THE UPPER CHART WOULD REFER TO THOSE CASES THAT
1g POSSESS THIS HYPOTHETICAL STRONG MITIGATOR -- LET'S CALL iT
13 THAT. AND THIS LOWER GRAPH WOULD BE THE CASES WHERE THE STRONG
20 MITIGATOR IS ABSENT.
21 NOW IF THE STRONG MITIGATOR WERE PRESENT, THEN YOU
22 WOULD SEE RATES CLOSE TO ZERO ALL THE WAY ACROSS AT ALL LEVELS
23 OF POINT VALUES?
24 THE COURT: RATES?
25 THE WITNESS: DECATH SENTENCING RATES.
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WOODWORTH - DIRECT
THE COURT: I HAVE IT. I WASN'T SURE WHETHER THE
REPORTER UNDERSTOOD YOU TO SAY RATES OR RACE.
THE WITNESS: SO THE DEATH SENTENCING RATES WOULD BE
CLOSE TO ZERO ALL THE WAY ACROSS, WHEREAS IN THOSE CASES WHERE
THE STRONG MITIGATOR WAS ABSENT AS IN THE ACTUAL EXAMPLES WE
HAVE USED HERE SEE A RISING DEATH SENTENCING RATE AS THE POINT
VALUE INCREASES. SO IN COMPARING THE TWO STRAIGHT LINES WE
WOULD SEE QUITE A STRONG SEPARATION BETWEEN THESE IF THEY WERE
PLOTTED ON THE SAME GRAPH.
SO THE REGRESSION TECENIQUES EMPLOYED WOULD PICK UP
SUCH A VARIABLE. IT WOULD BE VIRTUALLY IMPOSSIBLE TO MISS SUCH
A VARIABLE IF IT OCCURRED IN ANY SUBSTANTIAL NUMBER OF CASES.
BY MR. BOGER: |
Q. SO, IF ONE HAS EMPLOYED AS YOU DID IN YOUR STUDIES
REGRESSION TECHNIQUES AND YOU DON'T FIND BOTH KINDS OF LINES,
WHAT DOES THAT TELL YOU?
A. WOULD YOU REPHRASE THE QUESTION?
Q. IF YOU EMPLOYED IN YOUR STUDIES AND PROFESSOR BALDUS'
STUDIES THESE KIND OF REGRESSION TECHNIQUES AND YOU HAVE NOT
FOUND FLAT LINES SUCH AS THE ONE YOU DESCRIBED SUCH AS A STRONG
MITIGATOR AND THE RISING LINE WITH THE MITIGATOR ABSENT, WHAT
DOES THAT TELL YOU ABOUT THE ANALYSIS YOU HAVE CONDUCTED?
A. WHAT THIS PARTICULAR HYPOTHETICAL TELLS ME IS THAT IT GIVES
ME SOME COMFORT THAT IF SUCH A VARIABLE EXISTED WE WOULD NOT
MISS IT. IN POINT OF FACT WE ARE UNAWARE OF THE EXISTENCE OF
OW
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WOODWORTH - DIRECT
ANY SUCH VARIABLES BECAUSE THEY WOULD BE DETECTED IN A SIMPLE
CROSS TABULATION OF THAT VARIABLE AGAINST THE SENTENCING
OUTCOME
THE COURT: DID YOU CONDUCT THAT ANALYSIS?
THE WITNESS: YES. THAT WAS ONE OF THE VERY EARLY
TRAINING STEPS IN WHICH EACH VARIABLE WAS CROSS TABULATED
AGAINST THE OUTCOME AND TO MY KNOWLEDGE NO INSTANCES OF THESE
STRONG EXCLUDERS OR STRONG AGGRAVATORS OCCURRED. I WOULD HAVE
TO CONSULT PROFESSOR BALDUS ON THIS POINT, I CAN'T CALL TO MIND
ANY THAT ACTUALLY SHOWED UP.
HOWEVER, THE POINT I AM TRYING TO MAKE HERE, EVEN IF
THEY DID WE WOULD PIND THEM. WE WOULD FIND THEM IN THE SENSE
THEY WOULD BE SWEPT INTO THE REGRESSION MODEL AS IMPORTANT
VARIABLES.
BY MR. BOGER:
Q. DR. WOODWORTH, LET'S LOOK AT GW 9. YOU TESTIFIED THIS
MORNING THERE EXISTS CASES AT PARTICULAR AGGRAVATION LEVELS
ALONG THE X AXIS; IS THAT CORRECT? 3
A. YES, PARTICULAR POINT VALUES.
Q. LET'S SAY -- ARE ALL OF THE CASES AT POINT ZERO FOUR IN THE
UPPER GRAPH ON GW 9 FACTUALLY SIMILAR?
A. NO. THERE WOULD BE NO GUARANTEE THEY WOULD BE FACTUALLY
SIMILAR BECAUSE OF THE POINT COUNT METHOD OF DETERMINING THE
POSITION OF A CASE ON THAT AXIS.
Q. SO YOU MIGHT HAVE SOME CASES TERRIBLY AGGRAVATED BUT A LOT
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WOODWORTH -~ DIRECT
OF MITIGATION AND OTHER CASES THAT ARE MODERATELY AGGRAVATED AND
LESS MITIGATION AND NEVERTHELESS WIND UP WITH THE SAME POINT
VALUE; IS THAT CORRECT?
A. THEORETICALLY POSSIBLE, YES.
Q. ARE THERE ANY STATISTICAL PROCEDURES YOU CAN EMPLOY TO
DISTINQUISH OUT FURTHER CASES OF THE POINT ZERO FOUR LEVELOF
AGGRAVATION?
A. YES. THERE ARE ADDITIONAL PROCEDURES.
Q. AND WHAT ARE THEY?
A. ANY PROCEDURE WHICH INVOLVES INTRODUCING A NEW VARIABLE INTQ
THE REGRESSION IS ATTEMPTING TO TAKE THESE GROUPS OF CASES AND
IS BEING DONE IN GW 9. WE ARE TRYING TO DISTINGUISH HIGH
ALCOHOL CASES FROM LOW ALCOHOL CASES, I MEAN DISTINQUISHED IN
THE SENSE OF FINDING THE -—- ONCE WE SORT OUT THE CASES ON THIS
VARIABLE WE GET AN INCREASE OR DECREASE IN THE DEATH SENTENCING
RATE. IN GENERAL WHAT ONE DOES ANY TIME A REGRESSION ANALYSIS
1S PERFORMED IS TO ATTEMPT TO FIND ADDITIONAL VARIABLES THAT
MIGHT ACHIEVE THIS SEPARATION, THIS DISTINCTION OF CASES WITHIN
WITH SIMILAR POINT COUNTS.
SO FOR EXAMPLE, STEPWISE REGRESSION NOT STARTING FRCHM 7
FEATURELES MODEL, BUT STARTING FROM A SENSIBLE MODEL AND
ESSENTIALLY BEING USED AS A TOCL FOR SCREENING FOR ADDITIONAL
VARIABLES IS CAPABLE OF DETECTING VARIABLES THAT WOULD SERVE TO
DISTINQUISH CASES AT THE SAME POINT COUNT LEVEL, AN ADDITIONAL
DISTINGUISH THEM ON THAT OTHER VARIABLE. THAT IS PRECISELY WHAT
WOCDWORTH - DIRECT ds
3 METHOD OF ATTEMPTING TO DISTINQUISH THESE CASES IS BY THE
2 INTRODUCTION OF WHAT ARE CALLED INTERACTIONS.
3 INTERACTIONS IS A SCORE THAT IS AWARDED, A POINT COUNT
4 OR REGRESSION COEFFICIENT THAT IS AWARDED TO A CASE WHICH
5 POSSESSES A CERTAIN COMBINATION, FOR EXAMPLE A CASE THAT WAS
6 HIGHLY AGGRAVATED AND HIGHLY MITIGATED BOTH MIGHT HAVE ITS TOTAL
7 POINT COUNT MODIFIED BY THE FACT IT HAD THAT COMBINATION.
8 WHEREAS THE CASE THAT WAS MODERATELY AGGRAVATED AND MODERATELY
9 MITIGATED MIGHT NOT HAVE ITS POINT COUNT ALTERED.
10 IT'S MY UNDERSTANDING THAT -- FIRST OF ALL IT IS A
11 STANDARD PRACTICE IN REGRESSION ANALYSIS TO SEARCH FOR THESE
12 SORT OF EFFECTS. I DID SOME OF THESE =-- I DID SOME ATTEMPTS TO
13 FIND THESE INTERACTIONS.
14 SIMPLY STATED AN INTERACTION MEANS THAT THE EFFECT OF
15 ONE FACTOR DEPENDS UPON WHAT OTHER FACTORS ARE PRESENT. IN MY
16 GW 4 I DID REPORT THE RESULTS OF SOME OF THESE RUNS IN WHICH I
x7 LOOKED FOR THESE POSSIBILITIES.
18 IN ADDITION TO THIS, PRO PROFESSOR BALDUS AT VARIQUS
19 POINTS DID SEARCH == DID RUNS INVOLVING INTERACTION.
20 Qe. IN THE STUDIES AND REPORTS WHICH YOU TESTIFIED EARLIER THIS
. 21 SUMMER, DID YOU FIND THROUGH STEPWISE REGRESSION COR THROUGH
22 INTERACTION ANALYSIS OTHER VARIABLES WHICH WOULD DISTINQUISH
23 THESE CASES OUT WHICH WERE NOT EMPLOYED?
24 A. NONE THAT WOULD AFFECT THE RACE OF VICTIM COEFFICIENT.
25 Q. BEFORE WE LEAVE THIS GENERAL POINT, CAN REGRESSION ANALYSIS
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THE PRESENCE OF THIRY-SIX VARIABLES AND THE ABSENCE OF FOURTEEN
WOODWORTH - DIRECT
LOOK AT CASES THAT ARE SIMILAR WITH RESPECT TO ALL OF THE
PACTORS EMPLOYED IN THE MODEL EXCEPT FOR A PARTICULAR FACTOR AND
SORT THOSE CASES OUT THE WAY THE COURT SUGGESTED PRIOR TO CUR
NOON RECESS SO THAT WE HAVE CATEGORIES THAT HAVE ONLY CASES WITH
MORE, THAT KIND OF THING, IS THAT SOMETHING THAT REGRESSION
ANALYSIS CAN DO DIRECTLY?
A. NO.
THE COURT: ANY OTHER TECHNIQUE -- OTHER THAN CROSS
TABULATION, IS THERE A TECHNIQUE THAT CAN DO THAT?
THE WITNESS: NOT TO MY KNOWLEDGE.
BY MR. BOGER:
Q. CAN REGRESSION ANALYSIS ACHIEVE THE SAME RESULT THROUGH THE
KIND OF ALGEBRAIC TECHNIQUES ABOUT WHICH YOU JUST TESTIFIED AND
ABOUT WHICH YOU HAVE GIVEN SOME CONCEPTUAL EXPLANATION?
A. IT IS CAPABLE OF APPROACHING THOSE RESULTS, YES.
Q. AND IS THAT REGRESSION TECHNIQUE THAT YOU DESCRIBED EARLIER
TODAY ACCEPTED WITHIN THE STATISTICAL PROFESSION AS ACCURATE ANI
VALID FOR CONTROLLING FOR THE VARIABLES IN A UNIVERSE?
A. YES.
Q. FOR EXAMPLE IN A TWO HUNDRED THIRTY VARIABLE MODEL, IN A
REGRESSION SETTING, WHAT WOULD THE PRESENCE OF A RACE OF VICTIM
COEFFICIENT OF SAY POINT ZERO FIVE MEAN?
A. IT WOULD MEAN THE RACES OF VICTIM -- THE AVERAGE RACE OF
VICTIM DISPARITY CANNOT BE EXPLAINED BY THE ADDITIVE EFFECTS OF
—— —— — —— —— —— ———
WOODWORTH = DIRECT 4
1 | THE OTHER VARIABLES, THE OTHER TWO HUNDRED AND THIRTY.
2 | Q. SO IN OTHER WORDS, THERE IS AN ADDITIONAL EFFECT POR RACE
3 | BEYOND THE COMBINED EFFECTS OF ALL THE TWO HUNDRED THIRTY
4 | ADDITIONAL VARIABLES?
5 | A. SAYS THAT IT IS POSSIBLE TO MAKE A DISTINCTION UPON CASES
6 | WHICH ARE MATCHED IN TERMS OF THEIR POINT SCORES ON THE TWO
7 HUNDRED THIRTY VARIABLES. IT IS POSSIBLE TO MAKE A DISTINCTION
8 | ON THE BASIS OF RACE AND THOSE WITH -- WHITE VICTIMS WOULD HAVE
9 | ON THE AVERAGE A HIGHER, FIVE PERCENTAGE POINT HIGHER DEATH
10 | SENTENCING RATE THAN THOSE WITHOUT WHITE VICTIMS.
11 | Q. WE ARE TALKING ABOUT HYPOTHETICALS ABOUT THAT POINT ZERO
12 | FIVE?
13 1 ‘A. OH, YES, THAD 15°A HYPOTHETICAL.
14 | Q. THERE WAS SOME TESTIMONY GIVEN BY THE STATE IN THIS CASE IN
15 | THE SUMMER, DO YOU RECALL THAT? WERE YOU HERE FOR THAT
16 | TESTIMONY?
17 1 sa, wBs,
18 | QO. AND HAVE YOU READ THE STATE'S REPORT THAT WAS TRANSMITTED TQ
19 | US DURING THE SUMMER BEFORE THE HEARING?
4 20 A, YES.
21 | Q. STATISTICALLY SPEAKING DID THE STATE'S EVIDENCE PURPORT TO
22 | TRY TO CONTROL FOR THE PRESENCE OR ABSENCE OF AGGRAVATING
23 | CIRCUMSTANCES ON THE RACES -- THE RACIAL EFFECTS?
24.4 a, M0,
25 | Q. IN OTHER WORDS IT DID NOT EVEN CLAIM TO DO THAT
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WOODWORTH ~ DIRECT
STATISTICALLY SPEAKING?
A. I DON'T BELIEVE ANY SUCH CLAIM WAS MADE.
MS. WESTMORELAND: I THINK WE ARE GETTING OUTSIDE THE
SCOPE OF THE HEARING. I DIDN'T THINK THE SCOPE OF THE HEARING
WAS TO GET BACK INTO THE EVIDENCE PRESENTED BUT TO EXPLAIN THE
STATISTICAL AREAS AND I OBJECT TO THIS LINE OF QUESTIONING.
MR. BOGER: YOUR HONOR, THESE LAST TWO QUESTIONS I THNK
IS RESPONSIVE TO YOUR HONOR'S OBSERVATION THIS MORNING THAT YOU
EXPECTED, MS. WESTMORELAND, TO TALK ABOUT THE STATE'S CASE
INSOFAR AS THERE MAY HAVE BEEN CONTROLS INTRODUCED FCR
AGGRAVATING CIRCUMSTANCE AND THAT MASK OR BE A PROXY FOR RACE.
INSOFAR AS THAT OBSERVATION BORE ON WHAT CONTROLS
MEANT, I SIMPLY THOUGHT IT WAS WITHIN THE SCOPE OF THE HEARING
AS IT DEVELOPED TO ASK DR. WOODWORTH WHETHER CONTROLLING WAS
EVEN SOMETHING THAT THE STATE'S EVIDENCE DID. I DIDN'T TALK
SPECIFICALLY ABOUT ANY NUMBERS THAT WERE USED.
THE COURT: I DON'T KNOW THAT THEY DID. BUT I THINK
YOU HAVE ADDED A PHRASE TO WHAT I SAID AND THAT IS CONTROL OF
ASD WHAT I THINK I SAID OR WHAT I MEANT TO SAY, I EXPECT MS.
CORRELATIONS AND THE MITIGATION CORRELATIONS WHICH APPARENTLY DC
EXIST ARE THE PHENOMENON THAT WE ARE OBSERVING AND NOT A RACE CF
THE VICTIM EFFECT.
MR. BOGER: IN THAT SENSE, WHAT I WAS TRYING TO DO WITH
MY QUESTIONING=--
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Pr — — ———— —
HOODWORTH - DIRECT 2
1 THE COURT: I KNOW THEY DIDN'T RUN AS FAR I KNOW A
2 | SINGLE MULTI-REGRESSION ANALYSIS.
3 MR. BOGER: OKAY. THAT IS THE ONLY POINT I WAS TRYING
4 | TO ESTABLISH AND THAT WAS WITHIN THE TERMS OF ONE, WHAT DOES
5 | CONTROLLING FOR VARIABLES MEAN AND I WAS TRYING TO ESTABLISH
6 | WHAT WAS DONE WAS NOT SIMPLY A CONTROL, BUT I HAVE NO FURTHER
7 | INTEREST IN TRYING TO PURSUE THAT.
8 THE COURT: LET ME ASK YOU A QUESTION, DOCTOR. I AM
9 | STILL TAKING THE MEAT YOU HAVE GIVEN ME HERE ON THIS CONCEPT,
10 | IN A TWO HUNDRED THIRTY VARIABLE ANALYSIS YOU WOULD AGAIN ADD UP
11 | ALL OF THE COEFFICIENTS, GIVING THEM THEIR PLUS OR MINUS VALUE
12 | AND THAT WOULD SPREAD IT ON THE AGGRAVATION INDEX.
13 THE WITNESS: RIGHT.
14 THE COURT: SUPPOSE FOR EXAMPLE IN SOME FRACTION,
15 | TWENTY OR THIRTY PERCENT OF THE CASES, YOU DID NOT HAVE AN ENTRY
16 | POR ALL TWO HUNDRED THIRTY VARIABLES. THAT WOULD SUGGEST TO ME
17 | THERE IS A LIKELIHOOD THAT THE NUMBER YOU GET COULD BE SKEWD
18 | BECAUSE YOU ARE SUBTRACTING THE POSSIBILITY OF HAVING A
19 | NUMERICAL QUANTITY ADDED TO THE WHOLE.
20 WHAT DID YOU DO ABOUT THAT?
; 21 THE WITNESS: I BELIEVE PROFESSOR BALDUS TESTIFIED TO
22 | THIS POINT AND IF I CAN RECALL WHAT HE SAID, THE FIRST POINT
23 | WAS THAT THERE WERE COMPARATIVELY FEW CASES WITH GENUINE MISSING
24 | DATA IN THEM AND THE REMAKING CASES WHERE A FACTOR WAS ABSENCE
25 | IT WAS ASSUMED TO BE UNKNOWN BY THE DECISION MAKER.
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WOODWORTH ~ DIRECT
THE COURT: I REMEMBER WHAT HIS TESTIMONY WAS ON THE
CODING OF THE THING BUT I DON'T KNOW IF THE CODING IS THE
EQUIVALENT -- EVERY FOIL WOULD BE THE EQIVALENT OF THE TWO
HUNDRED THIRTY-ONE VARIABLES OR NOT. THE POINT IS THAT TO THE
EXTENT YOU HAD MISSING DATA -- TO THE POINT THAT YOU HAD ANY
MISSING DATA IN A GIVEN CASE IT WOULD EITHER OVER OR
UNDERESTIMATE THE VALUE OF THAT CASE DEPENDING ON WHETHER WHAT
WAS MISSING WAS AN AGGRAVATOR OR A MITIGATOR?
THE WITNESS: THAT 1S A FAIR STATEMENT. IT HAS BEEN MY
EXPERIENCE AND 1 BELIEVE PROFESSOR BERG TESTIFIED TO THIS POINT
THAT A MODERATE AMOUNT OF MISSING DATA WOULD NOT SERIOUSLY SKEW
THE POSITION OF POINTS ON THE AXIS.
THE COURT: I ASK THE QUESTION MORE IN THE SENSE CF
TRYING TO MAKE SURE I UNDERSTAND HOW THE AGGRAVATION INDEX WORKS
THAT SUGGESTS IT IS A MAJOR FAILING.
I HAD ONE OTHER QUESTION AND LET ME STOP AND THINK
ABOUT IT. I THINK I KNOW THE ANSWER WHEN YOU RELATE IT TO THE
GRAPH BUT I WANT TO MAKE SURE IT IS THE SAME AFTER YOU DO YOUR
MATHEMATICS. NO PLOT, VISUALLY CONCEPTUAL -- I AM NOT SPEAKING
VERY WELL TODAY.
NONE OF THESE POINTS PLOTTED HERE EVEN IF WE WERE
THINKING ABOUT THE ALGEBRAIC MODEL WOULD INDICATE THE PRESENCE
OR ABSENCE OF ANY GIVEN VARIABLE?
THE WITNESS: OTHER THAN THE ALCOHOL VARIABLE WHICH IS
ACHIEVED BY SEPARATION,
— — — — — —
WOODWORTH = DIRECT Be
1 THE COURT: I AM TALKING ABOUT THESE POINTS ON GW 9.
2 THE WITNESS: THAT IS RIGHT.
3 THE COURT: NONE OF THOSE INDICATE SPECIFICALLY A GROUP
4 OF CASES IN WHICH A GIVEN VARIABLE OR COMBINATION OF GIVEN
. . VARIABLES IS PRESENT OR ABSENT, RIGHT?
6 THE WITNESS: THAT IS RIGHT.
7 THE COURT: I COULD THINK ABOUT THE SAME THING AS BEING
8 TRUE ABOUT THE ALGEBRAIC MODEL?
9 THE WITNESS: CORRECT REFLECTION OF WHAT THE ALGEBRA
10 DOES.
11 BY MR. BOGER:
12 Q. BEFORE I MOVE TO QUESTION TWO IF THERE ARE NC FURTHER
13 QUESTIONS BY THE COURT ON QUESTION ONE, I WANTED TO MOVE THE
14 ADMISSION INTO EVIDENCE OF GW 9 THROUGH GW 12 FOR PURPOSES OF
18 ILLUSTRATION ONLY.
16 MS. WESTMORELAND: NO OBJECTION.
17 THE COURT: THEY WILL BE ADMITTED TO ILLUSTRATE HIS
18 TESTIMONY.
18 BY MR. BOGER:
20 Q. I AM GOING TO ADDRESS THE SECOND QUESTION IN THE PREHEARING
. 21 ORDER AND ASK YOU TO LOOK AT IT AND GIVE US AN ANSWER, IF YOU
22 CAN.
23 THE QUESTION IS AS FOLLOWS: WHAT DOES THE ®U" REFER TO IN THE
24 FOLLOWING MULTIPLE REGRESSION FORMULA -- ¥ = A + Bl X1 + B2 X2 +
25 U -- AND WHAT IS THE ROLE OF THE "U" CONCEPT IN MULTIVARIATE
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WOODWORTH - DIRECT
ANALYSIS?
A. MOST OF THE LITERATURE ON REGRESSION WILL BEAR ME OUT, THE
REGRESSION MODEL CONSISTS OF TWO PARTS. THE SYSTEMATIC PART IS
THE A + Bl X1 + B2 X2. THIS PART MODELS THE AVERAGE VALUE OF X
AS I MENTIONED EARLIER.
THE "U®" TERM IS A SYMBOL FOR THE FACT THAT THERE ARE
ADDITONAL UNIQUE, PERHAPS CHAOTIC, PERHAPS RANDOM REASONS FOR A
PARTICULAR OUTCOME AND THAT THESE ARE UNIQUE TO EACH CASE, NOT
SYSTEM-WIDE AND NOT RELATED TO THE X VARIABLES.
QO. I AM GOING TO SHOW YOU WHAT HAS BEEN MARKED AND I THINK
ADMITTED INTO EVIDENCE AS DB 65 WHICH INCLUDES TWO REGRESSION
FORMULI AND ASK YOU TO LOOK AT THEN?
A. DB 65 SHOWS A BIVARIATE REGRESSION MODEL AND MULTI-
REGRESSION MODEL WHICH 1S OF EXACTLY THE SAME FORM ~~ EXCUSE ME,
WHICH IS OF THE FORM IN QUESTION TWO WITHOUT THE °U® TERM.
Q. WHERE IS THE MISSING TERM? WHERE IS THE "U" TERM IN DB 657
A. WELL DB -- THE MODELS IN DB 65 ARE MODELS FOR THE AVERAGE
VALUE OF Y WHEREAS THE MODEL IN QUESTION TWO OF THE PREHEARING
MODEL IS A MODEL FOR INDIVIDUAL OUTCOME, AN INDIVIDUAL CR ZERO
CUTCCHME
Q. DOES THAT MEAN IN ONE CASE?
A, YES.
Q. SO THERE IS NO OVERALL CONSTANT NUMBER THAT IS THE U FOR THE
AVERAGE REGRESSION ANALYSIS?
A. NO. IN FACT THE U AVERAGES OUT TO ZERO. THERE IS ONE "U°
WOODWORTH - DIRECT 35
1 TERM FOR EACH OF THE OBSERVATIONS AND IN THE CASE OF THESE
2 EXAMPLES THERE WOULD BE TWO HUNDRED TEN DIFFERENT INDIVIDUAL U
3 VALUES.
4 Q. DOES ONE -- IF ONE LEAVES THE U OUT OF THE TERM WHEN ONE
5 DOES THE REGRESSION ANALYSIS SUCH AS THE ONE YOU REPORTED IN THE
6 BALDUS AND WOODWORTH STUDIES, DOES THAT MEAN YOU BAVEN'T TAKE Ei
7 THE U'S INTO ACCOUNT IN YOUR STATISTICAL ANALYSIS?
8 A. THE ®"U"™ TERM IS ALWAYS PRESENT. THE COMPUTER PROGRAMS, THE
9 ALGEBRAIC FORMULAS WORK WITH THE OBSERVED DATA. THEY CANNOT
10 WORK WITH THE UNOBSERVED U TERMS. THE "U®" TERM IS ALWAYS THERE
11 BY IMPLICATION AND CAN IN FACT BE ESTIMATED.
12 THE COURT: I HAD CONCEPTULIZED AFTER READING HMR.
13 FISHEER'S ARTICLE AND LISTENING TO YOUR TESTIMONY THAT YOUR R
14 FACTOR 1S SOMETHING OF THE RECIPROCAL OF THE ®"U" TERM; IS THAT
15 ANYWHERE CLOSE?
16 THE WITNESS: THE "U® TERM IS THE UNIQUE COMPONENT OF
17 EACH OBSERVATION SO THERE IS TWO HUNDRED TEN OF THEM. WHAT THE
18 R VALUE IS IS A SUMMARY STATISTIC WHICH DECRIBES COLLECTIVELY
19 ALL OF THE U TERNS.
; 20 THE COURT: IT WILL BE THE AVERAGE U, IF YOU WILL?
. 21 THE WITNESS: NOT EXACTLY. THE AVERAGE U WOULD BE THE
22 SQUARE ROOT OF ONE MINUS R SQUARED. THAT WOULD BE THE STANDARD
23 DEVIATION OF THE U'S EXPRESSED AS A PROPORTION OF THE STANDARD
24 DEVIATION OF Y. SO IN OTHER WORDS, IF R SQUARED IS EQUAL TO
25 POINT NINE FOR INSTANCE THEN =-
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WOODWORTH - DIRECT
THE COURT: THAT WOULD BE A GOOD FIT, IF I REMEMBER
CORRECTLY,
THE WITNESS: THAT WOULD BE A GOOD FIT AND WHAT IT
WOULD INDICATE IS THAT IN THE MODEL, THE VARIATION IN THE
OUTCOME -- IF WE TAKE THE VARIATION IN TEE OUTCOME TO BE ONE
HUNDRED, THEN THE VARIATION THAT IS EXPLAINED BY THE "U" TERM
WOULD BE TEN OUT OF THAT ONE HUNDRED, SO ONE MINUS R SQUARED
SUMMARIZES THE SIZE OF -- COLLECTIVELY SUMMARIZES THE SIZE OF
THE ®"U® TERM.
THE COURT: ONE MINUS R SQUARED?
THE WITNESS: CORRECT.
BY MR. BOGER:
Q. DOES THE EXISTENCE OF THE U FACTOR OR "U"™ TERM INDICATE
THERE ARE NECESSARILY VARIABLES WHICH ONE HAS NOT TAKEN INTO
ACCOUNT IN THE STATISTICAL ANALYSIS?
A. IF ONE BELIEVES THAT THE WORLD IS DETERMINISTIC.
Q. WHAT DO YOU MEAN BY THAT?
A. THAT EVERYTHING HAS AN EXPLANATION, THEN YES THERE ARE
VARIABLES LEFT CUT,
Q. ARE THEY SYSTEMATIC VARIABLES NECESSARILY?
A. THERE WOULD BE NO SYSTEMATIC VARIABLES. THAT IS ASSUMING WE
HAVE LOOKED FOR ANY SYSTEMATIC VARIABLES WE CAN FIND THAT THE
"(U®* TERM BY DEFINITION HAS NON-SYSTEMATIC EFFECTS. WE HAVE
CHECKED ALL OF THE OTHER VARIABLES TO SEE IF THERE ARE
SYSTEMATIC EFFECTS.
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WOODWORTH - DIRECT 4
1 Q. DOES THE EXISTENCE OF A "U" TERM MEAN THAT ONE CANNOT HAVE
2 CONFIDENCE THAT THE COEFFICIENTS REPORTED FOR THE VARIABLES ON
3 WHICH YOU DO HAVE ANALYSIS ARE ACCURATE OR CORRECT?
> 4 A. NO. THE ACCURACY OF Bl AND B2 FOR EXAMPLE HAS VERY LITTLE
. 5 TO DO WITH THE SIZE OF U. IT'S A SIGNAL AND NOISE SITUATION.
6 Q. CAN YOU GIVE US AN ANALOGY OF WHAT YOU MEAN BY SIGNAL AND
7 NOISE SITUATION? :
8 A. IT'S A ROUGH ANALOGY BUT IT'S LIKE LISTENING TO A SHORT WAV
9 BROADCAST. THERE IS SOME -- YOU ARE LISTENING TO SOMEONE READ
10 TEXT, PERHAPS IN ENGLISH, OVER THE RADIO BUT THERE IS STATIC.
1} NOW THE "U" TERM -- THE STATIC WOULD CORRESPOND TO THE "U®" TERM}
12 IN OTHER WORDS THIS RANDOM UNPREDICTABLE NOISE THAT COMES IN ON
33 YOUR SHORT WAVE SPEAKER. THE SYSTEMATIC PART OF THE MODEL, THE
14 A + Bl X1 + B2 X2 IS WHATEVER MESSAGE IS BEING SENT IN THIS
15 BROADCAST.
16 NOW THE PRESENCE OF A "U" TERM, THE PRESENCE OF STATIC
17 IN THIS BROADCAST DOESN'T CHANGE THE MESSAGE. SOMETIMES IT
18 MAKES IT HARDER TO DETECT WHAT THE MESSAGE IS OR DETECT THAT IT
19 IS THERE. BOUT IT DOESN'T CHANGE WHAT IS BEING SAID.
20 Q. SO IN EFFECT IN TERMS OF YOUR ANALOGY THE COEFFICIENT OF A
4 21 VARIABLE IS PART OF THE TEXT; IS THAT CORRECT?
22 A. SO TO SPEAK. AS I SAID, IT IS A ROUGH ANALOGY.
23 THE COURT: SUPPOSE YOU WERE LISTENING TO MESSAGES FRON
24 OUTER SPACE AND YOU HEARD A LOT OF DIFFERENT NOISE, HOW DC YOU
25 KNOW WHICH IS NOISE AND WHICH IS SYSTEMATIC COMMUNICATION?
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WOODWORTH - DIRECT
THE WITNESS: THE WAY YOU DETECT NOISE IS BY THE FACT
IT IS FEATURELESS. WHAT THAT MEANS IS THAT YOU CANNOT -- HERE
1S WHERE THE ANALOGY BREAKS DOWN. IF YOU COMPARE THE NOISE AT
ONE MINUTE INTERVALS WITH THE NOISE IN ANOTHER ONE MINUTE
INTERVAL, YOU CAN'T TELL THE DIFFERENCE BETWEEN THE TWO. THE
WAY YOU KNOW YOU ARE LOOKING AT NOISE IS THE SPECTRUM OT IT
DOESN'T CHANGE. THE WAY YOU KNOW YOU ARE LOOKING AT A SIGNAL
AND YOU LOOK AT ONE PART OF THE SIGNAL AND ANOTHER PART OF THE
SIGNAL, THERE HAS BEEN SOME CHANGE IN THE TWO. THIS IN FACT IS
THE PHILOSOPHY BEHIND GW 9.
WE LOOK AT -- IF WHAT WE EAVE BEEN LOOKING AT WERE PURE
NOISE WE WOULDN'T SEE ANY DIFFERENCE BETWEEN THESE TWO GRAPH,
THE UPPER ONE AND LOWER ONE IN GW 9. SO IN SIGNAL DETECTION THE
METHOD, AS IN STATISTICS, THE METHOD OF SIGNAL DETECTION IS BY
COMPARING, IF WE COMPARE IN THE CASE OF SIGNALS FROM OUTER
SPACE YOU WOULD LOOK AT A SIGNAL OVER AT ONE TIME AND A SIGNAL
AT ANOTHER TIME TO SEE IF THERE WAS ANY DIFFERENCE. IF THEY
BOTH SEEM TO BE THE SAME KIND OF RANDOM SCATTER, I SUGGEST NO
OME IS TRYING TO TALK TO YOU.
BY MR. BOGER:
Q. CORRESPONDINGLY IN TERMS OF YOUR ANALOGY IF -- THE REPORTING
OF A COEFFICIENT MEANS WHAT, THAT YOU HAVE DETECTED SOMETHING
THAT IS SYSTEMATIC IN ITS EFFECT ON THE OUTCOME VARIABLE?
A. THAT IS ROUGHLY. YOU MAY BE PRESSING THE ANALOGY.
THE COURT: REMEMBERING AT ALL TIMES THE NOISE IS ONE
WOODWORTH - DIRECT bs
1 MINUS R SQUARE?
2 THE WITNESS: THAT IS RIGHT.
3 THE COURT: AS R SQUARE INCREASES OR DECREASES YOUR
% ABILITY TO EXPLAIN THE RESULT IN A GIVEN CASE INCREASES OR
y 5 DECREASES IN INVERSE CORRELATION OF THAT? .
6 THE WITNESS: THAT IS CORRECT. OUR ABILITY TO DETECT
7 THE DIFFERENCE BETWEEN WHITE AND BLACK VICTIM CASES IS NOT
8 DIRECTLY AFPECTED BY THE AMOUNT OF NOISE. ASSUMING WE HAVE A
9 SUFFICIENT NUMBER OF CASES THAT WE CAN MAKE THE COMPARISON, WE
10 AVERAGE OUT THE NOISE BY COMPARING RATES.
11 BY MR. BOGER:
12 Q. LET ME ASK YOU THIS. YOU COULD HAVE A LOW ABILITY TO
13 PREDICT OVERALL OUTCOME AND NEVERTHELESS BE ABLE TO DETECT THAT
14 SOME FACTOR WAS HAVING AN IMPACT THAT WAS INDEPENDENT OF OTHER
15 FACTORS?
16 A. THAT IS CORRECT.
17 Q. SO, IN SUMMARY LET ME ASK YOU ABOUT THE LARGE QUESTION OF
18 TWO AND SEE IF THERE IS A SUMMARY ANSWER. WE HAVE DECIDED WHAT
19 THE "U® TERM REFERS TO IN THE MULTI-REGRESSION FORMULA, WHAT IS
20 THE ROLE OF THE U CONCEPT IN THE MULTIVARIATE ANALYSIS?
" 21 A. TO CAPTURE THE RANDOM ELEMENT IN THE SYSTEM.
22 MR. BOGER: IF THERE ARE NO OTHER QUESTIONS FROM THE
23 COURT, I AM GOING TO MOVE ON TO THE THIRD QUESTION.
24 THE COURT: DO YOU MEAN TO TELL ME THAT IN AN ELEVEN -=
25 LET'S TAKE NINE AND TEN. IF YOU TAKE WHAT YOU KNOW ABOUT THE
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WOODWORTH -~ DIRECT
IMPOSITION OF THE DEATH PENALTY AFTER CONTROLLING FOR TEN
FACTORS AND WE NOW KNOW THERE IS AN ELEVENTH WHICH HAS SOME
BEARING, ARE YOU TELLING ME THAT THE ELEVENTH -- AT THE STAGE AY
WRICH YOU ADJUSTED FOR TEN, IS THE ELEVENTH WITHIN THE U FACTOR
OR IS IT --
THE WITNESS: YES.
THE COURT: OKAY. THAT IS ALL I WANT TO KNOW.
THE COURT: SO U =—— U MAY CONTAIN RANDOM INFLUENCES AND
IT MAY ALSO CONTAIN SYSTEMATIC INFLUENCES?
THE WITNESS: THAT IS WHY WE LOOK FOR VARIABLES THAT
ARE STATISTICALLY SIGNIFICANT.
BY MR. BOGER: |
Q. LET ME CLEAR UP THE LAST POINT. WHAT DO YOU MEAN THAT IS
WHY WE LOOK FOR VARIABLES THAT ARE STATISTICALLY SIGNIFICANT?
A. THAT IS WHAT IT MEANS TO LOOK FOR A SIGNAL. YOU LOOK FOR A
PATTERN IN THE "U" TERM. YOU TRY TO SEE IF THE *U® TERM DOES IN
FACT CONTAIN ONE OF THE OTHER VARIABLES.
THE COURT: YOU HAVE TO BE ABLE TO CONCEPTULIZE WHAT IT
IS BEFORE YOU CAN LOOK FOR IT?
THE WITNESS: IT HAS TO BE IN YOUR DATA SET AND THAT Ig
WEERE KNOWLEDGE OF THE CHARGING AND SENTENCING SYSTEM COMES IN,
THAT IS NOT A JUDGMENT I AM QUALIFIED TO MAKE.
THE COURT: I DON'T KNOW IF IT IS YALE OR WHO IT IS,
BUT THERE IS SOMEBODY THAT IS AN ADVOCATE OF WHAT THE JUDGE HAD
FOR BREAKFAST IS THE BIGGEST DETERMINANT OF HOW CASES COME OUT,
—— — p—— ——— —
WOODWORTH - DIRECT pe
1 IF IN YOUR SEARCH FOR AN EXPLANATION OF THE RATIONAL UNIVERSE
2 YOU DIDN'T HAPPEN TO NOTICE WHETHER THEY HAD A GOOD INTAKE OF
3 PROTEIN OR NOT, THEN THAT WOULD BE IN THE U?
4 THE WITNESS: THAT WOULD PRESENT A PROBLEM IN OUR
y 5 ANALYSIS ONLY IF THE JUDGE HAD POOR BREAKFAST FOR WHITE VICTIM
6 CASES AND GOOD BREAKFAST FOR BLACK VICTIM CASES.
7 THE COURT: I UNDERSTAND,
8 THE WITNESS: THERE MAY BE TERMS LIKE THIS WHICH ARE
Sg SYSTEMATIC BUT WHICH ARE IN EPFECT RANDOM IN THAT THEY ARE NOT
10 CORRELATED WITH ANY OTHER VARIABLE IN THE SYSTEM.
11 THE COURT: YOU SEE THE PROBLEM YOU GET IS YOU GET BACK
12 TO ONE FACTOR AND YOU MAKE THE ANALYSIS AND THEN THE WHOLE THING
33 BREAKS DOWN.
14 IT'S LIKE THE FALLACY OF THE BEARD IN REVERSE, ONE
i5 WHISKER ISN'T A BEARD SO TWO ISN'T. WHAT YOU ARE SAYING IS THAT
16 SOMEWHERE OUT THERE TEN TO THIRTY OR FORTY VARIABLES IS A
17 REASONABLE MEASURE OF REALITY AND I LOST MY TRAIN OF THOUGHT --
18 SO WHAT YOU'RE LOOKING AT IS THE DIFFERENCE. IT DOESN'T REALLY
19 MATTER, ALL THESE OTHER THINGS, YOU'RE LOOKING AT THE
20 DIPFERENCE. IF WE DROP BACK AND WE DROP VARIABLE, AND WE DROP
’ 21 VARIABLE AND WE DROP VARIABLE AND WE DROP VARIAELE AND WE DROP
22 VARIABLE AND WE ARE BACK TO ONE VARIABLE, AND YOU OBSERVE A
23 DIFFERENCE, I THINK YOUR ATTORNEY WOULD TELL ¥YOU THAT IS LEGALLY
24 NOT SIGNIFICANT AND I THINK YOU MIGHT SUGGEST THAT IS KNOT
25 STATISTICALLY SIGNIFICANT AND I AM NOT EXACTLY CLEAR HOW FAR --
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WOODWORTH - DIRECT
HOW WELL THAT ARGUMENT OF A DISPARAITY IS WHAT WE HAVE TO PROVE
HOLDS UP BECAUSE THAT IS NOT ALL YOU HAVE TO PROVE IT SEEMS TO
ME.
THE WITNESS: I WOULD ANSWER BY SAYING WE WERE UNABLE
TO FIND ANY VARIABLES THAT MADE THE DISPARITY GO AWAY.
PROFESSOR BALDUS SEARCHED PRETTY THOROUGHLY FOR THEM.
TEE COURT: NOW THE QUESTION IS NOT DID YOU FIND SOME
VARIABLES THAT MADE IT GO AWAY, THE QUESTION IS DID YOU FIND
SOME VARIABLES THAT CREATED IT. I THINK THAT IS WHAT MS.
WESTMORELAND IS GOING TO ARGUE.
AM I CLOSE TO YOUR POINT OF VIEW? VIEW?
MS. WESTOMORELAND: YES, YOUR HONOR, AT LEAST
PARTIALLY.
THE COURT: GO AHEAD.
MR. BOGER: THANK YOU, YOUR HONOR.
BY MR. BOGER:
Q. DR. WOODWORTH, LET'S TURN TO QUESTION THREE. I THINK WE MAY
FIND WE HAVE TALKED ABOUT A FAIR BIT OF IT THIS MORNING. LET'S
ADDRESS IT AGAIN SPECIFICALLY.
WHAT ARE THE MATHEMATICAL, STATISTICAL AND PRACTICAL
REASONS FOR EMPLOYMENT OF A "DUMMY VARIABLE" IN A REGRESSION
FORMULA AND HOW DOES IT AFFECT THE MEASUREMENT OF THE INFLUENCE
OF THAT VARIABLE? DO YOU UNDERSTAND WHAT IS MEANT BY THE USE OF
THE TERM "DUMMY VARIABLE" IN THIS QUESTION?
A. YES. I UNDERSTAND IT TO MEAN A ZERO CONE VARIABLE.
4
]
WOODWORTH - DIRECT 8
1 THE COURT: NO. THAT IS NOT WHAT IT MEANS. DID YOU =v
2 THIS RECORD IS BURDENED BY THE NON-EXISTENCE OF SOMETHING THAT
3 HAS OCCURRED AND THAT IS YOU AND I DISCUSSED THE FISHER AND
hl FINKELSTEIN NOTES IN COLUMBIA LAW REVIEW, DO YOU REMEMBER THAT?
" 5 MR, BOGER: WE DID, YOUR HOROCR.
6 THE COURT: AND THE DUMMY VARIABLE TO WHICH I REFER IS
7 ONE REFERRED TO BY THE ARTICLE AND IT IS AN S VARIABLE.
8 MR. BOGER: I THINK DR. WOODWORTH HAS A COPY OF THE
9 ARTICLE. I PERHAPS SHOULD HAVE INTRODUCED IT JUST TO CLARIFY
10 THE RECORD.
th! THE COURT: IT APPEARS AT 722 AND MY RECOLLECTION OF
12 THE ARTICLE IS NOW DIMMED BY THE PASSAGE OF A FEW MONTHS BUT IN
13 | THIS PARTICULAR EXAMPLE AS I UNDERSTAND IT, HE ALSC TAKES A
14 DICHOTOMOUS VARIABLE WHICH COMPLICATES IT. BUT IF I -- THIS IS
5 WHAT I AM GETTING AT. IF I UNDERSTAND HIS ARTICLE AND IF I AM
16 CORRECT IN BELIEVING YOU USED THE SAME TECHNIQUE RATHER THAN
17 "FIGURE A COEFFICIENT FCR BLACK VICTIM CASES AND THEN FIGURE A
18 | COEFFICIENT FOR WHITE VICTIM CASES AND SUBTRACT THEM, YOU DID
1s | WEAT HE DID BY PUTTING THE DUMMY VARIABLE IN THE SEQUENCE WITH
20 THE -- I CAN'T REMEMBER THE EQUATION NOW -- AX + BX + CX.
A 21 IF THAT IS TRUE, WHAT IS THE SIGNIFICANCE OF THAT?
22 THE WITNESS: THAT IS THE ALGEBRAIC INSTRUMENT FOR
23 FITTING TWO DIFFERENT STRAIGHT LINES.
24 THE COURT: IT IS NOT IMMEDIATELY APPARENT TO ME AS TO
25 HOW IT IS THE SAME AS ARRIVING AT TWO SEPARATE COEFFICIENTS AND
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WOODWORTH -~ DIRECT
THEM SUBTRACTING THEM AND THAT IS WHY I ASK THE QUESTION.
THE WITNESS: IF WE COULD LOOK AT FISHER'S =-- EITHER
LOOK AT FISHER'S EQUATION SIX OR =--
TRE COURT: WHAT PAGE?
THE WITNESS: 722. IT SAYS Y= A + BS + CA + U. § IS
THE SEX VARIABLE, ZERO FOR WOMAN AND ONE FOR MAN. IF WE HAVE A
MALE, THE EQUATION READS: Y = A + B + C TIMES A, BECAUSE FOR A
MAN S IS EQUAL TO ONE. IF THE CASE IS FEMALE, THEN THE BQUATIOY
READS: Y = A + C TIMES CAPITAL A. SEE BY VIRTUE OF THE PACT S
IS BQUAL TO ZERO, THE B DROPS OUT FROM THE FEMALE EQUATION.
THE COURT: I UNDERSTAND.
BY MR, BOGER:
Q. IN TERMS OF THE MATTERS THAT ARE IN EVIDENCE IS THIS THE
SAME KIND OF THING YOU ARE GETTING AT WITH GW 9 AND 10? THE
DUMMY VARIABLE IN EFFECT ALGEBRAICALLY PERFORMANING THE FUNCTION
OF THAT SUBSTRACTION THAT YOU BAVE REFERRED TO?
VARIABLE JUST ELEVATES THE BQUATION BY THAT MANY UNITS.
Q. SO IN EFFECT IN GW 9 AND 10 WHAT WAS THE DUMMY VARIABLE?
A. THE DUMMY VARIABLE WAS =-~ LET'S SEE, LIGHT OR NO ALCOHOL USH
WOULD BE CODED ONE AND MODERATE TO EXCESSIVE WOULD BE CODED ZERQ
IN THIS CASE. I MIGHT POINT OUT THE SIMILARITY OF GW 9 TO
FIGURE TWO AT 723 IN THE FISHER ARTICLE.
THE COURT: BEFORE WE HAD THIS GET TOGETHER I
UNDERSTOOD YOU, THAT IS YOU PERSONALLY NCT THE LETTER ®U" TO THS
WOODWORTH - DIRECT pe
1 | POINT OF THAT FIGURE AND I UNDERSTOOD MR. FISHER TO THE POINT OF
> | THAT FIGURE. IT WAS ONLY WHEN WE LEFT GRAPHIC PRESENTATION AND
3 | WENT INTO A MATHEMATICAL BLACK BOX THAT I STARTED BEING INSECURE
4 | AND THAT IS WHY I HAVE US BACK HERE.
‘ 5 MR. BOGER: LET ME =- IP YOU LIKE I WILL BE GLAD TO
6 | SUPPLEMENT THE RECORD WITH THAT ARTICLE SO IT IS ALL CLEAR OR
7 | you couLD JUDICIALLY NOTICE, WHICHEVER YOU PREFER.
8 THE COURT: MS. WESTMORELAND?
9 MS. WESTMORELAND: I HAVE NO PREFERENCE, YOUR HONOR.
10 | APPARENTLY THE COURT IS REFERRING TO IT, WE NEED TO HAVE IT IN
11 | THE RECORD OR MAKE SOME JUDICIAL NOTICE OF THE ARTICLE, EITHER
12 | wav.
13 THE COURT: I THINK IT IS MAGNANIMOUS OF MR. BOGER TO
14 | OFFER TO PUT IT IN BECAUSE THERE ARE A COUPLE OF STATEMENTS IN
15 | THERE THAT ARE NOT FAVORABLE TO HIM, BUT IF HE WANTS TO OFFER IT
16 | I WILL BE GLAD TO--
17; MR. BOGER: I THOUGHT I WAS OFFERING IT FOR THE
18 | ILLUSTRATIVE PURPOSES OF THE GRAPH. YOU AND I HAVE TALKED A
19 | LITTLE ABOUT SOME OF THE STATEMENTS IN THERE THAT DON'T BEAR IN
20 | YOUR JUDGMENT ON OUR CASE WITH THE GREATEST OF GRACE.
. 21 THE COURT: HE 1S KIND OF UNKIND ABOUT THE USE OF STEP
22 | WIDE REGRESSION, FOR EXAMPLE.
23 MR. BOGER: OUR POSITION ON THAT IS STEPWISE REGRESSION
24 | AS AN ALTERNATIVE IN A TRIANGULATION HYPOTHESIS OR TRIANGULATION
25 | APPROACH SIMPLY SHOWS WE HAVE GONE TO THAT METHOD. IT DOES NOT
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96
WOODWORTH - DIRECT
REFLECT FAVORABLY IN OUR JUDGMENT AS A METHOD OF CHOICE. BUT 1
WOULD BE HAPPY TO HAVE IT IN EITHER FOR ILLUSTRATIVE PURPOSES OR
FOR ALL PURPOSES ON THAT UNDERSTANDING. WE ARE NOT OFFERING MR,
FISHER, PROFESSOR FISHER As OUR EXPERT.
THE COURT: OBVIOUSLY SO MUCH OF IT I HAVE DIRECTLY
ASKED HIM ABOUT WHICH REALLY GETS TO BE SOME FORMULATIONS AND I
GUESS WHERE WE ARE NOW IS THE U AND DUMMY VARIABLE. I GUESS
UNDER THE RULES OF EVIDENCE THAT PORTION OF IT IS CLEARLY IN
EVIDENCE. NOW FOR THE DOCTRINE OF COMPLETENESS, IF YOU WANT TO
OFFER THE REST OF IT, MS. WESTMORELAND I WILL ACCEPT IT.
MS. WESTMORELAND: YOUR HONOR, I REALLY HAVE NO
PARTICULAR PREFERENCE. IF THE COURT WOULD LIKE IT I WOULD BE
HAPPY TO OFFER IT. I WAS NOT AWARE THAT THE COURT HAD DISCUSSED
THIS PARTICULAR ARTICLE.
THE COURT: I HAD TO TELL MR. BOGER WHERE 1 GOT MY
QUESTIONS FROM.
MR. BOGER: IF SHE HASN'T HAD A CHANCE TO READ AND
THEIR EXPERT HASN'T HAD A CHANCE TO READ IT WE CAN DEFER THIS
MATTER AND SIMPLY TAKE IT UP LATER AFTER THEY KNOW WHAT 1S
THERE. SO I WITHDRAW THE OFFER AT THIS POINT.
THE COURT: I PROBABLY WAS CHEATING EVEN TO LOOK AT IT
BUT I WAS TRYING TO KEEP YOU FROM HAVING TO GET THIS GOOD DOCTCR
BACK DOWN HERE AGAIN AND I KNEW WE WOULD PROBABLY END UP
DISTURBING DR. KATZ AND I THOUGHT MAYBE IF IT WAS SOMETHING THAT
WAS WRITTEN FOR A LAWYER THAT IT WOULD MAKE IT CRYSTAL CLEAR TO
WOODWORTH - DIRECT r
1 | HME, I COULD SIMPLY READ IT.
2 BUT AFTER I READ IT AND READ WHAT DR. BALDUS HAD TO SAY
3 | ABOUT IT, SOME OF THESE QUESTIONS I ASKED HAD NOT BEEN ANSWERED
4 | SO THAT IS WHY WE ARE HERE TODAY. IF THE COURT OF APPEALS OR
- 5 ‘| SUPREME COURT CAN READ THE COLUMBIA LAW REVIEW AND UNDERSTAND
6 | THE PROCESS BETTER THAN I, SO BE IT.
7 | BY MR. BOGER:
8 | Q. LET'S TURN TO QUESTION FOUR TO WIT DO THE COEFFICIENTS
9 | REPORTED FOR THE VARIABLES IN A MULTIPLE REGRESSION ANALYSIS
10 | REFLECT THE ACTUAL DIFFERENCE IN THE OUTCOME OF INTEREST, E.G.,
11 | DO THE RACE OF VICTIM COEFFICIENTS REPRESENT AN ACTUAL
12 | DIFFERENCE IN THE DEATH SENTENCING RATE OR RATHER A DISPARITY?
13 | A. THEY REPRESENT BOTH. I DON'T MAKE A DISTINCTION BETWEEN
14 | THESE TWO WORDS. THERE IS A DISTINCTION TO BE MADE AND THAT
15 | WOULD BE BETWEEN AN AVERAGE DISPARITY AND A SPECIFIC DISPARITY
16 | AT SOME LEVEL OF AGGRAVATION.
17 | Q. WHAT DO YOU MEAN BY THAT? MAYBE MAKING REFERENCE TO YOUR
18 | FIGURES--
19 | A. WELL, FOR INSTANCE IF I COULD REFER TO MY PREVIOUS
: 20 | TESTIMONY. GW 5 FOR INSTANCE -- GW 8 EXCUSE ME.
21 | Q. JUST ONE MOMENT.
22 MR, BOGER: FOR THE COURT'S BENEFIT I HAVE A COPY OF GY
23 | 8 AND I WOULD BE HAPPY TO MAKE IT AVAILABLE TO THE COURT.
24 THE COURT: I REMEMBER THE CHART.
25 | A. THE REGRESSION METHOD WOULD PRODUCE AN AVERAGE DISPARITY
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WOODWORTH - DIRECT
BETWEEN THE TWO GROUPS. FIGURE TWO WOULD BE THE ANTILOG OF GW
10. WHEN ONE LOOKS AT THE MODEL IN DETAIL IN RESPONSE TO SOME
OF YOUR HONOR'S CONCERNS THE EFFECTS OF A VARIABLE MIGHT DEPEND
UPON WHAT OTHER VARIABLES ARE PRESENT. WE DID LOOK AT
INTERACTIVE MODELS AND THIS IS AN INSTANCE OF THAT AND HERE WE
SEE AT SPECIFIC LEVELS OF AGGRAVATION THE DISPARITY SEEMS TO BE
DIFFERENT. SO WHILE GOING BACK TO THE GENERAL CASE, THE
REGRESSION COEFFICIENT IS AN AVERAGE DISPARITY BUT IT IS NOT A
SPECIFIC DISPARITY THAT THE DISPARITIES MAY WELL DEPEND ON THE
LEVEL OF THE AGGRAVATION.
THE COURT: THAT ANSWERS PART OF MY QUESTION BUT I WANI
TO MAKE ABSOLUTELY SURE WHEN YOU WERE GIVING ME A RACE OF THE
VICTIM COEFFICIENT OF FOR EXAMPLE POINT ZERO FIVE THAT YOU MEANT
THAT THE ACTUAL DEATH PENALTY RATE WENT UP POINT ZETO FIVE.
THE WITNESS: NOT UNIFORMLY.
THE COURT: ON THE AVERAGE.
THE WITNESS: RIGHT.
THE COURT: NOT THAT A KILLER OF A WHITE HAD A FIVE
PERCENT GREATER CHANCE OF GETTING THE DEATH PENALTY THAN A
KILLER OF A BLACK?
THE WITNESS: THAT IS CORRECT. IT DOESN'T MEAN THAT.
IT MEANS FOR SOME CLASSES OF KILLERS THE DISPARITY WOULD BE
GREATER AND FOR OTHER CLASSES IT WOULD BE SMALLER.
BY MR. BOGER:
Q. IS THERE ANY WAY TO--
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WOODWORTH - DIRECT 5
1 THE COURT: I AM NOT SURE IF YOU HAVE STILL =-- I THINK
2 | I KNOW WHAT THE ANSWER IS BUT I AM NOT SURE YOU UNDERSTAND THE
3 | QUESTION.
: 4 | BY MR. BOGER:
: 5 | Q. MAYBE I CAN ASK IN TERMS OF GW 10. THAT MIGHT HELP, THE
6 | TESTIMONY FROM TODAY. LOOKING AT YOUR GW 10, WHAT DOES A —- IF
7 | WE WERE TALKING HYPOTHETICALLY NOT ABOUT ALCOHOL USE BUT ABOUT
8 | RACE OF VICTIM, WHAT DOES A RACE OF VICTIM COEFFICIENT OF POINT
9 | ZERO FIVE OR POINT ONE SIX, WHAT WOULD THAT MEAN?
10 | A. IT MEANS -- IT'S IN THE SENSE OF BEING THE SEPARATION
11 | BETWEEN THESE TWO STRAIGHT LINES WHICH ARE THEMSELVES SO TO
12 | SPEAR AVERAGE TRENDS FOR THE DATA, IT'S AN AVERAGE DIFFERENCE
13 | OF SIXTEEN PERCENTAGE POINTS. |
14 | Q. SO THE DEATH SENTENCING RATE AMONG BLACK VICTIM CASES WOULD
15 | BE SIXTEEN POINTS LOWER THAN THAT SAME RATE AMONG WHITE
16 | DEFENDANTS OR WHITE VICTIMS ON THE AVERAGE?
17 | A. ON THE AVERAGE, YES.
18 THE COURT: TO MAKE IT EVEN ABSOLUTELY CONCRETE, YOU DO
19 | NOT —- WHERE YOU HAVE GW 10 AND YOU HAVE THE DOUBLE HEADED
20 | ARROWS YOU DON'T MEAN TO SUGGEST THAT IS A SIXTEEN PERCENT
21 | INCREASE OF ONE LINE OVER THE OTHER. YOU MEAN IT IS AN ABSOLUTE
22 | INCREASE OF SIXTEEN PERCENT OR SIXTEEN POINTS?
23 THE WITNESS: IT'S A PERCENTAGE POINT INCREASE, RIGHT;
24 | NOT A SIXTEEN PERCENT INCREASE.
25 MR. BOGER: I DON'T BELIEVE I HAVE ANY FURTHER
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WOODWORTH - DIRECT
QUESTIONS BASED ON THE PRETRIAL OTHER, IF THE COURT HAS FURTHER
QUESTIONS OF DR. WOODWORTH, WE OF COURSE WELCOME THEM.
THE COURT: TOMORROW I WILL HAVE A MILLION. I CAN'T
THINK OF ANY RIGHT NOW.
MAYBE MS. WESTMORELAND HAS SOME SHE WANTS TO ASK.
MS. WESTOMORELAND: NO, YOUR HONOR, I DON'T HAVE ANY I
WISH TO ASK.
THE COURT: IF I UNDERSTAND GOING BACK TO THE ONE
EXHIBIT, MR. BOGER, THAT YOU SHOWED ME WHICH IS~--
MR, BOGER: GW 8.
THE COURT: THE ONE WITH THE CURVES IN IT.
MR, BOGER: THERE ARE SEVERAL WITH CURVES. I THINK IT
STARTS WITH GW 6.
THE COURT: SIX YOU SHOWED ME I THINK FIRST. TALK TO
ME ABOUT THE LOGISTICS METHOD. I CAN SEE IT IS ABLE TO SHOW A
CURVE SO THAT THE LINE BY CURVING CAN FIT THE DATA MORE
CAREFULLY AT GIVEN POINTS ON THE AGGRAVATION SCALE. AM I RIGHT
SO FAR?
THE WITNESS: THAT IS A FAIR STATEMENT.
THE COURT: BUT ARE ALL OF THE OTHER CONCEPTS THE SAME}
THE WITNESS: YES.
THE COURT: THERE IS NO DISTINQUISHING BETWEEN PRECISE
FACTORS; YOU HAVE THROWN ALL OF THE FACTORS IN THE POT AND YOU
ARE DISTINQUISHING BETWEEN CASES OF LIKE AGGRAVATION AND NOT
BETWEEN CASES OF LIKE FACTORS?
>
— —— — — —— —
101
WOODWORTH —- DIRECT
1 THE WITNESS: THAT IS CORRECT. I KNOW YOU PROBABLY
2 | WON'T WANT TO TEACH ME AND I AM NOT SURE I WANT TO LEARN BUT THE
3 | ONE THING THAT TROUBLES ME SOME STILL IS THE DERIVATION OF THE
4 | COEPFICIENTS ALGEBRAICALLY AND YOU SAY IT SOLVES FOR THEM
. 5 | SIMULTANEOUSLY AND IT BEGINS WITH SOMETHING WITH GUESS.
6 THE WITNESS: NO. IT DOESN'T. I WAS CONCEPTUALIZING.
7 | 1 CAN EASILY WRITE DOWN THE ALGEBRA.
8 THE COURT: . COULD YOU TAKE A BIVARIATE OR TRIVARIATE
9 | EXAMPLE AND WALK THROUGH NUMBERS, IS THAT THEORETIALLY POSSIBLE}
10 MR. BOGER: YOU MEAN ONE WITH THREE VARIABLES, FOR
11 | EXAMPLE?
12 THE COURT: YES. I DON'T KNOW WHAT IS INVOLVED SO I
13 | DON'T KNOW WHAT I AM ASKING YOU TO DO.
14 THE WITNESS: I CAN DO IT WITH A LITTLE ARM WAVING. I
15 | MIGHT NOT HAVE THE STAMINA TO DO THE ARITHMETIC, YOUR HONOR, BUT
16 | I WILL SEE WHAT I CAN DO.
17 MR. BOGER: LET ME MARK GW 13, ANOTHER PAGE.
18 THE COURT: ALL RIGHT.
19 THE WITNESS: WELL FIRST OF ALL LET ME MAYBE GO ONE
; 20 | STEP FURTHER TO GIVE YOU THE MATHEMATICAL PRINCIPLE BY WHICH
‘ 21 | THESE REGRESSION COEFFICIENTS ARE DERIVED AND THAT'S == LET HE
22 | WRITE DOWN THE DATA. THE DATA CONSISTS OF Y VARIABLE AND LET MA
23 | USE TWO X VARIABLES.
24 THE COURT: ALL RIGHT.
25 THE WITNESS: AND I WILL MAKE THEM BOTH DICHOTOMOUS
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102
WOODWORTH - DIRECT
BECAUSE THAT 1S MOSTLY WHEAT WE ARE DEALING WITH.
SUPPOSE WE HAVE TEN CASES AND X VARIABLES ARE LET'S SAY
PERHAPS TWO ZEROS, PERHAPS, SOMETHING LIKE THAT. AND THEN FOR
THE Y VARIABLES LET'S SAY WE GOT -- WE GOT THOSE OUTCOMES. ALL
RIGET. SHALL I READ THESE OFF ON THE RECORD?
FIRST OF ALL, CONCEPTUALLY THEY EAD TO FIT THIS
EQUATION BY WHAT IS CALLED LEAST SQUARES AND WHAT WE DO THERE 13
SET UP THE EQUATION IN WHICH REGRESSION COEFFICIENTS ARE
UNKNOWN, YOU TAKE THE Y VALUE MINUS Bl X1 MINUS B2 X2, AND
SQUARE IT AND ADD IT UP OVER ALL THE CASES. AND THIS IS THE
COMBINATION OF Y MINUS Bl X1 MINUS B2 X2. Bl AND B2 ARE
UNKNOWN. WE DON'T KNOW THEM YET, BUT WHAT WE WANT TO DO IS MAKE
THIS AS SMALL AS POSSIBLE. THIS PORTION RIGHT HERE IS THE "U"
TERM. IT'S THE DEVIATION BETWEEN THE SYSTEMATIC PART OF THE
MODEL AND THE Y PART.
EXCUSE ME I LEFT OFF THE INTERCEPT, SO WHAT WE WOULD
LIKE DO 1S MAKE THIS SUM OP SQUARES AS SMALL AS POSSIBLE.
NOW, THE WAY THAT WE ARE TAUGHT IN CALCULUS CLASS IS TG
TAKE THE DERIVATIVE AND SET IT EQUAL TO ZERO. SO WHAT WE DO IS
TAKE THE PARTIAL DERIVATIVES OF REGRESSION WITH RESPECT TO A AND
Bl AND B2 AND GIVES US THREE DIFFERENT DERIVATIVES. WE SET
THOSE BQUAL TO ZERO AND THAT GIVES US THREE PQUATIONS WITH THREE
UNKNOWNS AND THE UNKNOWNS BEING THE REGRESSION COEFFICIENTS FROM
THE INTERCEPT.
OW TO WRITE THIS DOWN ALGEBRAICALLY-- DO I NEED TO
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1 GIVE IT A NUMBER IF I TURN THE PAGE?
2 THE COURT: CONTINUATION OF THE SAME.
3 THE WITNESS: ALGEBRA LOOKS LIKE THIS. WE CONSTRUCT A
4 SYSTEM OF EQUATIONS WE GET BY THE LEAST SQUARES ANALYSIS, !
' 5 LOOKING LIKE THIS. WE =-- SEE IF I CAN GET THIS OFF THE TOP OF
6 MY HEAD. WE FORM THE SUMMATION OF -- THAT IS ONE EQUATION.
7 THE SECOND EQUATION IS AND THE THIRD EQUATION. SC THE
8 LEAST SQUARES PRINCIPLE WHICH IS DERIVED AT TARING THE
9 DERIVATIVE -OF THIS SUM OF THE SQUARES WITH RESPECT TO THE
10 UNKNOWNS, NAMELY THE INTERCEPT OF THE TWO SLOPES AND THEN
1} SETTING THOSE DERIVATIVES EQUAL TO ZERO GIVES US A SET CF
12 SIMULTANEOUS EQUATIONS, WE HAVE THREE UNKNOWNS, A, Bl AND B2.
13 EVERYTHING ELSE ABOUT THIS EQUATION IS KNOWN.
14 FOR EXAMPLE I CAN FILL IT IN. N STANDS FOR THE NUMBER
13 OF CASES, SO THIS EQUATION BECOMES A TIMES SIX PLUS Bl TIMES THE
16 SUM OF X1. AND THE SUM OF X1 IS ZERO PLUS ZERO PLUS ZERO PLUS
17 ONE PLUS ONE PLUS ONE IS THREE. Bl TIMES THREE PLUS B2 TIMES
18 THE SUM OF X2 WHICH IS FOUR EQUALS THE SUM OF Y WHICH IS THREE.
19 SO THERE IS THE EQUATION THAT HAS THREE UNRNOWNS. SO THAT IS
v 20 EQUATION CONE. |
% 21 EQUATION TWO IS A TIMES 3, THE SUM OF THE X'S, PLUS Bl
22 TIMES THE SUM OF THE SQUARES CF THE X'S AND THAT IS ZERO SQUARED
23 PLUS ZERO SQUARED PLUS ZERO SQUARED PLUS ONE SQUARED PLUS ONE
24 SQUARED PLUS ONE SQUARED AND THAT COMES TO THREE PLUS B2 TIMES
25 THE SUM OP %1 TIMES X2. Xl TIMES X2 IS 2ERO, ZERO, ZERO, ZERO,
AY
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WOODWORTH - DIRECT
ONE, ONE. SO WE TAKE X1 TIMES X2 AND WE ADD UP ALL OF THOSE
PRODUCTS WE ARE GOING TO GET TWO, ONE FROM HERE AND ONE FROM
HERE, SO THAT IS B2 TIMES TWO, EQUALS THE SUM OF X1 TIMES Y.
X1 TIMES Y IS ZERO, ZERO, ZERO, ZERO, AND TWC ONES AGAIN. SO
THAT 1S BQUAL TO TWO. THERE ARE TWO OF OUR THREE EQUATIONS.
THE THIRD EQUATION I SHOULD BE ABLE TO DO WITHOUT
FLIPPING, THE SUM OF X2, UP HERE THAT IS FOUR PLUS Bl TIMES THE
SUM OF X1 TIMES X2, THAT'S TWO; AND B2 TIMES THE SUM OF X2
SQUARED. AND X2 SQUARED ADDS UP TO FOUR AND THAT IS BQUAL TO
THE SUM OP THE PRODUCTS OF X2 TIMES Y WHICH IS ZERO, ZERO, ONE
PLUS ONE PLUS ONE AND THAT'S THREE. SO NOW WE HAVE THE SYSTEM
OF EQUATION SOLVED. THREE EQUATIONS AND THREE UNKNOWNS. WE USE
STANDARD ALGEBRA TO SOLVE THEM SIMULTANEOUSLY WITH THE INTERCEPT
CF THE TWO SLOPES.
NOW THERE IS A FORMULA THAT YOU WILL FIND IN ANY -- A
LOT OF STATISTICS BOOKS WHICH I CAN WRITE THIS WAY. THIS IS IN
MATRIX AND VECTOR NOTATION. YOU TAKE THE SUM OF PRODUCTS OF X
WITH ITSELF TIMES A VECTOR CONTAINING THE COEFFICIENTS A, Bl AND
B2 AND SET THAT EQUAL TO THE SUM OF PRODUCTS OF X AND Y. THAT
1S OUR SYSTEM EQUATION. THAT IS THE WAY IT IS WRITTEN IN THE
TEXTBOOK.
BUT OPERATIONALLY WHAT IT BOILS DOWN TO AND I THINK YOU
CAN SEE HOW TO EXTEND THIS FORMULA BECAUSE THE GENERAL PATTERN
IS YOU HAVE SUMS ACROSS THE TOP ROLL AND THE BODY OF THE TABLE
YOU EITHER BAVE SQUARES RUNNING DOWN THE DIAGONAL OR SOME OF THE
105
WOODWORTH - DIRECT
1 PRODUCTS OF THE DIAGONAL, SO IT IS A SYSTEMATIC PATTERN. THE
2 COMPUTATION IS LABORIOUS.
3 THE COURT: I SEE WHERE IT WAS.
4 THE WITNESS: I WAS ASSIGNED TO DO A TEN VARIABLE
v 5 REGRESSION BY HAND WHEN I WAS A GRADUATE STUDENT. IT TOOK ME
6 THE BETTER PART OF A WEEK. NOW IT IS DONE IN THE TWINKLING OF
7 THE EYE AND THERE ARE SOME POCKET CALCULATORS THAT CAN HANDLE
8 THE SYSTEM OF THE TEN VARIABLES, |
9 THE COURT: HAVING SOLVED THOSE THREE EQUATIONS HAVE
10 YOU THEN GOT YOUR COEFFICIENTS?
11 THE WITNESS: YES. THAT GIVES YOU COEFFICIENTS. THE
12 ONLY MODIFICATION I MIGHT ADD AT VARIOUS POINTS WE MENTIONED
13 WEIGHTED REGRESSION. IN THAT CASE WHEN WE FORM THESE SUMS HERE
14 WE WOULD WEIGH EACH CASE USING THE WEIGHING SCHEME.
15 THE COURT: THAT IS TO GET YOUR WEIGHTED SAMPLE?
16 THE WITNESS: YES. AND THAT IS REFERRED AS
17 GENERALIZING LEAST SQUARES.
18 THE COURT: BUT YOU HAVE NOT WEIGHTED THE FACTOR, YOU
L 19 HAVE WEIGHTED THE CASE IN WHICH THE FACTOR OCCURS?
4 20 THE WITNESS: THAT IS RIGHT. EVERY TIME WE GET TO THAT
Y, 21 CASE IN THE SUMMATION WE MULTIPLY BY A WEIGHT.
22 THE COURT: I WILL TAKE IT HOME AND LET MY SON SOLVE
23 IT.
24 THE WITNESS: I MAY NOT HAVE CONSTRUCTED IT SO IT IS
25 SOLVABLE. IT MAY BE COLINEAR.
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WOODWORTH - DIRECT
THE COURT: I DON'T KNOW IF I CAN TELL ANYTHING BY
STUDYING IT OR NOT. I WOULD LIKE TO SEE WHAT IS GOING TO BE
PRODUCED BY A NUMBER.
ANYTHING ELSE?
MR. BOGER: NO, YOUR HONOR. I GUESS WE MOVE GW 13 INTQ
EVIDENCE FOR ILLUSTRATIVE PURPOSES. i
THE COURT: FINE, IT WILL BE ADMITTED.
ANYTHING ELSE, MS. WESTMORELAND?
MS, WESTMORELAND: NO, YOUR HONOR.
THE COURT: HAS THIS OCCASIONED EITHER SIDE TO WANT TO
FILE ANY MORE BRIEFS THAN WHAT HAS BEEN FILED?
MR. BOGER: YOUR HONOR, I AM AFRAID IT MIGHT ON OUR
PART. I HATE TO BURDEN THE COURT WITH ADDITIONAL BRIEFS.
THE COURT: HAVE YOU FILED YET?
MS. WESTMORELAND: NO, YOUR HONOR. WE CALLED LAST WEEK
AND OUR IS DUE THIS FRIDAY,
THE COURT: I COULD PUT HER OFF SO WE WON'T END UP WITH
ONE REPLY FROM HER IF YOU CAN HAVE -- DO YOURS IN A FAIRLY SHORT
TIME.
MR. BOGER: I HAVE NO AVAILABLE TIME UNTIL NEXT
TUESDAY,
THE COURT: WHEN CAN YOU DO IT REASONABLY?
MR. BOGER: BETWEEN NEXT TUESDAY AND THE WEEK
FOLLOWING. NEXT TUESDAY IS THE 25TH. I HAVE ONE OTHER
EVIDENTIARY HEARING AND A COUPLE OF OTHER MAJOR THINGS I HAVE TQ
r— | —o—— v—...g——— | — ——
107
WOODWORTH - DIRECT
1 | PREPARE FOR THIS WEEK AND 1 HAVE AN ORAL ARGUEMENT IN THE
2 | ELEVENTH CIRCUIT NEXT MONDAY. STARTING NEXT TUESDAY WITHIN THE
3 | NEXT WEEK AFTER THAT UNTIL THE PIRST OF NOVEMBER I CAN GET IN A
x 4 | BRIEF.
y 5 THE COURT: SEND OUT YOUR SUPPLEMENTAL AND THEN I WILL
6 | GIVE YOU A TOTAL OF A WEEK FROM RECEIPT OF HIS SUPPLEMENTAL IN
7 | WHICH TO PILE YOUR WHOLE THING.
8 MS, WESTMORELAND: THAT IS FINE.
9 MR. BOGER: THAT IS FINE, YOUR HONOR.
10 THE COURT: THANK YOU VERY MUCH. WE WILL BE IN RECESS
11 | UNTIL 9:30 A.M.
12 ® * %
13 (RECESS.)
14 *
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1 CZRTIFICATE
2
3 | UNITED STATES OF AMERICA
4 | STATE OF GEORGIA
5
6 I, KIMBERLY C. BRAMLETT, OFFICIAL COURT REPORTER
p 7 | OF THE UNITED STATES DISTRICT COURT FOR THE NORTHERN DISTRICT
8 OF GEORGIA, DO HEREBY CERTIFY THAT THE FOREGOING 105 PAGES
9 |‘ CONSTITUTE A TRUE TRANSCRIPf OF PROCEEDINGS HAD BEFORE THE
12 | SAID conne HELD IN THE CITY OF ATLANTA, GEORGIA, IN THE
11 | MATTER HEREIN STATED.
12 IN TESTIMONY WHEREOF I HEREUNTO SET MY HAND ON
13 | THIS THE DAY OF , 1983.
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18 KIMBERLY C. BRAMLETT
OFFICIAL COURT REPORTER
> 19 NORTHERN DISTRICT OF GEORGIA
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