# Bivariate relationships

```					Crosstabs to Multivariate Regression

Missouri Death Penalty Charges by
Race of Defendant and Race of
Victim, 1978-1996
Research Question
   What causes a capital defendant to get
the death sentence?
Theory
   Death sentence is caused by race of
defendant
   Death sentence is caused by race of
victim
Frequencies

Frequency   Percent
0 Not
Death                9281       94.3
death
Penalty
1 death      562        5.7
Race of 1 white       3199       32.5
defendant 2 black      6644       67.5
Race of   1 white     3544       36.0
victim    2 black     6299       64.0
Model

Race of
Defendant
+

+                    Death sentence

Race of Victim   -
Correlation syntax
   corr death racedef racevic.
Pearson r Correlation Table

Race of    Race of
Death
defendant   victim
Death         1       -.097      -.146
Race of
-.097      1         .810
defendant
Race of
-.146     .810        1
victim
Death by Race of Defendant
death * racedef Crosstabulation

racedef
1.00 white         2.00 black    Total
death    .00 Not      Count                      2913               6368        9281
death        % within
91.1%             95.8%       94.3%
racedef
1.00 death   Count                       286               276         562
% within
8.9%              4.2%        5.7%
racedef
Total                 Count                      3199              6644        9843
% within
100.0%            100.0%     100.0%
racedef
Regression syntax
   regr vars = death racedef /depe =
death/enter.
Regression of Death Penalty
on Race of Defendant

Coefficients a

Standardized
Unstandardized Coefficients     Coefficients
Model                       B            Std. Error          Beta       t            Sig.
1        (Constan
.137          .009                        15.878          .000
t)
racedef                -.048           .005            -.097       -9.629          .000
a. Dependent Variable: death
Death By Victim Race
death * racevic Crosstabulation

racevic
1.00 white         2.00 black    Total
death   .00 Not      Count                      3182               6099        9281
death        % within
89.8%              96.8%       94.3%
racevic
1.00 death   Count                       362               200         562
% within
10.2%               3.2%        5.7%
racevic
Total                Count                      3544              6299        9843
% within
100.0%             100.0%     100.0%
racevic
Death By Victim Race

Coefficients a

Standardized
Unstandardized Coefficients     Coefficients
Model                       B            Std. Error          Beta       t            Sig.
1        (Constan
.173          .008                        20.946          .000
t)
racevic                -.070           .005            -.146   -14.602             .000
a. Dependent Variable: death
Death by Defendant Race by
Victim Race
death * racedef * racev ic Crosstabulation

racedef
racevic                                                  1.00 white         2.00 black    Total
1.00      death   .00 Not          Count                        2671                511        3182
white             death            % within
90.7%              85.3%       89.8%
racedef
1.00 death       Count                         274                88         362
% within
9.3%              14.7%       10.2%
racedef
Total                    Count                        2945               599        3544
% within
100.0%             100.0%     100.0%
racedef
2.00      death   .00 Not          Count                         242              5857        6099
black             death            % within
95.3%              96.9%       96.8%
racedef
1.00 death       Count                          12               188         200
% within
4.7%               3.1%        3.2%
racedef
Total                    Count                         254              6045        6299
% within
100.0%             100.0%     100.0%
racedef
Previous Crosstab Simplifed:
Percent Receiving Death Penalty

Victim
White     Black
Defendant White 8.4%       4.7%
Black   14.7%     3.1%
Pearson r between Defendant
Race and Death by Victim Race

Symmetric Measures

a           b
racevic                                                            Value          Asymp. Std. Error       Approx. T    Approx. Sig .
1.00        Interval by Interval   Pearson's R                          .067                   .019            3.977            .000c
white       Ordinal by Ordinal     Spearman                                                                                         c
.067               .019             3.977           .000
Correlation
N of Valid Cases                                               3544
2.00        Interval by Interval   Pearson's R                         -.018                  .015            -1.438           .151c
black       Ordinal by Ordinal     Spearman                                                                                         c
-.018                  .015            -1.438           .151
Correlation
N of Valid Cases                                               6299
a. Not assuming the null hypothesis.

b. Using the asymptotic standard error assuming the null hypothesis.

c. Based on normal approximation.
Histogram syntax
   sort cases by racevic.
   split file by racevic.
   GRAPH /BAR(GROUPED)=PCT BY
death BY racedef .
Histograms
White Victim                        Black Victim
Race Defendant
100                                100

White
80                                 80                                     Black

60                                 60

40                                 40

20                                 20

0                                  0
Not death           death         Not death           death
death                             death
Multivariate Death on Victim’s
Race and Defendant’s Race

Coefficients a

Standardized
Unstandardized Coefficients     Coefficients
Model                        B            Std. Error          Beta          t            Sig.
1         (Constan
.161          .009                           18.222          .000
t)
racevic                -.095           .008            -.196      -11.530             .000
racedef                  .031          .008                .062        3.662          .000
a. Dependent Variable: death

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