Chapter5p2Lecture

8/14/2019 Chapter5p2Lecture

1/3

Chap. 5, part II, page 1

Chapter 5, part II: Comparisons among several samples

Testing Equality in a Subset of Groups: The Spock Conspiracy Trial Data.

In 1968, Dr. Benjamin Spock was tried in the United States District Court of Boston on charges

of conspiring to violate the Selective Service Act by encouraging young men to resist the draftfor Vietnam. The defense challenged the jury selection, claiming that women had beensystematically under-represented. The Spock jury had no women.

Juries in Boston are selected in 3 stages. From the city directory, the Clerk of the Court selects300 names at random. Before the trial, a venire of 30 or more jurors is selected from the 300names, according to law, at random. The final jury is selected from the venire in a nonrandomprocess allowing each side to exclude certain jurors for a variety of reasons.

The Spock defense pointed to the venire for their trial, which contained only one woman. Thatwoman was released by the prosecution, resulting in an all male jury. The defense argued that the

judge in the trial had a history of venires in which women were under-represented, contrary tolaw.

The data consist of the percent women in the venires of Spocks judge and six other Boston areaDistrict Court judges. Here are the summary statistics:

Descriptives

percent

9 14.6222 5.03879 1.67960 10.7491 18.4954 6.40 23.105 34.1200 11.94182 5.34054 19.2923 48.9477 16.80 48.906 33.6167 6.58222 2.68718 26.7090 40.5243 27.00 45.609 29.1000 4.59293 1.53098 25.5696 32.6304 21.00 33.802 27.0000 3.81838 2.70000 -7.3068 61.3068 24.30 29.706 26.9667 9.01014 3.67838 17.5111 36.4222 17.70 40.209 26.8000 5.96888 1.98963 22.2119 31.3881 16.50 36.20

46 26.5826 9.17911 1.35339 23.8567 29.3085 6.40 48.90

SPOCK'SABCDEFTotal

N Mean Std. Deviation Std. Error Lower Bound Upper Bound

95% Confidence Interval forMean

Minimum Maximum

Here is the ANOVA table comparing the equal means model to the separate means model:

ANOVA

percent

1927.081 6 321.180 6.718 .0001864.445 39 47.8063791.526 45

Between GroupsWithin GroupsTotal

Sum ofSquares df Mean Square F Sig.


2/3


So, we see that the separate means model is significantly better than the equal means model.Now, the question becomes: Is the venire from Spocks judge significantly different from theother 6, and are the other six basically the same?

Here is the ANOVA table comparing the two means model to the equal means model, where

Spocks venire has parameter 1 and the other venires have mean 0.ANOVA

percent

1600.623 1 1600.623 32.145 .0002190.903 44 49.7933791.526 45

Between GroupsWithin GroupsTotal

Sum ofSquares df Mean Square F Sig.

Now, finally, we want to compare the two-means model to the separate means model. How dowe do this? Remember: SPSS will always use the equal means model as the reduced model. Weneed to calculate the Extra Sum of Squares where the two means model serves as the reducedmodel.

2 7 ESS SSR SSR= =

Then, our F statistic is:

F =

Our rejection decision is then made by comparing this value to the 95 th quantile of theappropriate F distribution, or the value closest to this in the table.

From the table we find,

F =

What is our decision?


3/3


Kruskal Wallis Nonparametric Analysis of Variance

When outliers are present, but the data are thought to be meaningful, one alternative to ANOVAis the Kruskal-Wallis nonparametric analysis of variance. Here, we use the rank transform andthen conduct the F test on the ranks. The test statistic is:

2

1 R

R

KW SSB

=

where 2 R is the sample variance of all n ranks, where n is the number of observations in allgroups.

Results of Kruskal-Wallis Test for the Spock Data

Ranks

9 6.395 33.206 34.009 28.062 23.506 24.089 23.28

46

JudgeSPOCK'SABCDEFTotal

percentN Mean Rank

Test Statistics a,b

21.9656

.001

Chi-SquaredfAsymp. Sig.

percent

Kruskal Wallis Testa.

Grouping Variable: Judgeb.

To perform the KW test in SPSS, go to Analyze Nonparametric K independent samples,and then choose the Kruskal-Wallis test box.

Documents

Chapter5p2Lecture