User Guide

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Chapter 34
Chi-Square T
est
The Chi-Squ
are Test procedure tabulates a variable into categories and computes a
chi-square statistic. This goodness-of-fit test compares the observed and expected
frequencies in each category to test either that all categories contain the same
proportion
of values or that each category contains a user-specified proportion of
values.
Examples. The chi-square test could be used to determine if a bag of jelly beans
contains e
qual proportions of blue, brown, green, orange, red, and yellow candies.
You could also test to see if a bag of jelly beans contains 5% blue, 30% brown, 10%
green, 20% orange, 15% red, and 15% yellow candies.
Statistic
s.
Mean, standard deviation, minimum, maximum, and quartiles. The number
and the percentage of nonmissing and missing cases, the number of cases observed
and expected for each category, residuals, and the chi-square statistic.
Data. Use
ordered or unordered numeric categorical variables (ordinal or nominal
levels of measurement). To convert string variables to numeric variables, use the
Automatic Recode procedure, available on the Transform menu.
Assumpti
ons.
Nonparametric tests do not require assumptions about the shape of
the underlying distribution. The data are assumed to be a random sample. The
expected frequencies for each category should be at least 1. No more than 20% of the
categor
ies should have expected frequencies of less than 5.
Figure 34-1
Chi-Square Test output
6 18.8 -12.8
33 18.8 14.2
9 18.8 -9.8
17 18.8 -1.8
22 18.8 3.2
26 18.8 7.2
113
Blue
Brown
Green
Yellow
Orange
Red
Total
Observed
N
Expected
N
Residual
Color of Jelly Bean