Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SECTION 17.2 | An Example of the Chi-Square Test for Goodness of Fit 567
LEARNING CHECK
1. Occasionally researchers will transform numerical scores into nonnumerical
categories and use a nonparametric test instead of the standard parametric statistic.
Which of the following is not a reason for making this transformation?
a. The original scores have very high variance.
b. The original scores form a very large sample.
c. The original scores contain an undetermined or infinite value.
d. The original scores violate an assumption of the parametric test.
2. The data for a chi-square test for goodness of fit are called _________.
a. observed proportions
b. observed frequencies
c. expected proportions
d. expected frequencies
3. Data from a recent census indicates that 54% of the adults in the city are women.
A researcher selects a sample of n = 200 people who have been selected for
jury duty during the past month to determine whether the gender distribution for
jurors is significantly different from the distribution for the general population.
For this test, what is the expected frequency for female jurors?
a. 50
b. 54
c. 100
d. 108
ANSWERS
1. B, 2. B, 3. D
17.2 An Example of the Chi-Square Test for Goodness of Fit
LEARNING OBJECTIVES
4. Define the degrees of freedom for the chi-square test for goodness of fit and locate
the critical value for a specific alpha level in the chi-square distribution.
5. Conduct a chi-square test for goodness of fit.
■ The Chi-Square Distribution and Degrees of Freedom
It should be clear from the chi-square formula that the numerical value of chi-square is a
measure of the discrepancy between the observed frequencies (data) and the expected frequencies
(H 0
). As usual, the sample data are not expected to provide a perfectly accurate
representation of the population. In this case, the proportions or observed frequencies in
the sample are not expected to be exactly equal to the proportions in the population. Thus,
if there are small discrepancies between the f o
and f e
values, we obtain a small value for
chi-square and we conclude that there is a good fit between the data and the hypothesis (fail
to reject H 0
). However, when there are large discrepancies between f o
and f e
, we obtain a
large value for chi-square and conclude that the data do not fit the hypothesis (reject H 0
).