Levin and Fox
Chapter 12
Statistics for Nonparametric
Measures
Parametric measures
1. All of the statistical tests we have examined
thus far require:
a) Interval level data
b) Normality in the population (or at least large
samples so that the sampling distribution of
means is normal)
Nonparametric tests
What about social researchers who cannot
employ a parametric test, that is, who either
cannot….
a. Assume normality?
b. Does not work with large numbers of cases?
c. Not using measures that are interval?
Nonparametric tests
• Nonparametric tests make less stringent
demands, but are less powerful tests than
their parametric counterparts.
• An researchers is more likely to reject the null
hypothesis when using a parametric test than
when using a nonparametric test.
Examples of nonparametric tests
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One-Way Chi-Square (nominal data)
Two-Way Chi-Square (nominal data – 2 variables)
The Median Test (ordinal data)
Spearman’s Rank-Order Correlation (ordinal)
Goodman’s and Kruskal’s Gamma (ordinal)
Phi coefficient (nominal – 2 variables)
Contingency coefficient (nominal – more than 2)
Extra Credit Homework
• Two-Way Chi-Square (chapter 9)
• Convert Chi-Square into a Phi Coefficient
(ch.12)
• Check your Chi-Square statistic using the chiquare1.sav file on the webpage to check your
work.
• Replaces a low scoring homework