Chapter 17

I. Comparison of parametric and nonparametric tests

A.Nonparametric tests do not test hypotheses about population parameters, unlike all of the inferential statistical tests that we have considered. For example, z, t, and ANOVA are all parametric tests because they test hypotheses about the population mean.

B.Parametric tests require that the DV be measured at an interval or ratio level of measurement. The DV for nonparametric tests can be either nominal or ordinal. Often, as with the Chi-square test, the DV is a nominal-- a simple classification of the frequency of occurrence of some characteristic. Thus, subjects may not need to be "measured" at all.

C.Parametric tests have strict assumptions about the underlying distribution of the population on the DV. Nonparametric tests usually have few assumptions about the underlying distribution of the population on the DV. Sometimes, nonparametric tests may not have any assumptions about the underlying distribution of the population on the DV, in which case they are known as distribution-free tests.

II. Chi-square test

A.Chi-square is a nonparametric test for testing hypotheses about the proportions (relative frequency) of a sample to a population.

1.Chi-square test for goodness-of-fit - used to compare proportions on one IV to hypothesized population proportions.
2.Chi-square test for independence - used to test hypotheses about whether proportions on two IVs in sample came from the same population (Ho: are not independent) or whether they came from different populations (H1: are independent).

B. Assumptions for the Chi-square tests

1. Random sample
2.Independence of observations (i.e., no subject can be counted as belonging to more than one category).
3.Minimum expected frequency - expected frequency for any category should be at least 5.