ABSTRACT
This chapter focuses on nonparametric statistics that are analogous to the following parametric tests: correlation between two variables and differences between independent and dependent groups with one sample, two samples, and n samples. The test is analogous to the parametric Pearson product-moment correlation coefficient. Like the Pearson correlation, the limits for the phi coefficient are -1.00 to +1.00. Essentially, the phi coefficient is the Pearson correlation between variables that are dichotomous in nature. Recall the nonparametric tests are low in power, especially when sample sizes are small. A significant chi-square value, like a significant F-ratio in an ANOVA, indicates that significant differences exist among the groups, but, again like the F-ratio, it does not identify which differences are significant. The most fundamental one-sample case occurs when the population sampled is dichotomous. With large samples, the sampling distribution of the obtained value often approximates either a chi-square or a normal distribution.
