ABSTRACT
In this chapter, we will use a number of statistics to compare two groups or samples. In Problem 9.1, we will use a one-sample t test to compare one group or sample to a hypothesized population mean. Then, in Problems 9.2 – 9.6, we will examine two parametric and two nonparametric/ordinal statistics that compare two groups of participants. Problem 9.2 compares two independent groups (between-groups design), males and females, using the independent samples t test. Problem 9.3 uses the Mann-Whitney nonparametric test, which is similar to the independent t test. Problem 9.4 is a within-subjects design that uses a paired samples t to compare the average levels of education of students’ mothers and fathers. Problem 9.5 will also use the paired t but, in this case, to check the reliability of a repeated measure, namely, the visualization test and visualization retest. Problem 9.6 shows how to use the nonparametric Wilcoxon test for a within-subjects design. The top right side of Table 9.1 distinguishes between between-groups and within-subjects designs. This helps determine the specific statistic to use. The other determinant of which statistic to use has do with statistical assumptions. If the assumptions are not markedly violated, you can use a parametric test. If the assumptions are markedly violated, one can use a nonparametric test, which does not have the same assumptions, as indicated by the left side of Table 9.1. Another alternative is to transform the variable so that it meets the assumptions. That is beyond the scope of this book, but is covered in Leech et al. (in press). Note that chi-square was demonstrated in Chapter 7 so we will not use it here. The McNemar test, which is rarely used, will not be demonstrated, but is available in SPSS (see Fig. 9.6). Table 9.1. Selection of an Appropriate Inferential Statistic for Basic, Two Variable Difference Questions or Hypotheses
Dependent Variable Is Nominal or
(dichotomous) Data
Counts CHI-SQUARE MCNEMAR
In the next chapter, you will learn about ANOVA (F), which can be used to look at differences between the means of two or more groups. You might ask, why would you compute a t test when one-way ANOVA can be used to compare two groups as well as three or more groups? Because F = t2, both statistics provide the same information. Thus, the choice is mostly a matter of personal preference. However, t tests can be either one tailed or two-tailed, while one cannot have one-tailed ANOVAs. Thus, if you have a clear directional hypothesis that predicts which group will have the higher mean, you may want to use a t test rather than one-way ANOVA when comparing two groups. In addition, the t test output provides an adjustment to deal with the problem of unequal variances, whereas, the remedy for such problems in ANOVA may be less satisfactory. Finally, it is just more customary to use a t test if one is comparing only two groups. You must use ANOVA if you want to compare three or more groups. • Retrieve hsbdataB from your data file.
