ABSTRACT
In this chapter, we will use a number of statistics to compare two groups or samples. In Problem 10.1, we will use a one-sample t test to compare one group or sample to a hypothesized population mean. Then, in Problems 10.2-10.5, we will examine two parametric and two nonparametric/ordinal statistics that compare two groups of participants. Problem 10.2 compares two independent groups (between-groups design), males and females, using the independent samples t test. Problem 10.3 uses the Mann-Whitney nonparametric test, which is similar to the independent t test. Problem 10.4 is a within-subjects design that uses a paired samples t to compare the average levels of education of students’ mothers and fathers. Problem 10.5 shows how to use the nonparametric Wilcoxon test for a within-subjects design. The top right side of Table 10.1 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 10.1. 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. (2011). Note that chi-square was demonstrated in Chapter 8 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. 10.6). Table 10.1. Selection of an Appropriate Inferential Statistic for Basic, Two Variable Difference Questions or Hypotheses
Interpretation of Output 10.1 The One-Sample Statistics table provides basic descriptive statistics for the variable under consideration. The Mean SAT Math for the students in the sample was compared to the hypothesized population mean, displayed as the Test Value in the One-Sample Test table. On the bottom line of this table are the t value, df, and the two-tailed sig. (p) value, which are encircled. Note that p = .389, so we can say that the sample (M = 491) is not significantly different from the population mean of 500. The table also provides the difference (M = –9.47) between the sample and population means and the 95% Confidence Interval. The difference between the sample and the population mean is likely to be between +12.29 and –31.22 points. Notice that this range includes the value of zero, so it is possible that there is no difference. Thus, the difference is not statistically significant.
