ABSTRACT
In Chapter 10, the independent samples t-test and paired samples t-test were described. These tests are used for comparing numerical scale dependent variables between two independent and two related samples respectively. Chapter 11 described the one-way ANOVA test and the repeated measures ANOVA test which are used for comparing numerical scale dependent variables between three or more independent and three or more related samples respectively. These t-tests and ANOVA tests are parametric tests that are calculated using the measured values. The tests have assumptions that should be satisfied by the data they are applied to. The dependent variables should be interval or ratio scale variables, they should be normally distributed and there should be similar variances for the dependent variable between samples. The repeated measures ANOVA test has the additional assumption of sphericity which is homogeneity of variances and covariances between samples. The scale of measurement of the dependent variable can be checked by examining the definition of the variable. Normality is tested using either the Shapiro–Wilk test or the Kolmogorov–Smirnov test as described in Chapter 6. Homogeneity of variances can be tested using Levene’s test as described in Chapter 10 while sphericity is tested using Mauchly’s test as described in Chapter 11. Where the data fail to satisfy the assumptions of the given test and there are no transformations of the data that will result in the assumptions being satisfied, it may be necessary to use an alternative non-parametric test to compare the samples. Table 14.1 shows the alternative non-parametric tests that should be used in different comparisons. Parametric and alternative nonparametric tests https://www.niso.org/standards/z39-96/ns/oasis-exchange/table">
Comparison
Parametric Test
Non-Parametric Test
2 independent samples
Independent t-test
Mann-Whitney U test
2 related samples
Paired t-test
Wilcoxon Signed Ranks test
3+ independent samples
One-way ANOVA
Kruskal-Wallis H test
3+ related samples
Repeated measures ANOVA
Friedman test
