Both t-test and ANOVA rely on the Central Limit Theorem, which requires that the data follow normal distribution unless sample size is large (in which case the sample mean will follow normal distribution even if the population doesn’t). If this condition is far from being satisfied, then one should use non-parametric tests instead.
If the data is ordinal rather than scale-level, then the non-parametric tests should be used as well. Likert scale is an example of ordinal data.
Note: The non-parametric tests Change the wordings of the hypotheses to compare the population median rather then population mean.
SPSS has a procedure under Nonparametric Tests that will automatically choose the appropriate test based on the level of measurement of your data.
However, SPSS has a bug (feature?) that if the variable being tested is ordinal level, then some of the nonparametric tests may not work. If you see “Unable to compute” in the output, then try to set the level of measurement of the variable temporarily to scale. The test should work this way. Then you change the level back to ordinal after the test.
Analyze -> Nonparametric Tests -> One Sample -> Choose Customize analysis in the Objective tab -> Choose the Test Fields in the Fields tab -> Choose Compare median to hypothesized (Wilcoxon signed-rank test) and specify the Hypothesized median value in the Customize tests in the Settings tab -> Click Run -> Double-click the results table -> Check the p-value on the right.
Analyze -> Nonparametric Tests -> Independent Samples -> Choose Automatically compare distributions across groups -> Choose the Test Fields and the Groups in the Fields tab -> Choose Automatically choose the tests based on the data in the Settings tab -> Click Run -> Double-click the results table -> Check the p-value on the right.
SPSS will automatically choose Mann-Whitney Test for two-sample comparisons (analogous to independent-samples t-test).
Follow the same procedures as above for two independent samples. SPSS will choose the Kruskal-Wallis Test (analogous to ANOVA) automatically.
It will also run the post hoc tests if the null hypothesis is rejected. The results can be found by double-clicking the results table. (From SPSS 26 and above, the results will be shown in the output window directly.)
Analyze -> Nonparametric Tests -> Related Samples -> Choose two variables into Test Fields for pre-post comparison -> Click Run -> Double-click the results table -> Check the p-value on the right
SPSS will automatically run the Wilxocon signed-rank test.
Jamovi puts the t-tests and their non-parametric counterparts under the same procedures. For normally distributed continuous data, choose t-test, which will test the means. For non-normally distributed continuous data, or for ordinal data, choose the non-parametric test, which will test the medians. Normality check can be found under assumption checks in each of the procedures.
The non-parametric version of one-way ANOVA is in its own menu. Please see the procedures below for details.
Follow the same procedures of One Sample T-test except to select Wilcoxon rank test under Tests option.
Follow the same procedures of Independent-Samples T Test except to select Mann-Whitney U Test under Tests option.
Analyses -> ANOVA -> (under Non-Parametric) -> One-Way ANOVA -> Select the dependent variables into the Dependent Variables box -> Select the grouping variable.
Select DSCF pairwise comparison.
Jamovi will run the Kruskal-Wallis Test in this case.
Follow the same procedures of One Sample T-test except to select Wilcoxon rank test under Tests option.