24 Alternatives to the One-Way ANOVA
In the previous section, we noted some possible alternatives to ANOVA if we violate the assumptions. Here’s the table showing those alternatives, again:
| Normality: satisfied | Normality: not satisfied | |
| Homogeneity of the variance: satisfied | One-way ANOVA (using the ANOVA function) | Kruskal-Wallis test or robust ANOVA (Walrus package) |
| Homogeneity of the variance: not satisfied | Welch’s F-test (using the one-way ANOVA function) | Kruskal-Wallis test or robust ANOVA (Walrus package) |
With our clinical trial data, given that we have such a small sample size, I would go to a non-parametric test, which in this case would be the Kruskal-Wallis test. It’s easy to obtain this in jamovi by selecting ANOVA and then, under Non-Parametric, One-Way ANOVA Kruskal-Wallis. You can also ask jamovi to give you the effect size and some pairwise comparisons.
Write this up the same way as you would write-up the regular one-way ANOVA, but reporting Χ2 (chi-squared) instead of F, ε2 (epsilon-squared) for effect size for the ANOVA, and W instead of t for your post hoc tests.
Finally, if you need to run Welch’s test, select ANOVA and then one-way ANOVA, and under Variances click the box Don’t assume equal (Welch’s). You will see that the result is a bit limited. You cannot get a measure of effect size for the ANOVA and you cannot run contrasts. If you need these, your best bet will be to go back to the regular ANOVA menu to obtain them. You could report the Welch’s one-way ANOVA but then report the effect size and contrasts from the ANOVA results. It is not ideal but it will get you the information you need. For the post hoc tests, there are some other options presented that we did not see in the regular ANOVA menu. In particular, if you have unequal variances, you will want to use the Games-Howell test.
