In this case I would opt for non-parametric statistics. I am not a huge fan of using different t-tests for different groups, although it can provide insight of course. You can always do a bonferroni correction instead (i.e., as you have 2 tests, use p = .025 instead of p = .05).kaleidoscope wrote: Concerning the two-way ANOVA I conducted I know that generally they tend to be quite robust to slight deviations from normality, however, my levene's test was significant for ANOVA (and for t-test also but I wrote down equal variances not assumed stats for that line, no such line exists for ANOVA, as you're probably aware). I checked the variances for each group and one is 3 times greater than the smallest group variance, I read somewhere that as long as the variance doesn't reach this level that I currently have, ANOVA will remain relatively robust to these deviations. Given that would you suggest that I report t-test statistics instead (with equal variances not assumed) or due to the extent of heterogeneity of variance, elect to use non-parametric statistics? Or use t-test inferential and report means alongside medians for descriptives (as mean for that group will hardly be representative)?
There are different measures for effect size, most common for anova type of analyses is eta (squared). Effect sizes inform you about the magnitude of an effect, so indicate whether or not an observed difference is large.Regarding effect sizes you mentioned, do you mean look at effect sizes for both p values that suggest significance and for those that suggest non-significance? The mean difference from order 1 sample between groups was 2.09 and order 2 =2 so not much in it (but considering the scale was small, I guess it is a large difference given the context?)
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