jamovi

For the case of the above mentioned test, the normality assumption is checked (just once) for the selected dependent variable.

However, I am quite sure that the normality should be checked for the two groups separately, i.e. as it is done and implemented in Jamovi when one does an exploration of a variable using 'Analyses -> Exploration -> Descriptives'. If one chooses (there) one variable under 'Variables' to be analyzed and a factor (which has two possible levels) under 'Split by' and if Normality is then checked (under Statistics) as well as the Q-Q Plot (under diagrams), then the Shapiro-Wilk p-values as well as the Q-Q Plots are shown for the two factor levels separately.

Is there a specific reason why under 'Independent Samples t-Test' the normality assumption is not checked for the two factor levels separately?

Thanks for your response and kind regards, Thomas

I believe it's the residuals for the entire model that need no be normally distributed. https://statistics.laerd.com/statistica ... e%20result.

Also, since the Shapiro-Wilk test is a significance test, the power for detecting non-normality will be higher when testing the residuals as one set, since the N will be relatively large, as opposed to testing each group separately with relatively small Ns.

One problem I see with testing the all residuals together is that each group could could be perfectly normal while their variances could be unequal. That inequality of variances will make the QQ plot deviate from perfect diagonality despite despite each distribution being normal. I think one solution would be standardize the scores in each group, separately, prior to conducting a normality assessment of all the residuals together.

My experience is that most people want to test the residuals all together, and a small proportion of people want to test the residuals of the groups separately (for that, we provide the facility in descriptives that you describe).

jonathon

I would agree that, provided we can assume the variances to be the same, then the most appropriate approach is to check for normality in the residuals from all groups combined, after fitting the model (not in the original variable, where differences in group mean would make the distribution look less normal). This provides the most power/sensitivity for testing the assumption of normality.

The same applies to both the t test and one-way anova (and any other linear model for that matter). I would only consider looking for normality in each group separately if I had good evidence of a difference in variance.