Hi Yohannes Joressa Wordofa ,

I think, you have different possibilities.

For the decision if you should use a MANOVA or not:

You would use the MANOVA, if your hypothesis is meant for all skill aspects together and you want to trst it globally for the whole construct.

If not, so if you are interested in the result for esch skill component on its own, then you need seperate analyses for each parameter and would not use a MANOVA.

For the normality assumption:

With your sample size of 45 per group, I think it will be no problem to assume that the analysis is robust against deviations from normality. So you probably will be alle robuste parametric methods.

And then you should decide, if you want to use the Post measures as dependent variable and control for the pre measures( this would be an ANCOVA). Or if you want to investigate the change in the parameter over time. Then you would run a Mixed ANOVA with group and time effect and interaction. This decision depends on your exact hypothesis.

I hope, this helps. 😊

Best regards,

Daniela

If you have a 2 (group) x 2 (measure) design the most accurate statistical analysis is the mixed ANOVA. With this test you can compare measurements and groups at the same time. If the results indicate that there is no interaction effect, then you could perform t-tests, as long as there is significance in the main effects. You have to do this procedure for each variable. If you use RStudio there are packages that allow you to use robust tests to correct for normality violations.

I think performing a MANOVA would be too much and the assumptions are more strict.

I hope this helps you.

If this is a randomised experiment then I'd recommend ANCOVA. It's a simpler analysis really and more sensitive as a test of differences in pre and post between groups.

Expressed as a formula (R style)

reading_post ~ reading_pre + group

You can also test of the covariate has the same effect in each group:

reading_post ~ reading_pre + group + reading_pre:group

That's if testing them one at a time is fine. As for normality of the reading scores. Who cares? What matters is the approximate normality of the model residuals (and in practice that's more likely with the ANCOVA because if the non-normality is in both pre and post scores). Run the model and plot the residuals. Check for influential values with something like Cook's distance.

If you want a joint analysis of all three that's trickier but I'd actually just suggest a repeated measures ANCOVA treating reading score type as a within factor. However, that doesn't seem to be what you need - just run the separate tests for each reading score if that's what you want. If you need to adjust for multiple tests use a correction like Holm or Hochberg for the family wise error rates.

I would like to thank for your response.