When to use non-parametric testing with 2X2 within ANOVA?

I am running a within 2X2 ANOVA on SPSS. I have tested for normality prior and realised some of my conditions within a variable aren’t normally distributed. My question is say 1/4 conditions isnt normally distributed will I do a non-parametric test or ANOVA, same goes with the other way around if 1/4 is normal and rest aren’t do I do ANOVA Or non-parametric test. Trying to find papers which back up the reason why I am doing each test and struggling just really need a clear answer. Is it a majority rule kind of thing or is there set rules like taking outliers out that if one is not normally distributed it over-rules the others and I run that certain test with the 4 conditions (2X2) as a non-parametric test.

ANOVA

Normal Distribution

Outliers

8th Jun, 2021

Jayne Conlon

Queen's University Belfast

The same size is small my thesis superviser has advice to remove outliers and to do within subjects 2X2 anova, however may be need for non parametric tests (if not normally distributed). For an example I’m testing a 360 turn test pre and post lecture condition and dance condition and it has shown that 1 of the 4 conditions isn’t normally distributed so for that variable I.e 360 turn test do I do the ANOVA or the non-parametric test. Blaine Tomkins