Question
Asked 8th Jun, 2021

# 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.

## All Answers (3)

8th Jun, 2021
Blaine Tomkins
College of Saint Benedict and Saint John's University
Jayne Conlon What is the sample size per cell? ANOVA is robust to violations of normality, particularly when sample size is large. Take a look at the residual plot. To what extent do residuals deviate from normal? Only mildly or extremely?
If you haven't yet conducted the ANOVA, can you collect data from a few more participants? This might fix the problem. I do not recommend removing outliers unless there is strong theoretical reason for doing so - or there was an obvious error for a particular observation.
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
8th Jun, 2021
Blaine Tomkins
College of Saint Benedict and Saint John's University
Jayne Conlon I would probably use a nonlinear mixed effects model in this case. However, given that this is for a thesis an ANOVA will probably be fine. You could always do the ANOVA as planned, then do a nonparametric test with the data and see if the results of the two tests are consistent.
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