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.
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.
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
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.
Normal distribution is mostly used distribution in statistics, dating
back to the Karl F. Gauss. It is used in many branches of statistics,
however, testing for normality is not well understood. But which
deviations from theoretical normality are still acceptable for a given
statistical procedure? This contribution aims towards better
understanding...
Sample distributions provide clues about normality, which is a validity condition of t-and F-tests. Minor deviations from normality can have serious consequences for these tests whenever an additional validity condition (e.g., equal variances, equal sample sizes) does not hold. Additionally, a single outlier may badly distort the results of these t...
Statistical models are often based on normal distributions and procedures for testing this distributional assumption are needed.
Many goodness-of-fit tests suffer from the presence of outliers, in the sense that they may reject the null hypothesis even
in the case of a single extreme observation. We show a possible extension of the Shapiro-Wilk tes...