# How to check the assumption of normality in a two-way repeated measures ANOVA?

Hello all,

For a research project, I am looking at the human ability to path integrate , where humans have to navigate through a virtual corridor to a pre-seen target location. The dependent variable was the absolute error (m) (difference between the actual target location and the subjects stop location). The distance from the start of the corridor to the target was one of five different distances and thus 'target distance' was a within-subjects independent variable. The gain (difference in velocity from trial-to-trial) differed between sessions (3 sessions with 50 trials each). Thus, gain and distance were independent within-subject variables.

I have used the anova_test package (rather than the aov package) to perform my analysis as I believe that this package gives me corrections for the sphericity assumption of the repeated-measures ANOVA.

I also used this package for a one-way repeated measures ANOVA (as shown below); were I was only interested in the independent within-subject variable 'trial number'.

`Oneway <- anova_test(data=NewerErrortrialraw,transform~Trialnumber+Error(ID/Trialnumber),effect.size="pes")`

``````ANOVA Table (type III tests)

\$ANOVA

Effect DFn  DFd    F     p p<.05   pes

1 Trialnumber   4 1716 1.72 0.143       0.004

\$`Mauchly's Test for Sphericity`

Effect     W     p p<.05

1 Trialnumber 0.945 0.004     *

\$`Sphericity Corrections`

Effect   GGe        DF[GG] p[GG] p[GG]<.05   HFe        DF[HF] p[HF] p[HF]<.05

1 Trialnumber 0.974 3.89, 1670.82 0.145           0.984 3.93, 1688.03 0.144
``````

However, to check for the assumption of normality , I need to be able to use the residuals from the data. The package above does not seem to give me the residuals (unlike the aov package). When I use the aov package, I am able to obtain the residuals easily from the data. However, the aov package does not automatically check the assumption of sphericity.

Thus, I have a little dilemma...

I guess it's not ok to use the anova_test package to obtain the output for sphericity and then the aov package to obtain the normality residuals; as the p-values/output will slightly differ?

Would anyone be happy to give a helping hand?

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