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I'm currently trying to decide what test to run on SPSS for my data. I am comparing the effects of 3 different interventions on trauma scores. I have both pre and post-scores.I have created a difference score variable and will use this to run a one-way ANOVA. I'm trying to run normality tests to see if I instead need to run the non-parametric version, but I'm unsure which statistics I should use to test normality.

Should I analyse the normality of the pre and post-scores, or should I analyse the normality of the obtained difference score?

I ask as I have run all 3 and have obtained results that suggest the data is normally distributed for all my conditions in pre and post. However, when testing normality using the difference score one of my conditions(drug intervention) appears to not be normally distributed. Would this mean I need to run a non-paramnetic version.

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The assumption of normality is regarding the residuals of a regression analysis and not on the unmodeled data, so looking at the changes within group or absolute numbers or anything like that does not make sense.

There's plenty of previous questions addressing that testing for normality on the data under analysis is problematic (e.g. type I error inflation, if analysis is changed in response to the assessment) and that it is better to assess the appropriateness of a normality assumption on previous data (but to not use a null hypothesis test for this, but rather visual inspection of plots of the residuals).

Also note that randomized trials (I assume it is since you plan to do a simple group comparison) are reasonably robust to small/moderate deviations from normal residuals esp. for larger sample sizes. If this study is not a randomized trial, then a simple comparison of treatment groups is of course completely inappropriate and a normality assumptions would have to be looked at in the context of an appropriate analysis. E.g. if you are doing matching/stratifying for propensity scores, then the residuals of a regression with matching/stratification would be one thing one could look at.

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