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I am running mixed ANOVA as repeated measurement analysis for cognitive score at 2 time points for 2 groups (blood pressure low vs. High). The the score at time 1 was normally distributed and at time 2 was not normally distributed so I QURT transformed.

Can I still use mixed ANOVA? or both scores should be of same scale/ units? if both should be same, what should i do, transform time 1 or use the original time 2?

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You cannot transfom one variable but not the other. This simply doesn't make any sense, they need to be on the same scale (otherwise you trivially get a main effect of time).

Usually, people are overcutious with the normality assumption disregarding several important aspects:

  • Normality testing is potentially "essentially useless". So shouldn't be used for your different time points.

  • The assumption of normality does not concern the raw data, but the residuals, see here or here.

I would probably go with the raw values but plot those and the residuals and only consider alternatives if the deviations are dramatic.

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