Solved – Normality test for repeated measures data

goodness of fitnormal distributionrepeated measures

I've measured the motor function of the same subjects (n=6) over 7 different time points. I would like to know whether the mean motor function varies significantly with time (day 1 versus day 2 etc) and I know that a 1 way repeated measures anova will allow me to make this assessment. However, before I perform the repeated measures 1 way anova I'd like to assess whether my data are normally distributed. Which test would be most applicable for assessing whether repeated measures data are normally distributed?

Thank you

Best Answer

Assuming that your measure of the motor function is continuous, you need to check not only multivariate normality but also sphericity and independence.

  1. You can test multivariate normality with the various tests in the mvnormtest package if you use R. Otherwise you can check whether residuals based on your repeated-measures ANOVA model is normally distributed.
  2. Sphericity assumes, roughly speaking, that the difference between two adjacent measures are constant (e.g., $Y_{Day_2} - Y_{Day_1} \approx Y_{Day_3} - Y_{Day_2} \approx ... \approx Y_{Day_7} - Y_{Day_6}$, in your example). You can use Mauchly's test to test sphericity.
  3. Independence assumes that values obtained from one subjects are not in any way related to the values obtained from the other subjects.

For more information, see this post and this tutorial.

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