2

If my difference scores are not normally distributed - and I want to do a parametric paired t-test - do I:

  1. log transform the the original scores and perform a paired t-test on these scores
  2. log transform the difference scores and do a one sample t-test against a test value of 0
pomodoro
  • 723
  • 5
  • 15

1 Answers1

2

For a paired test, what is relevant is the distribution of the difference scores, not the individual distributions. Even if the original scores have a nonnormal distribution (difficult to say with only $n=17$), the difference might be normal (or at least symmetric). So I would have first a look at the qqplot of the differences against a normal distribution. Then, if necessary, transform the difference score. Or use a nonparametric procedure. More discussion in the related post at Skewness transformation for one but not the other variable?

An alternative could be a permutation test (permuting the signs of the absolute differences), which do not depend on distribution assumptions. For further discussion of alternatives see Best practice when analysing pre-post treatment-control designs

kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
  • Not sure OP's question was completely answered, Kjetil. Can he do either option 1 or 2? I personally would find it easier to interpret option 1 and we can also get a correlation score. – ScottEdwards2000 May 06 '21 at 02:19