# log transformation for paired t test

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
• What is your $n$? Dec 11, 2017 at 10:59
• 17 pre-post scores Dec 11, 2017 at 11:07
• Somewhat related: stats.stackexchange.com/questions/243975/… Dec 11, 2017 at 13:22

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

• 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. May 6, 2021 at 2:19