# Shapiro-Wilk test on transformed data

I used RStudio to perform Shapiro-Wilk test for normality. In the following data set calling it $$D$$, I have performed Shapiro-Wilk test for normality with p-value=0.7698.

34.681 26.291 33.280 36.169 41.471 31.528 25.502 43.211 35.330 30.447

If I consider log transform of data set $$D$$(i.e. take log on each element of $$D$$), I perform Shapiro-Wilk test on the transformed data set $$log(D)$$ with p-value=0.7707.

In particular, I have both $$D$$ and $$log(D)$$ data set following normal distribution as Shapiro-Wilk test did not reject either one of them.

$$Q$$: How should I resolve such contradiction? Note data $$D$$ and data $$log(D)$$ cannot both be normal.

• There's no contradiction in these results: they merely show that the logarithm does little to change the distribution of a set of data with a small CV. – whuber Jan 27 at 14:26