Transforming data to a normal distribution

If we were just to ignore this non-normality and perform a two-sample f-test on the raw data, the results would include a P value of 0.115, indicating a lack of statistical significance. However, we would be very unwise simply to accept this negative result, given that the test used is not appropriate for highly skewed data. 

There are two possible solutions and we are going to look at both. The first is to use the same trick we saw in Chapter 5 - transformation. 

W onder of wonders Data that were non-significant are now revealed as significant (P = 0.034). It is usually at about this point that the cynical cry cheat How dare we use this statistical fiddle to convert non-significant results into significant ones Essentially, we need have no qualms about this approach. It is entirely respectable and is definitely superior to the analysis of the original data, because the transformed data are much closer to a normal distribution. The only caveat would be that, if we are 

It is normal and legitimate practice to use transformations to convert data to a better approximation of a normal distribution and then carry out tests on the transformed 

The contrast between the successful outcome when testing the normally distributed transformed data and the failure with the highly skewed raw data is an example of the large loss of power that often accompanies the application of procedures such as a f-test to inappropriate data. 

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