Course Notes - Department of Mathematics and Statistics

6.3.2 Transforming DataTRANSFORMING DATAIf data are continuous but not normally distributed, we need totransform each value to create new values which are normally distributed- we use logs, square roots or reciprocals. We do this because:1) statistical procedures require normally distributed data2) to compare two samples, the standard deviations need to be similar3) to reduce the effect of outliers (log transformation).TRANSFORMING DATA ExampleFrom Assignment 3, we saw that daily river flow is typically skewedand is bounded below by zero (negative values are impossible in thiscontext).One set of 128 observations of Rangitata river flow during springand summer had mean = 105.29 and standard deviation 44.44. Theminimum and maximum values are 40.35 and 233.14 respectively.The data are not normally distributed.When the data are transformed by taking logs to base e the meanis 4.51 and the standard deviation is 0.43. The normal fit to thetransformed data is much better.106