Medical outcome data are often not Normally distributed. Occasionally however, data that are not Normally distributed can be transformed; ‘to make the distribution Normal’. For example, by taking the logarithm or square the data. This process is called transformation of data. For example, the concentration of H3O+ in the peripheral blood is not Normally distributed, but the pH (-Log [H3O+]) is.
Following transformation, it might be possible to use a more powerful parametric test (provided normality can be confirmed). As stated, it is possible to use a non parametric test on parametric data. However, a parametric test can’t be used on non parametric data. If in doubt about the distribution of our data, it is always possible to use a non parametric test.
In analysing the outcome of hip replacements, functional scores (such as Harris hip score) are often used. They consist of a questionnaire that contains questions for pain, function and range of movement. A score is given for each category. They are added together and expressed as a percentage of the maximal score. At first glance, the functional score obtained appears to be continuous data. So, provided Normality can be demonstrated it seems reasonable to use a parametric test (such as the t-test). However, the functional score is obtained by adding ordinal data together (the answer to each question is given as a number, but in essence the data is ordinal). Hopefully it is obvious that by adding ordinal data together, the data remain ordinal and can never become continuous (‘gaps’ remain in the data as only some values are possible). Consequently, a Normal distribution may not be the most appropriate model for the data and non parametric tests seem more appropriate.
In addition, the seems strange to add scores for function, pain and range of motion together as it is unclear what these added numbers represent. It may be more appropriate to analyse different categories separately.