Q&A from AQA: Parametric vs. Non-Parametric Tests

Below you will find a question and response from AQA in relation to: Parametric vs. Non-Parametric Tests.

Question

Could you confirm are students required to make a decision on whether to use a parametric test or non parametric test? Or just justify when they would use one over the other. For example researchers are looking at whether being a football player (yes or no) makes you less stressed (as measured by cortisol levels in salvia). This is interval data, so suggesting parametric tests would be more appropriate but how would the students know if the data was drawn from a normally distributed population? Or if there is homogeneity of variance between the conditions? Is this to be assumed from the information given regarding the sampling technique and the standard deviation, and this would be given in the scenario? Or would they be told that all assumptions of parametric tests are fulfilled/not fulfilled?

Response

"It’s not a silly question at all. Firstly, the terms parametric and non-parametric do not appear on the specification so students could not be asked about them directly. However, students will be expected to be able to choose an appropriate test and justify their choice. The primary criterion for choice of t-tests (parametric tests of difference) is that data should be at interval level (as you say in your example). After that, opinion is somewhat divided about the importance of the other two criteria, homogeneity of variance and normal distribution, and in the absence of much detail, students can often make an argument either way. Here are a few legitimate examples of creditworthy reasoning:

‘The data can be assumed to be normally distributed because the population from which it is drawn would seem to be normal for the variable in question’

‘The data might not be normally distributed because there seem to be a few extreme scores’

‘As we are not told otherwise we are assuming the data comes from a normally distributed population’

‘SDs seem quite similar so we can assume homogenous variances’

‘SDs seem quite different so we cannot assume homogenous variances’

The important thing is for students to make some reasoned justification based on the fairly limited information available in an examination."

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