Parametric and nonparametric tests

The new AQA specification includes parametric tests, therefore students no longer can justify a choice of test by saying it is ‘better than ordinal’ (which was possible when there were only nonparametric tests. A look at past AQA B mark schemes gives a clue about how this should be done:

AQA B paper (June 2015 paper 4 question 19) the following appeared:

  • Appropriate statistical test (eg Related t-test/Wilcoxon) and reasons. Answers may refer to parametric criteria. Justification: Related t-test as the design is repeated measures, the study is looking for a difference and the data collected (number of steps taken) is interval. Or, Wilcoxon as the design is repeated measures, the study is looking for a difference and the data collected (number of steps taken) should be treated as ordinal (as steps are not a recognised units of measurement) etc.

AQA B paper (June 2013 paper 4 question 13)

  • One mark for naming a test: Spearman’s rank order correlation/rho or Pearson’s product moment correlation. One mark for justification.
  • For Spearman’s rank order correlation accept: not all data is interval – data collected for empathy test score most likely treated at ordinal level of measurement due to self-report.
  • For Pearson accept: Pearson’s product moment correlation is a robust test, even if not all data can be treated as truly interval.
    Just stating ordinal/interval no credit. Accept ordinal or interval providing this is justified with reference to at least one variable.

AQA B paper (June 2012 paper 4 question 14)

  • Question: Explain why the psychologists decided to use a Wilcoxon signed ranks test to analyse the data.
  • Reason 1 – ordinal level of measurement/non-parametric
    Explanation – self reports/estimated scores of anger; data might not be normally distributed
    AQA B paper (June 2011 paper 4 question 14)
    1 mark for the appropriate test: Mann-Whitney.
    1 mark for identifying a reason. Accept a test of difference between the ratings for baby boys and baby girls; unrelated scores; a rating scale cannot claim to use units of equal intervals / not an objective measurement so level of measurement is ordinal / data is non-parametric.
    Only accept independent /unrelated t test if candidate refers to the scale being standardised.

AQA B paper (June 2010 paper 4 question 13)

  • Question: The psychologist chose to summarise the data using the median. Explain why the median might be the most appropriate measure of central tendency to summarise the raw scores in this study.
  • One mark for any of the following: the data are not at interval level; rated so best treated as ordinal data.
  • One mark for an expansion such as; a rating scale is too imprecise to make mathematical operations permissible; the numerical data not considered as values on a safe scale where intervals are equal.
  • Allow one mark max for alternative explanations eg better able to deal with extreme values/outliers; the mode is not as sensitive as the median.
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