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8 Non-parametric tests

Concepts

  • Parametric tests make assumptions that aspects of the data follow some sort of theoretical probability distribution. Non-parametric tests or distribution free methods┬ádo not, and are used when the distributional assumptions for a parametric test are not met. While this is an advantage, it often comes at a cost of power (in the sense they are less likely to be able to detect a difference when a true difference exists).
  • Most non-parametric tests are just hypothesis tests; there is no estimation of an effect size and no estimation of a confidence interval.
  • Most non-parametric methods are based on ranking the values of a variable in ascending order and then calculating a test statistic based on the sums of these ranks.

Connections with other material

  • Understanding and exploring data: Often the decision to use a non-parametric approach is made based on the type of data or after exploring the distribution of the sample data.
  • The p-values from a non-parametric test have exactly the same structure of interpretation as those already discussed (Probability of seeing such extreme data given the null hypothesis is true) and so no new concepts need to be understood to interpret them.