Non-parametric Tests

Non-parametric Tests

1. Definition & overview

• Non-parametric tests are significance tests that do not assume the data originate from a population following a defined parametric distribution (especially the Normal distribution); because the data are not Normally distributed, the distribution cannot be characterised by a few parameters such as the mean and standard deviation, hence these tests are called "nonparametric" (Swinscow & Campbell 10e Ch.10, p.102).
• Because they make no assumption about the shape of the underlying distribution, non-parametric tests are also termed "distribution-free tests" (Medhi Ch.11, p.127).
  • When a data set does not follow the Normal distribution and one wishes it to, transformation (logarithm, reciprocal of all values) may be attempted before resorting to a non-parametric test (Medhi Ch.11, p.127).
• The term "nonparametric" is somewhat of a misnomer: to be able to say anything useful about the population, one must ultimately still compare parameters (Swinscow & Campbell 10e Ch.10, p.102).
• Parametric tests (t test, ANOVA, z test) depend for their validity on the assumption that the data come from a Normally distributed population; when two groups are compared, the difference between the two samples is assumed to arise only because they differ in their mean value (Swinscow & Campbell 10e Ch.10, p.102).
• Rank score tests are the principal family of non-parametric tests for ordinal / non-Normal continuous data; they work by converting raw observations to ranks and operating on rank totals (Swinscow & Campbell 10e Ch.10, pp.102–105).
• Statistical power = the probability that a test correctly rejects a false null hypothesis (i.e. the probability of finding a significant result when a true difference exists); the higher the power, the more likely a true difference is detected (Medhi Ch.11, p.127).