Non-parametric Tests

Introduction & definition

• Definition — Significance tests that do not assume the data come from a population following a defined parametric distribution (especially the Normal); the distribution cannot be summarised by a few parameters such as mean & SD — hence "non-parametric".
• Distribution-free — Because they make no assumption about the shape of the underlying distribution they are also called distribution-free tests.
• Rank score tests — The principal family for ordinal / non-Normal continuous data — they work by converting raw observations to ranks and operating on rank totals.
• A slight misnomer — The term is somewhat of a misnomer: to say anything useful about the population one must ultimately still compare parameters.
• Try transformation first — If data are non-Normal but one wishes Normality, a transformation (logarithm, reciprocal) may be attempted before resorting to a non-parametric test.
• Statistical power — Power = probability a test correctly rejects a false null (finds a significant result when a true difference exists); the higher the power, the more likely a true difference is detected.