Nonparametric tests

Features of nonparametric statistical methods include:

• nonparametric statistical tests can be used when the data being analysed is not a normal distribution
• many nonparametric methods do not use the raw data and instead use the rank order of data for analysis
• nonparametric methods can be used with small samples
• two commonly used nonparametric methods are:
  • the Mann-Whitney U test
    • this is the nonparametric equivalent of the unpaired t-test
    • applied when there are two independent samples
  • the Wilcoxon matched-pairs signed ranks test
    • equivalent to the paired t-test
  • both of these tests have a power-efficiency of 95.5% when compared to their parametric equivalents (this means that the equivalent parametric test would be just as effective with a sample size that is 4.5% smaller than used in the nonparametric tests). The power-efficiency illustrates the fact that if all conditions of normality (of the sample distribution) are met, then nonparametric methods waste data

Reference:

1. Doctor (March 22nd 2005):33-5.