AGRI 2400 Lecture 34 - Non-Parametric Tests

Non-Parametric Tests

• used when assumptions of normality (or some other distribution) are not met

  • also called “distribution free” tests

• advantage: allow you to analyze data you would otherwise be unable to

• disadvantage: lower power relative to their parametric equivalents

Non-Parametric Tests Assumptions

• these tests should not be used where there are large differences in the distribution/variance among samples

  • i.e. samples need not be normally distributed, but samples should have an approx. similar distribution

  • if ratio of variance between samples is greater than 4:1, these tests are inappropriate

Mann-Whitney U Test (Independent Samples T-Test)

• to obtain the probability that two independent samples are from the same population

  • alternative to indep samples t-test or single factor ANOVA with only 2 treatment levels

  • Ho = the two samples are equal

  • also called the Wilcoxon rank sum test

Expectation Based on Ranked Data

• consider the situation where there is complete seperation of the groups, supporting the alternate hypothesis that the 2 samples are not equal

  • U1 = 0 and U2 = 25 (U is 0, difference between samples)

• situation where the low and high scores are approx evenly distributed in the two groups, supporting the null hypothesis that the groups are equal

  • U1 =10 and U2 = 15 (U is 10, no difference between populations)

Wilcoxon Signed Rank Test (Paired Samples T-Test)

• to obtain the probability that two paired samples are from the same population

  • alternative to paired samples t-test

  • Ho = median difference between samples is 0

• example data: honey bee hive varroa mite counts before and after treatment

Kruskal-Wallis Test (Single Factor ANOVA 2+ Treatment Levels)

• to obtain the probability that two or more independent samples are from the same population

  • Ho = sample medians are equal

  • Ha = sample medians are different