Because distribution-free tests do not assume normality, they can be less susceptible to non-normality and extreme values. Therefore, they can be more powerful than the standard tests of means that assume normality.
- 18.1: Benefits of Distribution Free Tests
- Tests assuming normality can have particularly low power when there are extreme values or outliers. A contributing factor is the sensitivity of the mean to extreme values. Although transformations can ameliorate this problem in some situations, they are not a universal solution. Tests assuming normality often have low power for leptokurtic distributions. Transformations are generally less effective for reducing kurtosis than for reducing skew.
- 18.4: Randomization Association
- A significance test for Pearson's r is described in the section inferential statistics for b and r . The significance test described in that section assumes normality. This section describes a method for testing the significance of r that makes no distributional assumptions.
- 18.5: Fisher's Exact Test
- The chapter on Chi Square showed one way to test the relationship between two nominal variables. A special case of this kind of relationship is the difference between proportions. This section shows how to compute a significance test for a difference in proportions using a randomization test.
- 18.6: Rank Randomization Two Conditions
- The major problem with randomization tests is that they are very difficult to compute. Rank randomization tests are performed by first converting the scores to ranks and then computing a randomization test. The primary advantage of rank randomization tests is that there are tables that can be used to determine significance. The disadvantage is that some information is lost when the numbers are converted to ranks. Rank randomization tests are generally less powerful than randomization tests.