Nonparametric Inference

Parametric tests are concerned with parameters, their validity depends on a definite set of assumptions—in particular, assumptions about the distribution of the population producing the sample.

A nonparametric test is a test that is not concerned with a parameter, or a test that makes minimal assumptions about the population from which the sample comes.

Primarily used in 3 situations:

when the data we use do not meet distributional assumptions,

when the data are given in ranks, or

when the hypothesis we are addressing does not concern a parameter.

[Practice Problems] An analyst is examining the monthly returns for two funds over one year. Both funds’ returns are non-normally distributed. To test whether the mean return of one fund is greater than the mean return of the other fund, the analyst can use:

A.       a parametric test only.

B.        a nonparametric test only.

C.        both parametric and nonparametric tests.

[Solutions] B

There are only 12 (monthly) observations over the one year of the sample and thus the samples are small. Additionally, the funds’ returns are non-normally distributed. Therefore, the samples do not meet the distributional assumptions for a parametric test.