LOS L requires us to:
distinguish between parametric and nonparametric tests and describe situations in which the use of nonparametric tests may be appropriate
a. Tests are said to be parametric when they are concerned with parameters and their validity depends on a definite set of assumptions, otherwise, they are considered non-parametric. This definition is particularly true when one of the assumptions deals with the underlying distributional characteristics of the test statistic.
b. Nonparametric tests, in contrast, are either not concerned with the value of a specific parameter or make minimal assumptions about the population from which the sample is drawn. In particular, no, or few, assumptions are made about the distribution of the population
c. Nonparametric tests are useful when:
i. The data do not meet necessary distributional assumptions.
ii. The data are given in ranks.
iii. The hypothesis does not address the value of the parameter or parameters.
d. The alternative to the parametric tests in the form of non-parametric tests are:
|
Parametric |
Non-Parametric |
Single Mean (x̄) |
t-test / z-test |
Wilcoxon Signed-Rank Test |
Differences between Mean (x̄1 – x̄2) |
t-test / tmod-test |
Mann-Whitney Test |
Mean Differences (đ) |
t-test |
Wilcoxon Signed-Rank Test |