Most statistics courses tend to focus on parametric statistics; however, you might find that as you prepare to analyze your dissertation data, parametric statistics might not be an appropriate choice for your research. The following are some of the differences between parametric and nonparametric statistics.
Parametric statistics are any statistical tests based on underlying assumptions about data’s distribution. In other words, parametric statistics are based on the parameters of the normal curve. Because parametric statistics are based on the normal curve, data must meet certain assumptions, or parametric statistics cannot be calculated. Prior to running any parametric statistics, you should always be sure to test the assumptions for the tests that you are planning to run.
As implied by the name, nonparametric statistics are not based on the parameters of the normal curve. Therefore, if your data violate the assumptions of a usual parametric and nonparametric statistics might better define the data, try running the nonparametric equivalent of the parametric test. You should also consider using nonparametric equivalent tests when you have limited sample sizes (e.g., n < 30). Though nonparametric statistical tests have more flexibility than do parametric statistical tests, nonparametric tests are not as robust; therefore, most statisticians recommend that when appropriate, parametric statistics are preferred.
Parametric and Nonparametric Equivalencies
The table below outlines some common research designs and their appropriate parametric and nonparametric equivalents.