Are the concepts of descriptive vs inferential statistics and parametric vs non-parametric statistics orthogonal? As in, can we have a descriptive parametric statistic or a descriptive non-parametric statistic? if so what are some examples of? I know you can have an inferential parametric or non-parametric statistic.
My original thought was that parametric vs non-parametric statistics falls in a subcategory of inferential statistics, and that inferential statistics makes use of descriptive statistics. but some sources I read seem to say that you can have descriptive non-parametric stats.
Anyone can shed some light on this?
Best Answer
You can have any combination of nonparametric/parametric and descriptive/inferential.
In plain language:
Descriptive statistics describe a sample. Inferential statistics infer from a sample to a population.
Nonparametric vs. parametric is trickier. See
http://en.wikipedia.org/wiki/Non-parametric_statisticsB.S. Everitt, in Dictionary of Statistics, defines "parametric methods" as "procedures for testing hypotheses about parameters in a population described by a specified distributional form...." and contrast them with "distribution free methods". However, I think that if you estimated an OLS regression on a sample without making any inferences to a population, that would be a parametric descriptive statistic.