Question

Explain the differences and similarities between parametric and non-parametric inferential statistics. When (under what circumstances) would a parametric statistic be your preferred statistic? When would a non-parametric statistic be your preferred statistic?

Answer 1

Difference and Similarities between Parametric and Non Parametric inferential Statistics

Parametric	Non Parametric
1. Data Should fit a particular Distribution.(Normal)	1.Can be used on data that are not Normally Distributed.
2.Used Mainly on interval and ratio Scale data	2.Can be used on Ordinal Nominal Scale data( although also on interval and ratio Scale )
3.Sample should be drawn randomly from the Population	3.Can be used where samples are not selected randomly
4.Tend to need larger samples	4.Can be used on small Samples.
5.More power than non- parametric equivalent	5. Have less power than the equivalent parametric test
6. Mean is used as measure of central tendency	6. Median is used as measure of central tendency

For the following circumstances parametric and non parametric are preferred statistic.

Parametric	Non Parametric
When parent population is normally distributed and sample drawn randomly from the population	There are some situations when outcome does not follow a normal distribution, for example when the outcome is an ordinal variable or a rank.