Question

What is nonparametric statistics? Provide an examples of a research hypothesis where researchers can use nonarametric statistical techniques.

Answer 1

We perform z-test, t-test, one-way ANOVA etc. in which it is required for the data to follow normal distribution. These are called parametric tests.
But in reality, the data you have usually doesn't follow normal distribution. Hence, non parametric statistics are statistical methods which are used in which data is not required to follow normal distribution.
It does not rely on numbers but on a ranking or order (ordinal data). Hence, when the data has a ranking but no numerical interpretation, non-parametric methods are often used. These methods are simple and easier to use than parametric methods because they make fewer assumptions.
Some of the non-parametric statistical methods are Kendall's W, Cohen's Kappa, Mann Whitney U (alternative of t-test), sign test etc.

Consider a dataset of two drugs where we need to find whether which drug is more effective to increase the sleep of a person.
The dependent variable we have is the difference in the number of hours of sleep between Drug 2 and Drug 1.

Ho: The difference in number of hours of sleep is equally likely to be + or -
Note that in the above hypothesis, we haven't used the numerical interpretation but we have used the sign of the difference.

The above hypothesis can be tested using non-parametric technique, Wilcoxon signed rank test. If the drugs are equally effective in increasing the sleep of a person, there should be the same number of positives and negatives.