Mathematical tools for natural sciences

The statistical methods used for hypothesis testing are generally classified into two broad categories: * parametric * and * nonparametric* tests.

In a *parametric test*, the hypothesis tested will be a statement about one or two stistical parameters of the population like mean, standard deviation or median. In order to do this, **we need the knowledge about the undrlying distributions** from which data is supposed to have been randomly drawn. For example, we assume that the population is normally distributed, and would like to test the hypothesis that the population mean is a partucular value.

In a *nonparametric test*, the statement of hypothesis will not involve the statistical parameters of the population. For example, in the *chi-square test*, we test whether a set of observations are significantly different from their expected values. This test does not compute any statistical parameter like mean, variance etc. from the data.

There are certain statistical tests which do not compute the statistical parameters from data for testing hypothesis on population mean or median. They compute quantities like ranks of data points which are not statistical parameters. These tests are also classified as *nomparametric* though thet do not strictly follow the definition of nonparametric in terms of hypothesis tested. Their hypothesis may be a statement on statistical parameters, but they do not compute these parametrs from the sample data. Still it is customary to classify them onto *nonparametric* tests. **These tests are used when we do not have information on the distributions underlying the populations from which data points are randomly drawn**.