The entire large sample theory was based on the application of “normal test”. However, if the sample size n is small, the distribution of the various statistics, e.g.,
are far from normality and as such ‘normal test’ cannot be applied if n is small. In such cases exact sample tests, pioneered by W.S. Gosset who wrote under the pen name of student, and later on developed and extended by Prof. R.A. Fisher are used.
The exact sample tests can, however be applied to large samples also though the converse is not true. In all the exact sample tests, the basic assumption is that “the population(s) from which sample(s) are drawn is normal that is the parent population(s) is normally distributed.
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