Test of Significance For Large Samples

The problems of sampling of variables such as height, weight, etc., which may take any value. It shall not, therefore, be possible for us to classify each member of a sample under one of two heads, success or failure. The values of the variable given by different trials will be spread over a range, which will be unlimited – limited by practical considerations, as in the case of weight of people or limited by theoretical considerations as in the case of correlation coefficient which cannot lie outside the range + 1 to – 1.

There are three main objects in studying problems relating to sampling for variables:

(i)    To compare observation with expectation and to see how far the deviation of one from the other can be attributed to fluctuation of sampling;

(ii)    To estimate from samples some characteristics of the parent population, such as the mean of a variable; and

(iii)    To gauge the reliability of our estimates.

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