TESTS OF SIGNIFICANCE

1. Introduction In applied investigations, one is often interested in comparing some characteristic (such as the mean, the variance or a measure of association between two characters) of a group with a specified value, or in comparing two or more groups with regard to the characteristic. For instance, one may wish to compare two varieties of wheat with regard to the mean yield per hectare or to know if the genetic fraction of the total variation in a strain is more than a given value or to compare different lines of a crop in respect of variation between plants within lines. In making such comparisons one cannot rely on the mere numerical magnitudes of the index of comparison such as the mean, variance or measure of association. This is because each group is represented only by a sample of observations and if another sample were drawn the numerical value would change. This variation between samples from the same population can at best be reduced in a well-designed controlled experiment but can never be eliminated. One is forced to draw inference in the presence of the sampling fluctuations which affect the observed differences between groups, clouding the real differences. Statistical science provides an objective procedure for distinguishing whether the observed difference connotes any real difference among groups. Such a procedure is called a test of significance. The test of significance is a method of making due allowance for the sampling fluctuation affecting the results of experiments or observations. The fact that the results of biological experiments are affected by a considerable amount of uncontrolled variation makes such tests necessary. These tests enable us to decide on the basis of the sample results, if i) the deviation between the observed sample statistic and the hypothetical parameter value, or ii) the deviation between two sample statistics, is significant or might be attributed to chance or the fluctuation of sampling.