In F (n1, n2) distribution if we let n2 à∞, then χ2 = n1F follows χ2 – distribution with n1 degrees of freedom.
Which is the probability density function of chi square distribution with n1 degrees of freedom.
If R is the observed multiple correlation coefficient of a variate with k other variates in a random sample of size n from a (k+1) variate population, then Prof. R.A. Fisher proved that under the null hypothesis (H0
) that the multiple correlation coefficient in the population is zero, the statistic
Conforms to F – distribution with (k, n-k-1) degrees of freedom.
Under the null hypothesis that population correlation ratio is zero, the test statistic is
Where N is the size of the sample (from a bivariate normal population) arranged in h arrays.
For a sample of size N arranged in h arrays, from a bi variate normal population, the test statistic for testing the hypothesis of linearity of regression is
This test is carried out by the technique of analysis of variance, which plays a very important and fundamental role in Design of Experiments in Agricultural Statistics.
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