In F (n1, n2) distribution if we let n2 à∞, then χ2 = n1F follows χ2 – distribution with n1 degrees of freedom.

We have

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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- Exact Sampling Z Distribution
- Student T Distribution
- Derivation Of students T Distribution
- Fishers T Distribution
- T Test For Difference Of Means
- T Test For Testing Significance Of An Observed Sample Correlation Coefficient
- Testing The Significance Of An Observed Partial Correlation Coefficient
- Distribution Of Sample Correlation Coefficient
- Non Central T Distribution

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