If r is the observed correlation coefficient in a sample of n pairs of observations from a bivariate normal population, then Prof. Fisher proved that under the null hypothesis H0: ρ = 0, that is population correlation coefficient is zero, the statistic:

Follows Student’s t – distribution with (n-2) degrees of freedom.

If the value of t comes out to be significant, we reject H0 at the level of significance adopted and conclude that ρ ≠ 0, that is, ‘r’ is significant of correlation in the population.

If t comes out to be non – significant then H0 may be accepted and we conclude that variables may be regarded as uncorrelated in the population.

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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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