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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