To test the significance of an observed sample correlation coefficient from an uncorrelated bivariate normal population, t – test is used. But in random sample of size ni, from a bivariate normal population in which ρ ≠ 0, Prof. R.A. Fisher proved that the distribution of ‘r’ is by no means normal and in the neighbourhood of ρ = ± 1, its probability curve is extremely skewed even for large n. if ρ ≠ 0, Fisher suggested the following transformation

And proved that even for small samples, the distribution of Z is approximately normal with mean

And variance and for large values of n, say > 50, the approximation is fairly good.

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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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