The probability integral of the sample correlation coefficient
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The probability integral (p.i.) values of the correlation coefficient in samples from a normal bi-variate population are usually computed by approximate methods, except for the first few values ofn. In this note we shall obtain the explicit expression for any sample size through a relation which also enables us to calculate easily and quickly the p.i. exact values as well as those of the density function (d.f.). From this p.i. expression it is also possible to obtain, among others, that of Student'st.
keywordscorrelation coefficient probability distributions normal bi-variate populations
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- Fisher R. A. (1915), Frequency Distribution of the Values of the Correlation Coefficient in Samples from an Indefinitely Large Population,Biometrika, 10, 507–521.Google Scholar
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