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Table of Contents Bivariate Data Correlation Distribution of the Correlation Coefficient | |
See also: correlation coefficient, random variable, chance correlation, testing the significance of r |
It should be noted that the correlation coefficient r is a random variable,
thus having a distribution function which depends on the population
value of the correlation coefficient r and the
number of samples n.
From the images above one can conclude that for a small number of observations it is quite likely that the correlation coefficient is high. A high correlation coefficient does not necessarily represent a high correlation between two variables. Especially with four sample values, any correlation coefficient is equally likely to occur. You may test this phenomenon yourself by starting the following .
As a consequence of this effect, one has to test
for the significance of a correlation coefficient.
Last Update: 2005-Jul-16