Distribution of the Correlation Coefficient

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.