Plot Graphs - The significance of Pearson's Correlation Coefficient

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As a reminder the correlation coefficient after pearson can be calculated as follows:

`r = (1/n sum_{i=0}^{n} (x_i-bar(x))*(y_i-bar(y)) ) / (sqrt(1/n sum_{i=0}^{n} (x_i-bar(x))^2)*sqrt(1/n sum_{i=0}^{n} (y_i-bar(y))^2) )`

In case of absence of a correlation the pearson coefficient follows a so called t-distribution of order (n-2) which can be written as

`t = r / (sqrt(1-r^2)) * sqrt(N-2) `

Using this distribution it is easy to calculate the p-value for an r which was obtained at a given sample size N. It can be written as: (Source: Base: SAS 9.3: Procedures Guide: Statistical Procedures, Second Edition) If the sample size is large already a relatively small correlation coefficient can indicate a significant correlation. You can use the following calculator to calculate the significance of your correlation coefficent:

Significance of a correlation coefficient

The sample size has to be greater or equal 6 to obtain a correct result:
r:
N



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