Confidence Intervals and Significance Tests for Correlation and Regression (1 of 5)

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Pearson's r

Confidence Interval
The formula for a confidence interval for Pearson's r is given elsewhere.

Significance Test
The significance test for Pearson's r is computed as follows:



with N - 2 degrees of freedom, r is Pearson's correlation and N is the number of pairs of scores that went into the computation of r. For example, consider the data shown below: . 
    X    Y 
    2    5
    3    7
    4    7
    5    9
    6   12
    9   11
With r = .8614 and N = 6,



with 6 - 2 = 4 degrees of freedom. From a t table, it can be found that the two-tailed probability value is p = 0.0275.
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