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# r Critical Values for the Product-Moment Correlation Coefficient

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It is assumed that X and Y are uncorrelated and have normal distributions.

Critical values for two-tailed tests

The values in the table are the two-tailed 5% and 1% points of the distribution of r and hence are appropriate for upper-tail 2.5% and 0.5% tests.

n5%1%n5%1%n5%1%n5%1%

4.950.99013.553.68422.423.53740.312.403

5.878.95914.532.66123.413.52650.279.361

6.811.91715.514.64124.404.51560.254.330

7.754.87416.497.62325.396.50570.235.306

8.707.83417.482.60626.388.49680.220.286

9.666.79818.468.59027.381.48790.207.270

10.632.76519.456.57528.374.478100.197.256

11.602.73520.444.56129.367.470110.187.245

12.576.70821.433.54930.361.463120.179.234

Critical values for one-tailed tests

The values in the table are the upper-tail 5% and 1% points of the distribution of r and hence are appropriate for two-tailed 10% and 2% tests.

n5%1%n5%1%n5%1%n5%1%

4.900.98013.476.63422.360.49240.264.367

5.805.93414.458.61223.352.48250.235.328

6.729.88215.441.59224.344.47260.214.300

7.669.83316.426.57425.337.46270.198.278

8.621.78917.412.55826.330.45380.185.260

9.582.75018.400.54327.323.44590.174.245

10.549.71519.389.52928.317.437100.165.232

11.521.68520.378.51629.312.430110.158.222

12.497.65821.369.50330.306.423120.151.212

For values outside the range of the tables, use the fact that, assuming independence, r√(n−2)/(1−r2) is an observation from a tn−2 distribution. Alternatively, use the result that rn−1 is approximately an observation from a N(0, 1) distribution.

From A Dictionary of Statistics in Oxford Reference.

Subjects: Probability and Statistics.

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