For example, for a data set having 20 observations (measurements), linear correlation coefficients greater than ~0.44 are statistically significant at a non-correlation probability (null hypothesis) of 0.05 (confidence limit = 95%) (this example is shown red in the table below and in the figure above) .
| Number of observations in a data set | Probability of correlation desired | Minimum linear correlation coefficient (r) |
| 20 | Non-correlation probability = 0.1 (90% confidence) | ~0.38 |
| 20 | Non-correlation probability = 0.05 (95% confidence) | ~0.44 |
| 20 | Non-correlation probability = 0.01 (99% confidence) | ~0.56 |
| 20 | Non-correlation probability = 0.001 (99.9% confidence) | ~0.68 |
The figure was photocopied from an old statistics text long ago. I do not know what book the figure comes from so I cannot give the reference. I apologize for this omission.