What does a statistically significant correlation mean

3.5.3.4.4 Significance of the correlation

The significance is a key figure that indicates the probability of a systematic relationship between the variables. It expresses whether an apparent connection could be of a purely coincidental nature or, with a high degree of probability, actually exists. One speaks at the Significance of Probabilities of error or Levels of significance. Common formulations are, for example, that between the variables A and B there is a correlation of r = 0.5 on the Level of significance or the Probability of error of p ≤ 1%. This means that the correlation found between variables A and B at this level and with this sample size occurs purely by chance in less than 1% of all cases.

The key figure p the Probability of error, the complex calculation of which is not discussed here, thus takes into account both the Correlation level as well as that Sample size. If the sample is very small, the correlation must be extremely large in order to significant to be able to be. On the other hand, a correlation of r = 0.2 can also be used for very large samples significant become.

Limits of significance at n = 20

For a sample of size n = 20 we find the following limit values ​​for one-sided error probability (significance):

Probability of error p ≤ 5%: r / R / TAU must be greater than 0.377

Probability of error p ≤ 1%: r / R / TAU must be greater than 0.534

This means that if a correlation of 0.6 is determined for a sample of n = 20, then the probability is less than 1% that this relationship is purely random.

Determination measure: proportion of the correlation in change

If the correlation coefficient is squared, this is what you get Coefficient of determination (R2), the proportion of the variance explained by one variable in the variance of the other. R / r = 0.8 does not mean that 80% of the sample corresponds to one another. R.2 indicates that 0.8 * 0.8 = 0.64 = 64% of the variability of the values ​​of both variables is determined by the relationship.