# 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** (R^{2}), 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.

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