Difference Between Correlation and Covariance
If you want to express relationships between variables or measures, you can use covariance or correlation. Both are not always suitable, because there are significant differences. The former size is unstandardized, so you cannot compare the results of different calculations.
Relationships between variables can be expressed with a covariance. But how these turn out also depends on how the values were measured. So if you compare the variances between variables that were recorded differently or have different value ranges, then you need correlations.
What is covariance?
The covariance indicates the relationship between two variables (e.g. B. between height and weight of people). Low values of one unit of measurement can also be associated with low values of the other unit, and if the values increase, then they do this to a similar extent for both variables.
- For example, taller people usually weigh more. In this case there is a positive covariance.
- On the other hand, there is a negative relationship when high values of one value are accompanied by low values of the other value. This is the case, for example, with the number of police stations in a region and the frequency of crimes (more police presence should mean fewer crimes).
- But sometimes there is no connection at all. This applies when differences in one area do not affect the other measurement variables at all. However, in order to specify exactly how big a relationship is, the specification of the correlation is required. This represents a normalization so that correlations of very different measured variables can be compared with one another.
Sometimes you are interested in relationships between characteristics, because this way ...
The difference to the correlation
- The correlation also expresses a relationship, but this measure is standardized in contrast to the covariance. The correlation can only assume values between -1 (negative relationship) and 1 (positive relationship).
- Values at zero indicate that differences in one variable have little or no effect on the other; here there is no significant connection and therefore no covariance either.
- In addition, the correlation is tested for significance. This means that it is calculated whether there is actually a correlation between the characteristics of the variables given the number of measured values.