Correlation

Deze pagina lezen in het Nederlands.

Author: prof. dr. R.J. de Haan
Authorship

This page was translated from the Dutch-language original using AI and has not been fully reviewed. Where the two differ, the Dutch version takes precedence.

Contents

• Pearson's r
  • When do I use Pearson's r?
  • How do I interpret Pearson's r?
  • Where do I find Pearson's r in SPSS?
• Spearman's rho
  • When do I use Spearman's rank correlation?
  • Where do I find Spearman's rank correlation in SPSS?

Pearson's r

Pearson's correlation coefficient r, sometimes also called the product-moment correlation coefficient (PMCC), expresses the strength of a linear relationship between two variables as a single number. The use of Pearson's r requires both variables to be continuous in nature.

When do I use Pearson's r?

You use this coefficient when you are interested in the linear relationship (= correlation) between two continuous variables X and Y, for example a study into the relationship between age and scores on a cognitive test. The values of the coefficient can range from -1 to +1. If there is a positive correlation, then as the value of X increases, the value of Y also increases. With a negative (opposite) correlation, as the value of X increases, the value of Y decreases. With a correlation of +1 or -1, there is a perfect relationship. In that case, the value of Y can be fully derived from the value of X (and vice versa). At a value of 0, there is no linear relationship at all.

The correlation value is dimensionless; this means that the correlation value is insensitive to the units in which X and Y are measured. Stated somewhat more statistically: r is insensitive to linear transformations of the variables X and Y. So if you had calculated a correlation between a patient's weight in kilograms and his body fat percentage, that correlation would be identical to what you would find if you had measured the patient's weight in pounds.

How do I interpret Pearson's r?

Pearson's r is a simple statistical measure. Yet its interpretation is not always easy. When interpreting it, you need to take a number of things into account. If the correlation is 0, there is no linear relationship. That does not mean there cannot be some other kind of relationship. It is therefore important to always make a scatterplot first. You must also take into account the fact that Pearson's r is very sensitive to extreme values (outliers) in your dataset. Also, do not confuse the concept of association with causation. X is the cause of Y if a change in Y is the result of a change in X. If there is a correlation between X and Y, that relationship does not have to be causal in nature. There may, after all, be mutual influence, or the correlation between X and Y may (partly) be explained by all kinds of other factors.

Where do I find Pearson's r in SPSS?

You can find this correlation technique in SPSS under Analyze -> Correlate -> Bivariate.

Spearman's rho

When do I use Spearman's rank correlation?

The variables X and Y are not always continuous in nature. If both, or one, of the variables is not continuous (but discrete ordinal) in nature, a Pearson correlation cannot be calculated. In that case, it is best to express the association between X and Y as a Spearman rank correlation. The Spearman rank correlation coefficient is essentially equal to the Pearson correlation coefficient, calculated on the ranks of the data. The Spearman correlation is also a good alternative to the Pearson correlation when your dataset contains outliers. By replacing the data with ranks, outliers are given much less weight than when calculating the Pearson correlation.

Where do I find Spearman's rank correlation in SPSS?

You can find this correlation technique in SPSS under Analyze -> Correlate -> Bivariate -> click Spearman.

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