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# Correlation

Explanations > Social ResearchAnalysis > Correlation

## Definition

Correlation of two variables is a measure of the degree to which they vary together.

More accurately, correlation is the covariation of standardized variables.

In positive correlation, as one variable increases, so also does the other.

In negative correlation, as one variable increases, the other variable decreases.

Correlation can be visually displayed in a Scatter Diagram.

Correlation is a descriptive statistic, as it simply describes data, telling you something about it. This is in contrast to inferential statistics.

## Coefficients

A correlation coefficient is a calculated number that indicates the degree of correlation between two variables:

• Perfect positive correlation usually is calculated as a value of 1 (or 100%).
• Perfect negative correlation usually is calculated as a value of -1.
• A values of zero shows no correlation at all.

A simple form of correlation is to calculate regression coefficients, m and c, so a line can be drawn on a scatter diagram with the equation y = mx + c. These coefficients are often calculated with the method of least squares.

The problem with simple regression coefficients is that they are tied to the units from which they are calculated, which does not make them very portable. This is compensated for in correlation coefficients by standardizing both measurement scales.

Three common types of correlation are Pearson, Spearman (for ranked data) and Kendall (for uneven or multiple rankings), and can be selected using the table below.

Parametric? (interval data, with normal distribution and linear relationship between x and y)

Y

Pearson correlation

N

 Equidistant positions on variables measured? Y Spearman correlation N Kendall correlation

## The causality trap

It is a very common trap to assume that correlation shows that changing one variable causes the other to change. In practice, when there is no direct causal link, this can be coincidence, but usually it is because they both have a common cause. For example sales of ice-cream correlate with drowning in the sea -- because they both increase with fine weather.

Inferring cause

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