**Correlation analysis**

Correlation analysis explores the **association between variables**. The purpose of correlational analysis is to discover whether there is a relationship between variables, which is unlikely to occur by sampling error. The null hypothesis is that there is no relationship between the two variables. Correlation analysis provides information about:

- The direction of the relationship: positive or negative- given by the sign of the correlation coefficient.
- The strength or magnitude of the relationship between the two variables- given by the correlation coefficient, which varies from 0 (no relationship between the variables) to 1 (perfect relationship between the variables).

**Direction of the relationship.**

A **positive correlation** indicates that high scores on one variable are associated with high scores on the other variable; low scores on one variable are associated with low scores on the second variable . For instance, in the figure below, higher scores on negative affect are associated with higher scores on perceived stress

Fig 1. Positive correlation between two variables. Adapted from Pallant, J. (2013). SPSS survival manual: A step by step guide to data analysis using IBM SPSS (5th ed.). Sydney, Melbourne, Auckland, London: Allen & Unwin

A **negative correlation** indicates that high scores on one variable are associated with low scores on the other variable. The graph shows that a person who scores high on perceived stress will probably score low on mastery. The slope of the graph is downwards- as it moves to the right. In the figure below, higher scores on mastery are associated with lower scores on perceived stress.

Fig 2. Negative correlation between two variables. Adapted from Pallant, J. (2013). SPSS survival manual: A step by step guide to data analysis using IBM SPSS (5th ed.). Sydney, Melbourne, Auckland, London: Allen & Unwin

**2. The strength or magnitude of the relationship**

The strength of a linear relationship between two variables is measured by a statistic known as the **correlation coefficient**, which varies from 0 to -1, and from 0 to +1. There are several correlation coefficients; the most widely used are Pearson’s r and Spearman’s rho. The strength of the relationship is interpreted as follows:

- Small/weak: r= .10 to .29
- Medium/moderate: r= .30 to .49
- Large/strong: r= .50 to 1

*It is important to note that correlation analysis does not imply causality. Correlation is used to explore the association between variables, however, it does not indicate that one variable causes the other. The correlation between two variables could be due to the fact that a third variable is affecting the two variables.*