# Correlation analysis

## Correlation coefficients

Correlation coefficients provide a numerical summary of the direction and strength of the linear relationship between two variables. The two main correlation coefficients are:

- Pearson product-moment correlation: for continuous variables, or one continuous variable and one dichotomous variable.

- Spearman rho: for ordinal level or ranked data.

The sign of the correlation coefficient indicates the direction of the correlation: a positive correlation indicates that as one variable increases, so does the other; a negative correlation indicates that as one variable increases, the other decreases. The strength of the relationship is given by the numeric value: 1 indicates a perfect relationship; 0 indicates no relationship between the variables.

## Obtaining Pearson r and Spearman rho

1. Click on Analyze\Correlate\Bivariate.
2. Select your two variables and move them into the box Variables.
3. In the Correlation Coefficients section, Pearson is the default option. If you wish to request the Spearman rho, tick the Spearman box as well (or instead).
4. Under Options, click on the Exclude cases pairwise box.
5. Click on Continue, then OK.

## Interpreting results

### Significance of the correlation

Assess whether the correlation between the variables is statistically significant.

For significant correlations, Sig. (2-tailed) will be less than .05 and the Pearson Correlation will be flagged with asterisks.

Reprint Courtesy of International Business Machines Corporation, © International Business Machines Corporation. SPSS Inc. was acquired by IBM in October, 2009.

### Direction of the relationship

It is given by the sign of the correlation coefficient - the Pearson Correlation. In the example above, the correlation between age and anxiety is negative (as one increases, the other decreases).

### Strength of the relationship

It is given by the numeric value of the correlation coefficient:

• small: from .10 to .29
• medium: from .30 to .49
• large: from .50 to 1