## Exercise 4: Making a Correlation

exercise 4

### 4. Values

 An (arbitrary) guide to effect sizes: 0 = no correlation ± 0.1 = small effect ± 0.3 = medium effect ± 0.5 = large effect BUT! Interpretation depends on context. And beware – if you have very many cases it is possible to see a ‘significant’ correlation even when the correlation coefficient is very small. You have to decide how meaningful the relationship actually is. The box gives a matrix of Pearson correlations for the two variables. Each variable has an r of 1 with itself, and the two variables have an r of .726 with each other. SPSS also gives the p-value associated with r. Significant p-values are highlighted with ** next to the r.

Is there a convincing correlation between the variables? SPSS can give correlation matrices for more than two variables at a time. Try some others.

Pearson’s correlation coefficient is parametric, i.e. it assumes your data are normally distributed and are on an interval scale with meaningful units. You might need to use Spearman’s ρ (rho), which is non-parametric, i.e. appropriate for non-normally distributed data or ordinal scale data (ranks not units). In fact, ρ is the r of the ranks of the data: If the data are put into order according to the variable, and assigned a number based on this order, the Pearson correlation coefficient for this rank number will form the Spearman coefficient. Alternatively, you might need to use Kendall’s τ (tau), which is like Spearman’s ρ but better for small data sets with many tied ranks. Spearman and Kendall can be accessed through the same menu as the Pearson correlation in SPSS.