Statistical Analysis for Education and Psychology Researchers

variables and other correlation type statistics are then appropriate for summarizing this
relationship (e.g., the eta statistic is the correlation coefficient which describes a
curvilinear relationship).
If you have access to SAS/INSIGHT, an interactive tool for data exploration and
analysis, graphical representation of bivariate relationships for any number of variables
taken two at a time can be shown using the menu driven analysis and data display
features (see exploring data in two dimensions SAS/INSIGHT User’s Guide). In this
chapter we will consider Spearman’s rank order correlation, which is appropriate
when variables are measured at an ordinal level, or when data is transformed to an ordinal
scale, this would include percentages. It is one of a number of alternative distribution-free
correlation-type statistics. Other nonparametric coefficients include: the point biserial
correlation (when both variables are discrete true dichotomies); biserial correlation
(when variables have been dichotomized from an underlying continuous distribution) and
Kendall’s Tau coefficient (an alternative to Spearman’s rank correlation which is
actually a measure of concordance—similarity of two rank orders rather than a
correlation). For discussion and illustrated examples of these alternative correlation
statistics see Siegel and Castellan, (1988); Hays, (1981); and Guilford and Fruchter
(1973).
We are concerned in this and in the subsequent chapter with the inferential use of
correlations and consequently, we should bear in mind how sample data was generated,
especially possible bias and range restrictions which can attenuate correlations (reduce
sample correlations).

7.2 Spearman’s rho (rank order correlation coefficient)

When to Use

Spearman’s rank order correlation should be used when:

• the relationship between two variables is not linear, (this can be checked by plotting the
  two variables);


• when measurement and distributional assumptions are not met (the variables are not
  interval or ratio measures and observations do not come from a bivariate normal
  distribution);


• when sample sizes are too small to establish an underlying distribution, or


• when the data naturally occur in the form of ranks.

Spearman’s rank order correlation is equivalent to the Pearson Product Moment
correlation (a parametric correlation procedure) performed on the ranks of the scores
rather than on the raw scores themselves. The rank order correlation procedure is
probably used less often than it should be. In the review of the BERJ and the BJEP
periodicals mentioned earlier only two papers used rank order correlations (Spearman’s
correlation coefficient). It is generally not good practice to go fishing for significant
correlations among researchers should note, a large number of variables.

Statistical Inference and Null Hypothesis

Inferences involving rank data 207