Research Journal (BERJ) and the British Journal of Educational Psychology (BJEP),
looking at two consecutive volumes over the same time period, the following was
observed. In the BERJ authors from 32 per cent (25) of the papers used some statistical
analyses, in total 12 per cent (9) used correlations; whereas in the BJEP authors from 84
per cent (61) of the papers reported statistical findings and in total 51 per cent (37) used
correlations. Correlational analysis, a statistical technique for examining the extent of
the relationship between two variables, is a technique with which researchers should
certainly be familiar.
Correlations coefficients, r, computed from sample data provide an index of the
strength of the relationship between two variables e.g., rxy is the sample correlation
between the variables X and Y. Data usually consists of a random sample of subjects each
of whom has two scores, one for each of the variables measured. When introducing the
idea of correlation it is helpful to make two distinctions:
1 We need to be clear about when a correlation from sample data is used as a descriptive
statistic and when it is used to make inferences about true relationships in the
population (whether there is a true linear relationship between two variables or indeed
any relationship). A population correlation is denoted by the Greek letter rho (ρ).
2 We should distinguish between correlation and association. When observations on
each variable can be ordered relative to all other observations on the same variable,
(for example, higher scores represent more of an attribute—continuous or rank
scores,) then we can speak of correlation. When observations are discrete counts and it
is not meaningful to arrange these counts in individual ranks or ordered categories
then we use the term association rather than correlation.
A correlation between two variables does not imply causality, however an underlying
causal relationship may exist. In Chapter 3, Initial Data Analysis, we described ways of
plotting data when examining the distribution of variables. A useful way to explore
bivariate (two-variable) relationships is to plot two variables at a time on a scatterplot
(one variable on the Y axis and the other on the X axis). The scatter of points depicted
enables interpretation of the relationship between the variables, for example, see Figure
7.1.
Inferences involving rank data 205