Statistical Analysis for Education and Psychology Researchers

The correlation between MATHS (M) and SMATHS (SM) is therefore

and the correlation between MATHS (M) and

RAVEN (R) is

Interpretation

The plot of MATHSSMATHS suggests an approximate linear trend but the plot of
MATHSRAVEN appears to be non-linear as far as it is possible to tell with as small a
sample as this. This later plot also has a very obvious outlier observation. If this pattern
(for MATHS vs RAVEN) had been obtained with a larger sample, it would provide good
evidence for not using a Pearson correlation statistic. It is noticeable that one variable,
RAVEN has a smaller range and less variability in the scores than the other variable
(SMATHS).
The correlation between MATHS and SMATHS is strong and positive suggesting a
linear relationship, higher scores on MATHS are associated with higher scores on
SMATHS. The moderate negative correlation between MATHS and RAVEN is generally
in keeping with what would be expected because smaller values on the Raven scale
indicate higher reasoning ability and higher reasoning ability might be expected to be
associated with higher maths ability scores. The scatterplot of this bivariate relationship
indicates, however, that the relationship is not linear. When a correlation is consistent
with what is expected it is easy to forget that there may not be a linear relationship
between the two variables (the obvious benefit of examining scatterplots is demonstrated
here). When a large correlation is found between two variables (rm.sm=0.89) it is tempting
to attribute a cause and effect relationship. This is incorrect. The only valid conclusions
to be drawn from these descriptive correlations is that there is a linear trend between
MATHS and SMATHS but not between MATHS and RAVEN. It is important to stress
that these interpretations are only illustrative, with a sample size of 10 a Pearson
correlation would not be generally appropriate.

Significance of Correlation r

Once a correlation has been computed the researcher may want to know how likely is this
obtained correlation, that is, is this a chance occurrence or does it represent a significant
population correlation?

Inferences involving continuous data 287