i) The similarity of the distributions of the two variables (X, Y) affects the magnitude of the correlation coefficient. Larger differences in the shapes of these distributions result in a smaller correlation coefficient. In addition, because the variance of a distribution influences its shape, larger differences between the distributions leads to lower homoscedasticity (or greater heteroscedasticity).

ii) Another factor that influences the magnitude of the correlation coefficient is the reliability of each measure (Some books refer to this as ‘measurement error’). To the extent that either or both variables are unreliable the correlation between them will be attenuated (see Cohen et al., 2003, page 55 to see how reliability coefficients can be used to estimate the ‘true’ correlation between variables).

iii) A third factor that influences correlation is the range of scores on X and Y. The correlation will be attenuated (i.e., lower than its actual or ‘true’ value) if the range of observed scores is restricted on one or both variables.

iv) A fourth factor that can influence correlation is whether there is a substantial non-linear component to the relation. The correlation coefficient is a measure of the linear relationship between two variables, so if there is substantial non-linearity the correlation coefficient will underestimate the magnitude of the relationship between the variables.