The existence of a strong positive correlation between a student’s scores on the S.A.T. test and the income of their family (Trochim, 2006) shows that there is a powerful tendency for each measure to rise or fall in association with the other. Had it been a strong negative correlation, then each measure would change in direct opposition to the other variable in the relationship. The strength of the association is reflective of each item’s connection to the changes in the other, and so a strong correlation demonstrates a high amount of association. So it is true that S.A.T. scores and family income of students are strongly related, and one will rise or fall with the other in a very obvious manner.
While the magnitude of the relationship between S.A.T. scores and income can be described by correlation, it is not possible for the technique to explain causal direction (Clegg, Jackson, & Wall, 2011). Correlations describe similarity of changes, and not the order in which they take place. S.A.T. scores being correlated with family income only means that they change together in a closely associated pattern, but it does not mean that either variable can lead to the other. It could be possible that low income families cannot afford the educational tools needed for high test scores, or it may be that students with high scores also contribute to family income more so than those with lower results. Many other possibilities are also available to explain the causal direction of the relationship, but statistical evidence will need to come from an analysis other than correlation.
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- Clegg, C. W., Jackson, P. R., & Wall, T. D. (2011). The potential of cross‐lagged correlation analysis in field research. Journal of Occupational Psychology, 50(3), 177-196.
- Trochim, W. M. (2006). Correlation. In Research Methods Knowledge Base. Retrieved from http://www.socialresearchmethods.net/kb/statcorr.php
