Correlation: Effect size

Effect size or "strength of effect" refers to the magnitude or strength of the treatment (the independent variable). How much of an impact did the predictor have?

There are statistics for calculating effect size. We will not go into them here. You can get a good idea of the strength of an effect by looking at the descriptive statistics (that is why it is very important to include them when describing research results). Are the differences between the means large? Or are they quite small, even though the null hypothesis was rejected? In very large samples, a small difference between two means may be statistically significant. Is the correlation coefficient large or small?

A small correlation coefficient may be statistically significant, but not be important. For example, there is a small but reliable positive correlation between height and intelligence. The relationship is of no value in predicting intelligence among individuals. No one has suggested that height be used as a criteria for college admission.

There is a reliable gender difference in spatial ability with regard to manipulating 3-dimensional objects. Men, on the average, do slightly better than women. Even though the difference is quite small, the finding is consistent, and therefore statistically significant. However, the distribution of scores from women and men show considerable overlap, meaning that even though men, on the average, do better than women, there are many women who do better than many men. More....

Using the term "significant" for results
described by inferential statistics such as ANOVA, t-test, Chi-square, and
correlation, is misleading because it is easily
confused with "importance." A "statistically
significant" result really means that the effect was greater than expected
by chance. "Statistically reliable" would be a better term. A small *p* value
means that if we repeated the study, there is a high likelihood that we would
get a very similar result. It might not be a strong effect, or not matter very
much. It only needs to be better than chance.

Next section: Which coefficient to use? (short)