A researcher is interested in studying the relationship between reading comprehension and grades in science. However, he or she is also concerned with the effect of IQ on the relationship. The researcher finally decides to compute a partial correlation coefficient between reading comprehension and grades in science when IQ is held constant.
SPSS for Windows
1. Enter Data
2. Choose Analysis \ Correlation \ Partial.
Select the two variables, read and science, to be correlated.
Note that you may press and hold down the Control key (the Ctrl key on your keyboard) while clicking on the two variables. Then click the arrow button to move them at the same time. You may also move the variables one by one.
Controlling for: Select the variable IQ.
Click Options. Click `Means and standard deviations` and `Zero-order correlations` to obtain a matrix of simple correlations between all variables. Click Continue. Click OK.
SPSS Output
The null hypothesis states that the correlation is equal to zero.
Is the correlation significantly different from zero?
There are three sets of bivariate correlations: read and science, read and IQ, scienc and IQ. Use the Bonferroni method to control for type I error across the 3 correlations.
Corrected Significance Level: Three correlations are tested (READ &SCIENCE, READ & IQ, and SCIENCE & IQ). Set the significance level as .017 (.05 / 3 = .017) for each test. Also, note that the degrees of freedom are equal to N - 2 = 9 - 2 = 7.
The correlation between reading comprehension and grades in science was significant, r(7) = .8072, p < .017.
The correlation between reading comprehension and IQ was significant, r(7) = .8742, p < .017.
The correlation between grades in science and IQ was significant, r(7) = .9005, p < .017.
Note that reading comprehension and grades in science are significantly influenced by IQ.Next, remove the effect of IQ from both reading comprehension and grades in science. Will the correlation between reading comprehension and grades in science still be significant?
The partial correlation between reading comprehension and grades in science with the influence of IQ ruled out from both variables is only .0949. It is not significant.
