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Example 6-2: Wechsler Adult Intelligence Scale
Section* *

To illustrate these calculations we will return to the Wechsler Adult Intelligence Scale data.

This dataset includes data on *n* = 37 subjects taking the Wechsler Adult Intelligence Test. This test is broken up into four components:

- Information
- Similarities
- Arithmetic
- Picture Completion

Recall from the last lesson that the correlation between Information and Similarities was \(r = 0.77153\).

#### Using SAS

The partial correlation between Information and Similarities given Arithmetic and Picture Completion may be computed using the SAS program shown below.

Download the SAS program: wechsler2.sas

Download the SAS Output: wechsler2.lst

View the video below to find the partial correlation of Information and Similarities given Arithmetic and Picture Completion using the Wechsler Adult Intelligence Test data in SAS.

#### Using Minitab

View the video below to find the partial correlation of Information and Similarities given Arithmetic and Picture Completion using the Wechsler Adult Intelligence Test data in Minitab.

#### Analysis

The output is in two tables. The first table gives the conditional variance-covariance matrix for Information and Similarities given Arithmetic and Picture Completion. The second table gives the partial correlation. Here we can see that the partial correlation is:

\(r = 0.71188\)

**Conclusion**: Comparing this to the previous value for the ordinary correlation, we can see that the partial correlation is not much smaller than the ordinary correlation. This suggests that little of the relationship between Information and Similarities can be explained by performance on the Arithmetic and Picture Completion portions of the test.

#### Interpretation

Partial correlations should be compared to the corresponding ordinary correlations. When interpreting partial correlations, three results can potentially occur. Each of these results yields a different interpretation.

- Partial and ordinary correlations are approximately equal. This occurred in our present setting. This suggests that the relationship between the variables of interest cannot be explained by the remaining explanatory variables upon which we are conditioning.
- Partial correlations are closer to zero than ordinary correlations. This is a common result and often what we anticipate. This suggests that the relationship between the variables of interest might be explained by their common relationships to the explanatory variables upon which we are conditioning. For example, we might find the ordinary correlation between blood pressure and blood cholesterol might be a high, strong positive correlation. We could potentially find a very small partial correlation between these two variables, after we have taken into account the age of the subject. If this were the case, this might suggest that both variables are related to age, and the observed correlation is only due to their common relationship to age.
- Partial correlations are farther from zero than ordinary correlations. This rarely happens. This situation would suggest that unless we take into account the explanatory variables upon which we are conditioning, the relationship between the variables of interest is hidden or masked.