Question

Give a plausible example of a three-variable research problem in which partial correlation would be a useful analysis. Define X1, X2, and Y. Make sure that you indicate which of your three variables is the "controlled for" variable ( X2). What results might you expect to obtain for this partial correlation, and how would you interpret your results (e.g., spurious correlation, mediation, moderation, and so on)?

Answer 1

Ans:

For partial correlation to provide accurate information about the relationship between variables, the following assumptions about the scores on X1 ,X2 , and Y must be reasonably well satisfied.

There are several different possible ways to analyze data when we introduce a third variable X2 into an analysis of variables X1 and Y. This chapter describes two preliminary or exploratory analyses that can be helpful in understanding what happens when a control variable X2 is included in an analysis:

1. We can obtain a bivariate correlation between X1 and Y separately for subjects who have different scores on X2 . For instance, if X2 is grade level (coded “1,”“5,” and “9”), we can compute three separate r1Y correlations between height and vocabulary for the students within Grades 1, 5, and 9.

2. We can obtain a partial correlation between X1 and Y, controlling for X2 . For example, we can compute the partial correlation between height and vocabulary score, controlling for grade level.