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Semi-Partial r

A semi-partial r (also referred to as a semi-partial correlation) provides some information about the correlation between two variables, removing the influence of a third variable, but only from one of the two variables. A semi-partial correlation is useful for communication researchers when they desire to remove the variability from one element of the analysis but not the other element. To provide further understanding of this correlation, this entry provides definitions and implications of correlation, partial correlation, and semi-partial correlation.

Correlation

A correlation between two variables (X and Y) is a measure of the degree of correspondence between the two variables, and is represented as rXY. Essentially, as the value of one variable changes, researchers want to know what happens to the value of the other variable. The key is that a good or high correlation provides information (a prediction) about the value of a second variable from a first variable. All correlations (regardless of type) are efforts to make a prediction (using one or many variables) about some outcome of interest. A bivariate correlation (one involving just two variables) is reflexive, which means that the prediction goes in both directions, either predicting the value of X from Y or the value of Y from X.

Suppose, for example, researchers know the level of fear or anxiety a person has about public speaking and they desire to confidently predict the level of competence exhibited by that person. A zero correlation means that no prediction (often called covariation) exists, which indicates that knowing the level of fear or anxiety about public speaking provides no information about the level of competence. Similarly, knowing the competence of the person provides no inference about the level of public speaking anxiety. A correlation that is 1.00 (or –1.00) provides perfect predictability, meaning knowing a value of one variable indicates knowledge of the precise value of the other variable. Most correlations usually fall between zero and perfection. The problem is that other sources of variability may exist that would change the level of association, if known. For example, whether or not a person has taken a prior public speaking course may influence both variables (i.e., level of anxiety and level of competence). So at least two sets of persons exist (i.e., those having taken a public speaking course and those that have not taken such a course). What researchers want to do is to remove the influence or the impact of having taken a course from the observed relationship between anxiety about speaking and speaking performance. This technique is called partial correlation and is described in the next section.

Partial Correlation

A partial correlation (some texts use the term part correlation) examines the relationship between two variables (X and Y) and then removes the influence or effect of a third variable (A) and is represented as rXY.A. One way to describe the new relationship is that it reveals what happens to the correlation between X and Y if the value of the third variable (A) is known. Essentially, the argument becomes that when the third variable is controlled or removed, a source of variability becomes removed and the observed zero order (i.e., a correlation without modification) bivariate relationship may change.

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