# How is a correlation different than a partial correlation?

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**What is a correlation?**

- Correlation is the measure of the
__strength__and__direction__of the relationship between the variables - Direction of the relationship can be either positive or negative. Correlations can vary between -1 and 1. A positive relationship is indicated by a positive value (e.g., ranging from 0 to 1). A negative relationship is indicated by a negative value (e.g., ranging from 0 to -1). - An example of a positive relationship is the relationship between height and weight. The higher the outcome on one variable, the higher the outcome on the other variable. - An example of a negative relationship is the relationship between exercise and weight. The higher the outcome on one variable, the lower the outcome on the other variable.
- Strength of the relationship is measured from 0 to 1/-1. The farther the value is away from 0, the stronger the relationship. The approximate criteria for strength is 0 for no effect, .1 for a small effect, .3 for a medium effect, and .5 for a large effect. Notice those values can be either positive or negative, depending upon the direction of the relationship, so a .2 and -.2 relationship indicate the same strength, but different direction

**What is a partial correlation?**

- Partial correlation is the relationship between two variables while controlling for a third variable. The purpose is to find the unique variance between two variables while eliminating the variance from a third variables.
- You typically only conduct partial correlation when the third variable has shown a relationship to one or both of the primary variables. In other words, you typically first conduct correlational analysis on all variables so that you can see whether there are significant relationships amongst the variables, including any "third variables" that may have a significant relationship to the variables under investigation.
- In addition to this statistical pre-requisite, you also want some theoretical reason why the third variable would be impacting the results.
- You can conduct Partial Correlation with more than just 1 third-variable. You can include as many third-variables as you wish.

**Example of partial correlation:**

- Output below is for the relationship between "commit1" and "commit3" while controlling for "prosecutor1". "Commit1" measures the participants beliefs about what percent of people brought to trial did in fact commit the crime. "Commit3" measures the participants beliefs about what percent of people convicted did in fact commit the crime. You would predict a positive relationship between those two variables. The top part of the output below represents the bivariate correlation between those two variables, r = .352, p = .000
- "Prosecutor1" measures how well the participants trust/like Prosecutors. "Prosecutor1" is entered as the controlling variable because: (1) statistically, it shows significant relationship to both commit1 and commit3. You can see that significant relationship in the top part of the "Correlations" box below which presents the correlations without controlling for a third variable, (2) theoretically, it is possible that the reason why commit1 and commit3 are connected is because if participants like/trust Prosecutors they may thus be more likely to believe that the Prosecutor is correct and the defendants are guilty.
- Thus, given this plausible (statistical and theoretical) third-variable relationship, it is interesting to note that controlling for "Prosecutor1" did not lower the strength of the relationship between commit1 and commit3 by that much because the outcome while controlling for prosecutor1 was r = .341, p < .001. In other words, the relationship between commit1 and commit3 is NOT due to subjects trusting/liking the prosecutor.

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