partial correlation

Partial correlation is a measure of the strength and direction of a linear relationship between two continuous variables whilst controlling for the effect of one or more other continuous variables (also known as 'covariates' or 'control' variables). Although partial correlation does not make the distinction between independent and dependent variables, the two variables are often considered in such a manner (i.e., you have one continuous dependent variable and one continuous independent variable, as well as one or more continuous control variables).

Note: Many aspects of partial correlation can be dealt with using multiple regression and it is sometimes recommended that this is how you approach your analysis. This is somewhat evident in the SPSS Statistics where you can carry out partial correlation using two different procedures: Correlate and Regression.

For example, you could use partial correlation to understand whether there is a linear relationship between 10,000 m running performance and VO₂max (a marker of aerobic fitness), whilst controlling for wind speed and relative humidity (i.e., the continuous dependent variable would be "10,000 m running performance", measured in minutes and seconds, the continuous independent variable would be VO₂max, which is measured in ml/min/kg, and the two control variables – that is, the two other continuous independent variables you are adjusting for – would be "wind speed", measured in mph, and "relative humidity", expressed as a percentage). You may believe that there is a relationship between 10,000 m running performance and VO₂max (i.e., the larger an athlete's VO₂max, the better their running performance), but you would like to know if this relationship is affected by wind speed and humidity (e.g., if the relationship changes when taking wind speed and humidity into account since you suspect that athletes' performance decreases in more windy and humid conditions). Alternately, you could use partial correlation to understand whether there is a linear relationship between ice cream sales and price, whilst controlling for daily temperature (i.e., the continuous dependent variable would be "ice cream sales", measured in US dollars, the continuous independent variable would be "price", also measured in US dollars, and the single control variable – that is, the single continuous independent variable you are adjusting for – would be daily temperature, measured in °C). You may believe that there is a relationship between ice cream sales and prices (i.e., sales go down as price goes up), but you would like to know if this relationship is affected by daily temperature (e.g., if the relationship changes when taking into account daily temperature since you suspect customers are more willing to buy ice creams, irrespective of price, when it is a really nice, hot day).

This "quick start" guide shows you how to carry out a partial correlation using SPSS Statistics, as well as interpret and report the results from this test. However, before we introduce you to this procedure, you need to understand the different assumptions that your data must meet in order for a partial correlation to give you a valid result. We discuss these assumptions next.