Scenario 4 might depict the strong negative association (r= -0.9) generally observed between the number of hours of aerobic exercise per week and percent body fat.Įxample - Correlation of Gestational Age and Birth WeightĪ small study is conducted involving 17 infants to investigate the association between gestational age at birth, measured in weeks, and birth weight, measured in grams.Scenario 3 might depict the lack of association (r approximately = 0) between the extent of media exposure in adolescence and age at which adolescents initiate sexual activity.Scenario 2 depicts a weaker association (r=0,2) that we might expect to see between age and body mass index (which tends to increase with age).Scenario 1 depicts a strong positive association (r=0.9), similar to what we might see for the correlation between infant birth weight and birth length.The figure below shows four hypothetical scenarios in which one continuous variable is plotted along the X-axis and the other along the Y-axis. Graphical displays are particularly useful to explore associations between variables. Therefore, it is always important to evaluate the data carefully before computing a correlation coefficient. It is important to note that there may be a non-linear association between two continuous variables, but computation of a correlation coefficient does not detect this. A correlation close to zero suggests no linear association between two continuous variables. The magnitude of the correlation coefficient indicates the strength of the association.įor example, a correlation of r = 0.9 suggests a strong, positive association between two variables, whereas a correlation of r = -0.2 suggest a weak, negative association. The sign of the correlation coefficient indicates the direction of the association. The correlation between two variables can be positive (i.e., higher levels of one variable are associated with higher levels of the other) or negative (i.e., higher levels of one variable are associated with lower levels of the other). Ranges between -1 and +1 and quantifies the direction and strength of the linear association between the two variables. The sample correlation coefficient, denoted r, Once you have established that a linear relationship exists, you can take the next step in model building.In correlation analysis, we estimate a sample correlation coefficient, more specifically the Pearson Product Moment correlation coefficient. The next step is to quantitatively describe the strength and direction of the linear relationship using “r”. This graph allows you to look for patterns (both linear and non-linear). When you investigate the relationship between two variables, always begin with a scatterplot. Ignoring the scatterplot could result in a serious mistake when describing the relationship between two variables. Pearson’s linear correlation coefficient only measures the strength and direction of a linear relationship. Plot 2 shows a strong non-linear relationship. Plot 1 shows little linear relationship between x and y variables. Both of these data sets have an r = 0.01, but they are very different.
Negative values of “r” are associated with negative relationships.Ĭorrelation is not causation!!! Just because two variables are correlated does not mean that one variable causes another variable to change.Įxamine these next two scatterplots.Positive values of “r” are associated with positive relationships.It is a unitless measure so “r” would be the same value whether you measured the two variables in pounds and inches or in grams and centimeters.This statistic numerically describes how strong the straight-line or linear relationship is between the two variables and the direction, positive or negative. The linear correlation coefficient is also referred to as Pearson’s product moment correlation coefficient in honor of Karl Pearson, who originally developed it.
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