Pearson Correlation Coefficient Handout
Understanding the Pearson Correlation Coefficient (r)
The Pearson product-moment correlation coefficient (r) assesses the degree that quantitative variables are linearly related in a sample. Each individual or case must have scores on two quantitative variables (i.e., continuous variables measured on the interval or ratio scales). The significance test for r evaluates whether there is a linear relationship between the two variables in the population. The appropriate correlation coefficient depends on the scales of measurement of the two variables being correlated.
There are two assumptions underlying the significance test associated with a Pearson correlation coefficient between two variables.
Assumption 1: The variables are bivariately normally distributed.
If the variables are bivariately normally distributed, each variable is normally distributed ignoring the other variable and each variable is normally distributed at all levels of the other variable. If the bivariate normality assumption is met, the only type of statistical relationship that can exist between two variables is a linear relationship. However, if the assumption is violated, a non-linear relationship may exist. It is important to determine if a non-linear relationship exists between two variables before describing the results using the Pearson correlation coefficient. Non-linearity can be assessed visually by examining a scatterplot of the data points.
Assumption 2: The cases represent a random sample from the population and the scores on variables for one case are independent of scores on the variables for other cases.
The significance test for a Pearson correlation coefficient is not robust to violations of the independence assumption. If this assumption is violated, the correlation significance test should not be computed.
SPSS© computes the Pearson correlation coefficient, an index of effect size. The index ranges in value from -1.00 to +1.00. This coefficient indicates the degree that low
The Pearson product-moment correlation coefficient (r) assesses the degree that quantitative variables are linearly related in a sample. Each individual or case must have scores on two quantitative variables (i.e., continuous variables measured on the interval or ratio scales). The significance test for r evaluates whether there is a linear relationship between the two variables in the population. The appropriate correlation coefficient depends on the scales of measurement of the two variables being correlated.
There are two assumptions underlying the significance test associated with a Pearson correlation coefficient between two variables.
Assumption 1: The variables are bivariately normally distributed.
If the variables are bivariately normally distributed, each variable is normally distributed ignoring the other variable and each variable is normally distributed at all levels of the other variable. If the bivariate normality assumption is met, the only type of statistical relationship that can exist between two variables is a linear relationship. However, if the assumption is violated, a non-linear relationship may exist. It is important to determine if a non-linear relationship exists between two variables before describing the results using the Pearson correlation coefficient. Non-linearity can be assessed visually by examining a scatterplot of the data points.
Assumption 2: The cases represent a random sample from the population and the scores on variables for one case are independent of scores on the variables for other cases.
The significance test for a Pearson correlation coefficient is not robust to violations of the independence assumption. If this assumption is violated, the correlation significance test should not be computed.
SPSS© computes the Pearson correlation coefficient, an index of effect size. The index ranges in value from -1.00 to +1.00. This coefficient indicates the degree that low