Pearson Product-Moment Correlation Coef?cient

Pearson Product-Moment Correlation Coef?cient

Calculating Pearson Product-Moment Correlation Coef?cient

Correlational analyses identify associations between two variables. There are many different kinds of statistics that yield a measure of correlation. All of these statistics address a research question or hypothesis that involves an association or relationship. Examples of research questions that are answered with correlation statistics are, “Is there an association between weight loss and depression?” and “Is there a relationship between patient satisfaction and health status?” A hypothesis is developed to identify the nature (positive or negative) of the relationship between the variables being studied.

The Pearson product-moment correlation was the ?rst of the correlation measures developed and is the most commonly used. As is explained in Exercise 13 , this coef?cient (statistic) is represented by the letter r , and the value of r is always between ? 1.00 and + 1.00. A value of zero indicates no relationship between the two variables. A positive correlation indicates that higher values of x are associated with higher values of y. A negative or inverse correlation indicates that higher values of x are associated with lower values of y.

The r value is indicative of the slope of the line (called a regression line) that can be drawn through a standard scatterplot of the two variables (see Exercise 11 ). The strengths of different relationships are identi? ed in Table 28-1 ( Cohen, 1988 ). EXERCISE 28 TABLE 28-1 STRENGTH OF ASSOCIATION FOR PEARSON r Strength of Association Positive Association Negative Association Weak association 0.00 to < 0.300.00 to < ? 0.30 Moderate association 0.30 to 0.49 ? 0.49 to ? 0.30 Strong association 0.50 or greater ? 1.00 to ? 0.50

RESEARCH DESIGNS APPROPRIATE FOR THE PEARSON r

Research designs that may utilize the Pearson r include any associational design ( Gliner, Morgan, & Leech, 2009 ). The variables involved in the design are attributional, meaning the variables are characteristics of the participant, such as health status, blood pressure, gender, diagnosis, or ethnicity. Regardless of the nature of variables, the variables submit-ted to a Pearson correlation must be measured as continuous or at the interval or ratio level.

STATISTICAL FORMULA AND ASSUMPTIONS

Use of the Pearson correlation involves the following assumptions: 1. Interval or ratio measurement of both variables (e.g., age, income, blood pressure, cholesterol levels). However, if the variables are measured with a Likert scale, and the frequency distribution is approximately normally distributed, these data are