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,Pearson Product-Moment Correlation Coefficient (r)
The most common measure of correlation that quantifies the strength and direction of the
relationship between two continuous variables.
Purpose of Correlation Analysis
Used to identify associations or relationships between two variables (e.g., weight loss and
depression, patient satisfaction and health status).
Pearson's r Value Range
Always between -1.00 and +1.00.
Zero Correlation (r = 0)
Indicates no relationship between variables.
Negative Correlation
Higher values of one variable (x) are associated with lower values of the other (y).
Positive Correlation
Higher values of one variable (x) are associated with higher values of the other. (y)
,sign of r value
Indicates the slope direction of the regression line (positive or negative) on a scatterplot
that compares two variables
Scatterplot
A visual graph of paired data points used to identify linear relationships between
variables.
Pearson's r: Weak positive association
0.00 to <0.30
Pearson's r: Weak negative association
0.00 to <-0.30
Pearson's r: Moderate positive association
0.30 to 0.49
Pearson's r: Moderate negative association
-0.49 to -0.30
, Pearson's r: Strong positive association
0.50 to 1.00
Pearson's r: Strong negative association
-1.00 to -0.50
Associational Research Design
Designs that use Pearson's r to measure the relationship between two or more
attributional (participant) variables.
Attributional Variables
Participant characteristics such as health status, blood pressure, gender, diagnosis, or
ethnicity.
Pearson's r assumptions: Level of measurement
Continuous or interval, or ratio level
Continuous Variables
Variables measured at the interval or ratio level
Interval Level Data
Data with equal intervals between points (e.g., temperature in °C or °F).
Ratio Level Data
Data with equal intervals and a true zero point (e.g., weight, height, income).