Pearson's r Formula

Restriction of Range

Cohen's Guidelines for Interpreting Pearson's r

What does Pearson's r specifically measure in statistics?

A psychology researcher calculates the following Pearson's r correlation coefficients across four different studies. Arrange these values in order from the weakest linear relationship to the strongest linear relationship.

Match each psychology research scenario with the Pearson's $r$ correlation coefficient that best represents the strength and direction of the described linear relationship.

A researcher reports a Pearson's $r$ of +0.05 for the relationship between 'arousal level' and 'test performance.' However, a scatterplot reveals a strong 'inverted-U' pattern where performance is highest at moderate arousal levels and low at both extremes. If the researcher concludes that there is no meaningful relationship between these variables, their conclusion is analytically flawed because Pearson's $r$ only quantifies the strength of linear associations.

Pearson's $r$ is a standardized metric designed to describe and quantify the strength and direction of the linear relationship between two continuous variables.

Pearson's $r$ is described as a 'standardized measure' of the linear relationship between two quantitative variables. What does it mean for this metric to be standardized, and why is this property useful to a psychology researcher?

A psychology researcher calculates a Pearson's $r$ to assess the relationship between 'Stress' and 'Physical Health' but only collects data from a group of high-stress emergency room doctors. In evaluating this study, a colleague notes that this restriction of range will likely _____ the true strength of the linear relationship between these variables compared to what would be found in a more diverse sample.

Match each research scenario involving quantitative variables with the aspect of Pearson's $r$ it applies.

A psychology researcher calculates Pearson's $r$ to analyze the association between anxiety and academic performance. However, because anxiety and performance have a U-shaped curvilinear relationship, Pearson's $r$ fails to capture the true association. This occurs because Pearson's $r$ is mathematically restricted to describing and quantifying only the _____ relationship between continuous variables.

A psychology student is evaluating whether Pearson's $r$ is the correct metric to describe the relationship between two variables in a dataset. Put the evaluation and calculation steps in the correct logical order.