A psychologist is interested in the relationship between job satisfaction and stress. Within a large corporation, the psychologist asked a random sample of workers two questions. The first question asked workers to rate their overall satisfaction with their job on a scale from 1 to 50. The second question asked the workers to rate their stress level during the past week on a scale from 1 to 50. What type of statistical test best assesses the relationship between job satisfaction and level of stress?
Correlation is a useful tool for assessing a linear relationship between two paired continuous variables, in this case job satisfaction and stress. Recall that finding that two variables are correlated does not allow a researcher to make causal statements about the relationship between the two variables. Correlation merely measures the strength of the linear relationship between the two variables. We also should plot the data to assess whether the relationship is linear and whether assumptions for the statistical test of significance have been met. A confidence interval would be useful to describe the precision of our estimate of the population correlation.
One-way ANOVA can be used to test hypotheses regarding the equality of means for three or more groups. In this example, we do not have multiple groups to compare. Both measures are continuous.
Analysis of covariance is used to remove/control for the effects of one or more confounding variables when we are comparing means for three or more groups on a continuous dependent variable. Here we have two continuous measures with no grouping variable.
Partial correlation is a statistical technique that is used to control for the effects of one or more confounding variables. Here we have only two variables.
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The Expert says…
The null hypothesis we are testing is that there is no linear relationship between two variables in the population from which the sample is selected.
The two measures are both continuous, and the participants in our study each provide both measures. We can test for a linear relationship between these two measures with correlation or regression.
As a first step, we should plot the data to assess whether a linear relationship is an appropriate model. Correlation is sensitive to only a linear relationship, so even if the correlation is zero there could be a nonlinear relationship, as with a U shaped curve. For the test of statistical significance to be appropriate we must satisfy assumptions for the test, including a normal distribution of errors around the linear model with equal variance for one of the variables for all values of the other variable. It would be useful to compute a confidence interval, to provide information on the precision of the sample correlation as an estimate of the population correlation.