Differentiate difference tests from relationship tests.
Difference tests—like z, t, and F tests—test for differences between groups on a dependent variable. Relationship tests determine if a relationship exists between two variables measured in one group of cases.
Define and describe a relationship.
If two variables are correlated, they vary together systematically. The relationship may be one of cause and effect, but correlation does not mean causation: it may just mean association.
Scatterplots display a relationship graphically. The scatterplot will look the same if it is made for z scores or raw scores. The strength of a Pearson correlation coefficient, which measures the degree of linear relationship between two interval and/or ratio variables, is shown by how well the points form a line. As the shape made by the points moves from a line to an oval, the relationship grows weaker. Scatterplots should be inspected for three conditions that can affect correlations: nonlinearity, outliers, and restriction of range.
A Pearson r is a number that summarizes the strength and direction of the linear relationship. It is defined as the average of the pairs of z scores for each case multiplied together. r ranges from –1.00 to +1.00 with r = .00 meaning no relationship and an r of 1.00 or –1.00 indicating a perfect relationship. Positive r’s are called direct relationships (larger values of X are associated with larger values of Y), and negative r ’s are called inverse relationships (larger values of X are associated with smaller values of Y).
Compute a Pearson r.
Pearson r is used to examine the linear relationship between two interval/ratio-level variables. The assumptions for it must be met and hypotheses, either directional or nondirectional, should be set. The decision rule depends on the hypotheses, the researcher’s willingness to run the risk of making a Type I error, and the number of cases.
Interpret the results of a Pearson r.
The interpretation of a Pearson r is based on the answers to three questions: (1) Was the null hypothesis rejected? (2) How big is the effect? (3) How wide is the confidence interval? The effect size, r2, gives a sense of the size of the effect in the sample, while the confidence interval offers a sense of ρ, the population value of the correlation. In addition, if the null hypothesis is not rejected, one can see how likely Type II error is and estimate how many cases one would need to have adequate power.
Take into account the effect of a confounding variable.
A partial correlation is a way, mathematically, to see how much a relationship between two variables is influenced by a third variable.