Adjusted Standardized Residual. The standardized residuals are a measure of the strength of the difference between observed values and expected values. They are calculated by dividing the raw residuals (or the difference between the observed counts and expected counts), by the square root of the expected counts. A general interpretation would be

• If the AR is less than -2, the observation is less than expected
• If the AR is greater than 2, the observation is greater than expected

Much larger adjusted standardized residuals suggest extreme differences between observations and expectations.

d

Cohen’s d effect size is the standardized difference between the mean of two groups. An estimate of the practical importance of an observed difference or relationship, often used to complement statistical significance. With NSSE Engagement Indicators, group differences >.1 are considered small, > .3 are medium, and > .5 are large (Rocconi & Gonyea, 2018).

p

The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis. Use the p-value to determine whether to reject or fail to reject the null hypothesis, which states that the variables are independent.

r

Pearson’s correlation. the correlation coefficient r measures the strength and direction of a linear relationship between two variables on a scatterplot. The value of r is always between +1 and –1.

r w/subscript 'pb'

A point-biserial correlation is very similar to a Pearsons r, except that it measures the strength and direction of the association that exists between one continuous variable and one dichotomous variable.