Assumptions Underlying the Tests
Assumptions Underlying the Pearson Correlation Coefficient
Interval-level measurement. Both the predictor and criterion variables should be assessed on an interval- or ratio-level of measurement.
Random sampling. Each participant in the file will contribute one score on the predictor variable, and one score on the criterion variable. These pairs of scores should represent a random sample drawn from the population of interest.
Linearity. The relationship between the criterion and predictor variables should be linear. This means that the mean criterion scores at each value of the predictor variable should fall on a straight line. The Pearson correlation coefficient is not appropriate for assessing the strength of the relationship between two variables with a curvilinear relationship.
Bivariate normal distribution. The pairs of scores should follow a bivariate normal distribution. That is, scores on the criterion variable should form a normal distribution at each value of the predictor variable. Similarly, scores of the predictor variable should form a normal distribution at each value of the criterion variable. When scores represent a bivariate normal distribution, they form an elliptical scattergram when plotted (i.e., their scattergram is shaped like a rugby ball: fat in the middle and tapered on the ends).
Assumptions Underlying the Spearman Correlation Coefficient
Ordinal-level measurement. Both the predictor and criterion variables should be assessed on an ordinal level of measurement. However, interval- or ratio-level variables are sometimes analyzed with the Spearman correlation coefficient when one or both variables are markedly skewed.
Assumptions Underlying the Chi-Square Test of Independence
Nominal-level measurement. Both variables should be assessed on a nominal scale.
Random sampling. Participants contributing data should represent a random sample drawn from the population of interest.
Independent cell entries. Each participant should appear in one cell only. The fact that a given participant appears in one cell should not affect the probability of another appearing in any other cell (i.e., independence of observations).
Expected frequencies of five or more. When analyzing a 2 × 2 classification table, no cell should display an expected frequency of less than 5. With larger tables (e.g., 3 × 4 tables), no more than 20% of the cells should have expected frequencies less than 5.