Statistics II is often about data analysis, and the trick is to know when to use which analysis method. The following table helps you compare, contrast, and decide what data analysis to use and when. Use it for an easy reference and to review for exams.

Analysis Purpose When It’s Used
Simple linear regression Use x to estimate y, using a line Response variable y quantitative; constant variance across x, which is quantitative
Multiple regression Use multiple x variables (x, i = 1 . . . , k) to estimate y using a plane y is quantitative; normal distribution for each xi combination with constant variance
Nonlinear regression Use x to estimate y using a curve y is quantitative; normal distribution; constant variance across x
Logistic regression Use x to estimate p = probability of success of y y is a yes/no variable with success p
One-way ANOVA Compare two population means using one factor y is quantitative; factor is x
Tukey’s test Multiple comparisons Confidence intervals for all pairs of means; keeps error rates low
Fisher’s LSD test Multiple comparisons Confidence intervals for all pairs of means; overall error rate higher than Tukey’s
Scheffe’s method Multiple comparisons Looks at linear combinations of means, not just pairs
Bonferroni adjustment Multiple comparisons All pairs of t-tests adjusted for number of tests
Dunnetts’s test Multiple comparisons Experiments; compares treatment versus control only
Student Newman-Keuls test (SNK) Multiple comparisons Stepwise approach, comparing pairs ordered from smallest to largest
Duncan’s multiple range test (MRT) Multiple comparisons Adjusts SNK test for more power
Two-way ANOVA Compare more than two population means, using two factors plus interaction y is quantitative; factors are (x1, x2)
Chi-square tests Test independence of two variables or goodness-of-fit for one qualitative variable All variables qualitative
Sign/Signed rank tests Test one population median y is quantitative or ordinal (based on ranks)
Rank sums test Compare two population medians y is quantitative or ordinal (based on ranks)
Kruskal-Wallis test Compare more than two population medians using one factor y is quantitative or ordinal (based on ranks); factor is x