First, determine which variable in the problem is the Response Variable. This is often called the Y Variable.
Next, determine which variable or variables are the Explanatory Variables. They are often called the X Variables.
Next, determine the design points, that is, all the distinct combinations of levels or values of the X-variables.
Finally, choose the analysis from the following chart.
Y | X | Pure Error? | Analysis |
Normal | 1 continuous | No | Regression ANOVA. |
Normal | 1 categorical | Yes | 1-Factor ANOVA [If the factor has only 2 levels, a 2-sided 2-sample t-test will give exactly the same analysis.] |
Normal | 1 categorical/continuous | Yes | Regression ANOVA with Lack of Fit test. |
Normal | 2 categorical | No | 2-Factor ANOVA without interaction. |
Normal | 2 categorical, one of them a "nuisance factor" | No | 2-Factor ANOVA without interaction, sometimes called "a complete block design". [If the factor of interest has only 2 levels, a 2-sided paired t-test will give the exactly same analysis. A sign test can also be used; it will be robust against non-normality but less powerful than the t-test.] |
Normal | 2 categorical | Yes | 2-Factor ANOVA with interaction. | Poisson | 2 categorical | NA | Pearson's chi-square test for independence. |