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Analysis of Variance includes a set of methods for testing hypothesis about differences between means. Its applications range from simple analysis where we compare the means of y across categories of x, to more complicated situations with multiple categorical and measurement x variables. t tests for hypotheses regarding a single mean that is one-sample or a pair of means that is two-sample correspond to elementary forms of ANOVA.

Rank-based “nonparametric” tests, including sign, Mann-Whitney and Kruskal-Wallis, take a different approach to comparing distributions. These tests make weaker assumptions about measurement, distribution shape and spread. Consequently, they remain valid under a wider range of conditions than ANOVA and its “parametric” relatives. Careful analysis sometimes uses parametric and nonparametric tests together and checking whether both point towards similar conclusions.

ANOVA is the first of stat’s model-fitting commands to be introduced. ANOVA has considerable flexibility encompassing a wide variety of models. It can fit one-way and N-way ANOVA or analysis of covariance (ANCOVA) for balanced and unbalanced designs, including designs with missing cells. It can also fit factorial, nested, mixed or repeated-measures designs. One follow-up command, predict, calculates predicted values, several types of residuals and assorted errors and diagnostic statistics after ANOVAs.

Example Commands:

• ANOVA y  x1 x2 Performs two-way ANOVA testing for difference among the means of y across categories of x1 and x2.
• ANOVA y x1 x2 x1*x2 Performs a two-way factorial ANOVA, including both the main and interaction (x1*x2) effects of categorical variables x1 and x2.
• ANOVA y x1 x2 x3  x1*x2  x1*x3  x2*x3  x1*x2*x3 Performs a three-way factorial ANOVA, including the three-way interaction x1*x2*x3, as well as all two-way interactions and main effects.
•  Kwallis y, by (x) performs a Krushkal-Wallis test of the null hypothesis that y has identical rank distributions across the k categories of x (k>2).
• One way y x Performs a one-way analysis of variance (ANOVA), testing for differences among the means of y across categories of x. The same analysis, with a different output table, is produced by anova y x.
• One way y x, tabulate scheffe: Performs one-way ANOVA, including a table of sample means and scheffe multiple comparison tests in the output.

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