Chapter 24

Comparing several means

1. Use boxplots generated using gf_boxplot to compare samples from two more more populations.
2. State the null and alternative hypotheses for a claim about equality amongst three or more population means.
3. Explain why the alternative hypothesis of a “all means are equal” null hypothesis does not specify precisely which population means, if any, differ.
4. Recognize that a test related to three or more population means is called an Analysis of Variance.
5. Recognize the acronym ANOVA for Analysis of Variance.

The \(F\) statistic

1. State the test statistic for a one-way ANOVA.
2. Explain the effect on the \(F\)-statistic of increasing / decreasing the variability amongst the sample means and increasing / decreasing the variability within each sample.
3. Indicate what values of an \(F\)-statistic indicate evidence against a null hypothesis.
4. Given rug plots and box plots for several samples, indicate whether the \(F\)-statistic will be small or large.
5. State the sampling distribution of the \(F\) statistic when the null hypothesis is true.
6. State the type of \(P\)-value (right-sided, left-sided, or two-sided) computed from the \(F\) distribution, and explain why this type of \(P\)-value is used.

The analysis of variance \(F\) test

1. Use the functions aov and summary to perform an \(F\) test in R.
2. Interpret the output of an aov object passed to summary.

Conditions for ANOVA

1. State the assumptions of a one-way ANOVA.
2. State an alternative to a one-way ANOVA when the assumptions of the one-way ANOVA fail or cannot be checked.

Pairwise Comparisons (Lecture Notes for Lecture 21)

1. Explain why pairwise comparisons are necessary after finding a statistically significant \(F\) statistic.
2. Recognize Tukey’s Honest Significant Difference as a pairwise comparison method.
3. Use the function TukeyHSD to perform pairwise comparsisons in R.
4. Interpret the output of TukeyHSD when passed an output from aov, including:
   • the estimated pairwise differences
   • the left and right confidence intervals for the pairwise differences
   • the adjusted \(P\)-value for the pairwise comparisons
5. State the null hypothesis implicit in the \(P\)-values reported by TukeyHSD.