Lesson 5.3: Inference for Multiple Means Using ANOVA

Readings 📖 and Instructional Video 🎦

Inference for Multiple Means

Read Section 7.5: Comparing Many Means with ANOVA in OpenIntro Statistics (Diez et al., 2019) CC BY-SA 3.0. We can compare means in two groups using the t-distribution. But to compare means in more than two groups, we use an F-distribution and a technique called Analysis of Variance (ANOVA). Note that the ANOVA F-test described here is sometimes referred to as Fisher’s ANOVA F-test. And, since we’re only concerned with a single explanatory variable here, it is called one-way ANOVA. As you read, look up new terminology in the Glossary and self-assess your understanding by attempting the guided practice exercises.

Watch the following two videos, 5 1B Inference for a Mean (duration 00:09:45) and 5 5B Conditions for ANOVA (duration 00:02:58) (Çetinkaya-Rundel, 2018-a, 2018-b), which provide an introduction to ANOVA and discuss the conditions.

If we reject the null hypothesis in favour of the alternative hypothesis in an ANOVA F-test, we next conduct post-hoc (after the event) tests to determine which means are significantly different. Watch the following video, 5 5C Multiple comparisons (Çetinkaya-Rundel, 2018-c), which discusses how to do these multiple comparisons (duration 00:06:48).

Analysis of Variance and Multiple Comparisons

Read Supplementary Notes 5.3, which works through a complete ANOVA F-test for the Major League Baseball batting example from the textbook.

Virtual Statistical Software Lab 💻

Work through the virtual statistical software lab: Software Lab 5.3. In this lab you’ll have a chance to conduct an ANOVA F-test to compare multiple means and to conduct a post-hoc analysis to determine which means are statistically different. As you work through the lab, answer the exercises in the shaded boxes. These exercises are not graded but the solutions are available: Software Lab 5.3 Solutions. The lab should take you no more than 45 minutes to complete.