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Ch. 12 - Analysis of Variance
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 12 - Analysis of VarianceProblem 12.Q.9b
Chapter 12, Problem 12.Q.9b

Interaction
b. If there does appear to be an interaction between gender and age bracket, how should we continue with the procedure for two-way analysis of variance?

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1
Understand that in a two-way ANOVA, an interaction between two factors (here, gender and age bracket) means the effect of one factor depends on the level of the other factor.
If an interaction is present, the main effects of gender and age bracket should not be interpreted in isolation because the combined effect influences the response variable.
Proceed by examining the simple effects, which means analyzing the effect of one factor at each level of the other factor separately. For example, analyze the effect of gender within each age bracket, and vice versa.
Use post hoc tests or multiple comparisons within each subgroup to identify where significant differences lie, since the interaction suggests that the differences vary across groups.
Report the interaction effect clearly and focus your conclusions on how the factors jointly influence the outcome, rather than only on the main effects.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Interaction Effect in Two-Way ANOVA

An interaction effect occurs when the effect of one factor (e.g., gender) on the response variable depends on the level of another factor (e.g., age bracket). Detecting interaction means the factors do not operate independently, and their combined influence must be considered in the analysis.
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Two-Way ANOVA Procedure with Interaction

When an interaction is present, the two-way ANOVA procedure involves analyzing both main effects and the interaction effect simultaneously. The interaction term is tested first, and if significant, interpretation focuses on the interaction rather than main effects alone.
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Post Hoc Analysis and Simple Effects

If interaction is significant, follow-up analyses such as simple effects tests or post hoc comparisons are conducted to explore differences within specific factor combinations. This helps clarify how the factors jointly influence the outcome across different groups.
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Related Practice
Textbook Question

Birth Weights The table below lists some of the same data used in the preceding exercise, but the seven days of the week are combined into weekday (Monday, Tuesday, Wednesday, Thursday, Friday) and weekend days (Saturday, Sunday). Also, the birth weights are converted to kilograms. What do you conclude?

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Textbook Question

Pulse Rates Shown below are pulse rates from Data Set 1 “Body Data” in Appendix B, and the StatCrunch display from two-way analysis of variance of these data. In analyzing these data, what important feature is addressed with two-way analysis of variance that is not addressed with two separate tests of (1) difference between mean pulse rates based on gender, or (2) differences among the mean pulse rates in the different age brackets?

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Textbook Question

One vs. Two What is the fundamental difference between one-way analysis of variance and two-way analysis of variance?

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Textbook Question

Gender and Age Bracket Based on the display included with Exercise 8, what are the final conclusions?

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Textbook Question

In Exercises 1–5, refer to the following list of numbers of years that deceased U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing, the last president is George H. W. Bush, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples from larger populations.


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Exploring the Data Include appropriate units in all answers.


e. What is the level of measurement of the data (nominal, ordinal, interval, ratio)?

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Textbook Question

"Interaction

a. Based on the display included with the preceding exercise, what do you conclude about an interaction between gender and age bracket?

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