ANOVA stands for what three words? What is the name of the test that can be conducted with an ANOVA? If the difference between a pair of means is tested with ANOVA, will the probability level be different from that where the difference was tested with a t test? Which statistic in an ANOVA table is of greatest interest to the typical consumer of research?

One-way ANOVA

Chapter Objectives
The reader will be able to:
-Know that analysis of variance is used to test the difference(s) among two or more means
-Understand how analysis of variance is reported
-Know the concept of one-way ANOVA and its purpose and use of post hoc tests

Exercise for Chapter 26
Factual Questions
1. ANOVA stands for what three words?

2. What is the name of the test that can be conducted with an ANOVA?

3. “An ANOVA can be appropriately used to test only the difference between two means.” Is this statement “true” or “false”?

4. If the difference between a pair of means is tested with ANOVA, will the probability level be different from that where the difference was tested with a t test?

5. Which statistic in an ANOVA table is of greatest interest to the typical consumer of research?

6. Suppose you read this statement: “The difference between the means was not statistically significant at the .05 level (F = 2.293, df = 12, 18).” Should you conclude that the null hypothesis was rejected?

7. Suppose you read this statement: “The difference between the means was statistically significant at the .01 level (F = 3.409, df = 14, 17).” Should you conclude that the null hypothesis was rejected?

8. Suppose you saw this in the footnote to a One-Way ANOVA table: “p < .05.” Are the differences statistically significant?

9. Suppose participants were classified according to their grade level in order to test the differences among the means for the grade levels. Does this call for a “One-Way ANOVA” or a “Two-Way ANOVA”?

10. Suppose that the participants were classified according to their grade levels and their country of birth in order to study differences among means for both grade level and country of birth. Does this call for a “One-Way ANOVA” or a “Two-Way ANOVA”?

Question for Discussion
11. Briefly describe a hypothetical study in which it would be appropriate to conduct a One- Way ANOVA but not appropriate to conduct a t test.

Notes
1. Historically, the t test preceded ANOVA. Because ANOVA will also test the difference between two means, the t test is no longer needed. However, for instructional purposes, the t test is still taught in introductory statistics classes and it is still widely used by researchers when only two means are being compared.
2. It would be inappropriate to run three separate t tests without adjusting the probabilities for interpreting t. Such adjustments are not straight- forward. However, a single F test automatically makes appropriate adjustments to the probabilities.
3. Procedures for determining which individual differences are significant are beyond the scope of this book.