Does there seem to be a main effect for type of instruction? Does there seem to be a main effect for experience? Does there seem to be an interaction? Does there seem to be a main effect for type of pain? Does there seem to be a main effect for type of pain reliever? Does there seem to be an interaction? Is the main effect for age level statistically significant at the .05 level? Can the null hypothesis for the main effect of region be rejected at the .05 level? Is the interaction between age and region statistically significant at the .05 level?

Two-way ANOVA

Chapter Objectives
The reader will be able to:
-Understand the use and examples of two-way ANOVA
-Understand that two-way ANOVA has two main effects and one interaction effect
-Interpret the main effects and interaction effect

Exercise for Chapter 27
Factual Questions
(Assume there are equal numbers of participants in each cell)

Questions 1 through 3 below refer to this information: Two types of basketball instruction were used with random samples of participants who either had previous experience of playing or did not have previous experience. The means indicate the proficiency at playing basketball at the end of treatment.
Type of instruction Row means
New Conventional
Previous experience M = 230.00 M = 200.00 M = 215.00
No previous experience M = 200.00 M = 230.00 M = 215.00
Column means M = 215.00 M = 215.00

1. Does there seem to be a main effect for type of instruction?

2. Does there seem to be a main effect for experience?

3. Does there seem to be an interaction?

Questions 4 through 6 below refer to this information: Random samples of participants with back pain and headache pain were randomly assigned to two types of pain relievers. The means below indicate the average amount of pain relief. A higher mean indicates greater pain relief.
Type of pain Row means
Back pain Headache
Type A pain reliever M = 25.00 M = 20.00 M = 22.50
Type B pain reliever M = 15.00 M = 10.00 M = 12.50
Column means M = 20.00 M = 15.00

4. Does there seem to be a main effect for type of pain (back pain versus headache pain)?

5. Does there seem to be a main effect for type of pain reliever?

6. Does there seem to be an interaction?

Questions 7 through 9 below refer to this ANOVA table:
Source F p
Age level (young, old) 13.25 .029
Region (north, south) 1.69 .321
Interaction (age region) 15.32 .043

7. Is the main effect for age level statistically significant at the .05 level?

8. Can the null hypothesis for the main effect of region be rejected at the .05 level?

9. Is the interaction between age and region statistically significant at the .05 level?

Question for Discussion
10. Briefly describe a hypothetical study in which it would be appropriate to conduct a two- way ANOVA.

Notes
1. Note that income in large populations is usually skewed, making the mean an inappropriate average (see Chapter 12); for these groups, assume that it was not skewed. Also note that the row means and column means were obtained by adding and dividing by 2; this is appropriate only if the number of participants in all cells is equal. If it is not, compute the row and column means using the original raw scores.
2. The basis for this second statement is that if you subtract across the rows, you get the same difference for each row. Earlier, you were instructed to subtract down columns; however, subtracting across the rows works equally well in determining whether there is an interaction.
3. It is also common to include the degrees of freedom, the sums of squares, and mean squares in an ANOVA table. As mentioned in the previous chapter, these are of little interest to the typical consumer of research