    Chapter 7: Analysing the Data Part IV : Analysis of Variance # Scenario and Data Set #5

This experiment involves presenting a group of students with a lecture on an unfamiliar topic. One week later, the students are given a test on the lecture material. To manipulate the conditions at the time of learning, some students receive the lecture in a large classroom, and some hear the lecture in a small classroom. For those students who were lectured in the large room, one half are tested in the same large room, and the others are changed to the small room for testing. Similarly, one-half of the students who were lectured in the small room are tested in the small room, and the other half are tested in the large room. Thus the experiment involves four groups of subjects in a two-factor design, as shown in the following table. The score for each subject is the number of correct answers on the test.

### Figure 7.8 Data for conditioned learning experiment.

 Lecture conditions Testing conditions Small room Large room Small lecture room 22 15 20 17 16 1 4 2 5 8 Large lecture room 5 8 1 1 5 15 20 11 18 16

## Hypotheses

There are three hypotheses, one each for the two IVs and one for the interaction.

## Assumptions

The assumptions for the two-way between groups ANOVA are the same as those for the one-way between groups ANOVA. The assumptions of interval scale or better measurement and independence of observations are again handled by design features. The assumptions that should be checked in the data are the NORMALITY and HOMOGENEITY OF VARIANCE assumptions.

The normality assumption is generally not a cause for concern when the sample size is reasonably large but the HOMOGENEITY OF VARIANCE assumption is relatively important. Violations of this assumption could mean that your data are evaluated at a significance level greater than initially assumed. Rather than being significant at the alpha level of .05, your results might really be significant at only an alpha level of .10. This is because violations of the homogeneity assumption distort the shape of the F-distribution such that the critical F-value no longer corresponds to a cut off of 5%.

 © Copyright 2000 University of New England, Armidale, NSW, 2351. All rights reserved Maintained by Dr Ian Price Email: iprice@turing.une.edu.au