Chapter 7: Analysing the Data Part IV : Analysis of Variance

# Scenario and Data Set #5 Report

 Testing conditions Small room Large room Lecture conditions Small room 18.0 (2.92) 4.0 (2.74) 11.0 Combined means for Lecture conditions Large room 4.0 (3.0) 16.0 (3.39) 10.0 11.0 10.0 Combined means for testing conditions

### The Summary Table

 SOURCE SS DF MS F Sig of F Lecroom 5.0 1 5.0 .55 .470 Testroom 5.0 1 5.0 .55 .470 Lecroom X 845.0 1 845.0 92.60 .000 Testroom - Error 146.0 16 9.13 Total 1001.0 19 52.68

The homogeneity of variance tests indicate that this assumption was not violated.

The only significant effect was the interaction. Tukey's HSD test on this interaction (i.e., the four cell means) follows.

Here there are 4 means being compared and the DF for the error term is 16. Howell, q = 4.05. Each cell mean is based on 5 observations, so N = 5.

 HSD = 4.05 * SQRT(9.13/5) = 4.05 * 1.351 = 5.47

All pairs of cell means that are greater than or equal to 5.47 apart are significantly different. It is easily seen from the table in Answer 1 that the two smallest means are not significantly different from each other and that the two largest means are not significantly different from each other. However, the two largest means are clearly significantly different to the two smallest means. It is hardly necessary to construct a matrix of ordered means, but for the exercise, it is shown below.

### Matrix of ordered means

 LlecStest 4.0 SlecLtest 4.0 LlecLtest 16.0 SlecStest 18.0 LlecStest 4.0 - 0.0 12.0* 14.0* SlecLtest 4.0 - 12.0* 14.0* LlecLtest 16.0 - 2.0 SlecStest 18.0 -

## Task 5. Graph of interaction

The plot of the cell means is shown in the previous figures 7.14 and 7.15 and clearly indicates a significant interaction with no main effects. The number of correct responses in the test depended on both the room the information was delivered and the room in which the testing occurred. The lowest number of correct responses occurred when the testing was in a room different to the one in which the material was learnt. Conversely, the greatest number correct occurred when the testing was in the same size room as where the material was learnt.

Note that this graph is still rather cludgy. It would not be good enough for a publication, but it is about the best I could do from SPSS. This data was obviously set up to show a remarkable interaction with no main effects.