ANOVA complex design

What is in a results section??? LOOK at the example in your textbook. You need to have subheading. You need to have figures and they must have useful figure captions. You must refer to your figures. You need to describe the data in some way You need to describe the analyses and what you found. Is it significant? Or not Then add some English to describe what you found.

e.g To examine the effects of memory training on retention of words, 20 college students were randomly assigned to four training conditions (n=5) defined by the instructions to participants: story method, imagery method, rhyme method, and control (no specific instructions). Mean recall out of a possible 20 words (and the sample standard deviation) for each condition was: story 13.2(1.3), imagery 14.4 (1.8), rhyme 13.4 (1.3) and control 10.0 (1.6). Confidence intervals for the means in each group are shown in figure 1. Mean recall differed significantly among the four instruction conditions, F(3,16) = 7.8, p<.05. MS = 240…. A paragraph that describes what is compared and what you found. Where I should look to find the information.

Reporting results of complex design What kind of test description of variables and definitions of levels (conditions) of each summary statistics for cells in design matrix (figure) report F tests for main effects and interactions effect size statement of power for nonsignificant results simple main effects analysis when interaction is statistically significant description of statistically significant interactions – looking at cell means description of statistically significant main effect analytical comparisons – to clarify sources of systematic variation conclusion from analysis

The data are from a statement by Texaco, Inc. to the Air and Water Pollution Subcommittee of the Senate Public Works Committee on June 26, Mr. John McKinley, President of Texaco, cited the Octel filter, developed by Associated Octel Company as effective in reducing pollution. However, questions had been raised about the effects of pollution filters on aspects of vehicle performance, including noise levels. He referred to data presented in the datafile associated with this story as evidence that the Octel filter was was at least as good as a standard silencer in controlling vehicle noise levels. Car Noise

The data constitute a 3-way factorial experiment with 3 replications. The factors are type of filter (2 types), vehicle size (3 sizes), and side of car (two sides).

Number of cases = 36 DV NOISE = Noise level reading (decibels) IV SIZE = Vehicle size: 1 small, 2 medium, 3 large TYPE = 1 standard silencer,2 Octel filter SIDE = 1 right side 2 left side of car

Main effect Size is significant Mean small sd = 7.63 Mean medium sd =13.5 Mean large sd= Need post hoc tests Main effect Type is significant Standard mean sd =32.2 Octel mean sd =25.63 Don’t need post hoc tests

All sizes differ.

Interaction Size by Side is significant Need to find out where is the difference Simple main effects analysis Do t-test for the small And one for the medium And one for large One anova for left side One anova for right side

m L s side

Small size left bigger than right Medium size no difference Large size right bigger than left

Right

Left

On right - small cars louder than large - medium cars louder than large - small cars quieter than medium On left - small cars louder than large - medium cars louder than large

Interaction Size by Type is significant Need to find out where is the difference Simple main effects analysis Do t-test for the small And one for the medium And one for large One for type standard One for type Octel

s m L

Standard

Octel

significant 3-way interaction. Size by type by side Need to separate the factors so can do 2-way analyses Hold one factor constant and test other Eg do a 2X2 of small cars 2X2 of medium and 2X2 of large….

Small car – type by side

Test small car Side is significant - left bigger than right Interaction is significant

Small car Type : t –tests for the interaction Right Left Octel louder than standard

Small car – t-tests for side Standard Octel Left louder than right

Medium car - type by side

Test Medium car Type is significant – standard louder than Octel

Large car – type by side

Test large car Side is significant – right is louder than left Interaction is significant -

Large car Type : t –tests for the interaction Right Left Standard louder than octel

Standard Octel