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### Figure 11.5: Three Possible Combinations of Main Effects and Interactions in a Two-Factor Experiment This figure illustrates three scenarios involving main effects and interactions in a two-factor experimental design. #### (a) Data showing a main effect for factor A but no main effect for factor B and no interaction - **Data Table**: - Factor A, Factor B: - M = 20 - M = 10 - Overall for Factor B: - M = 20 - M = 10 - Overall for Factor A: - M = 15 - **Graph**: - Line representing two levels of Factor A is parallel, indicating no interaction. - The overall mean increases from 10 to 20, showing a main effect for Factor A. #### (b) Data showing main effects for both factor A and factor B but no interaction - **Data Table**: - Factor A, Factor B: - M = 10 - M = 30 - Overall for Factor B: - M = 20 - M = 40 - Overall for Factor A: - M = 15 - M = 35 - **Graph**: - Two lines, each representing levels of Factor A, slope upwards with parallel alignment, indicating no interaction but main effects for both factors. #### (c) Data showing no main effect for either factor, but an interaction - **Data Table**: - Factor A, Factor B: - M = 10 - M = 20 - Overall for Factor B: - M = 10 - M = 20 - Overall for Factor A: - M = 15 - **Graph**: - The lines, representing the two levels of Factor A, intersect indicating an interaction effect. No main effect for either factor is evident as the overall means remain constant across the levels. This figure is helpful in understanding how different effects present visually and statistically in two-factor experiments.

### Figure 11.5: Three Possible Combinations of Main Effects and Interactions in a Two-Factor Experiment This figure illustrates three scenarios involving main effects and interactions in a two-factor experimental design. #### (a) Data showing a main effect for factor A but no main effect for factor B and no interaction - **Data Table**: - Factor A, Factor B: - M = 20 - M = 10 - Overall for Factor B: - M = 20 - M = 10 - Overall for Factor A: - M = 15 - **Graph**: - Line representing two levels of Factor A is parallel, indicating no interaction. - The overall mean increases from 10 to 20, showing a main effect for Factor A. #### (b) Data showing main effects for both factor A and factor B but no interaction - **Data Table**: - Factor A, Factor B: - M = 10 - M = 30 - Overall for Factor B: - M = 20 - M = 40 - Overall for Factor A: - M = 15 - M = 35 - **Graph**: - Two lines, each representing levels of Factor A, slope upwards with parallel alignment, indicating no interaction but main effects for both factors. #### (c) Data showing no main effect for either factor, but an interaction - **Data Table**: - Factor A, Factor B: - M = 10 - M = 20 - Overall for Factor B: - M = 10 - M = 20 - Overall for Factor A: - M = 15 - **Graph**: - The lines, representing the two levels of Factor A, intersect indicating an interaction effect. No main effect for either factor is evident as the overall means remain constant across the levels. This figure is helpful in understanding how different effects present visually and statistically in two-factor experiments.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Please look at the picture and explain all three examples (a, b, c). Explain what is the main effect of factor A and factor B and why do we have/do not have interaction in each example

### Figure 11.5: Three Possible Combinations of Main Effects and Interactions in a Two-Factor Experiment This figure illustrates three scenarios involving main effects and interactions in a two-factor experimental design. #### (a) Data showing a main effect for factor A but no main effect for factor B and no interaction - **Data Table**: - Factor A, Factor B: - M = 20 - M = 10 - Overall for Factor B: - M = 20 - M = 10 - Overall for Factor A: - M = 15 - **Graph**: - Line representing two levels of Factor A is parallel, indicating no interaction. - The overall mean increases from 10 to 20, showing a main effect for Factor A. #### (b) Data showing main effects for both factor A and factor B but no interaction - **Data Table**: - Factor A, Factor B: - M = 10 - M = 30 - Overall for Factor B: - M = 20 - M = 40 - Overall for Factor A: - M = 15 - M = 35 - **Graph**: - Two lines, each representing levels of Factor A, slope upwards with parallel alignment, indicating no interaction but main effects for both factors. #### (c) Data showing no main effect for either factor, but an interaction - **Data Table**: - Factor A, Factor B: - M = 10 - M = 20 - Overall for Factor B: - M = 10 - M = 20 - Overall for Factor A: - M = 15 - **Graph**: - The lines, representing the two levels of Factor A, intersect indicating an interaction effect. No main effect for either factor is evident as the overall means remain constant across the levels. This figure is helpful in understanding how different effects present visually and statistically in two-factor experiments.
Transcribed Image Text:### Figure 11.5: Three Possible Combinations of Main Effects and Interactions in a Two-Factor Experiment This figure illustrates three scenarios involving main effects and interactions in a two-factor experimental design. #### (a) Data showing a main effect for factor A but no main effect for factor B and no interaction - **Data Table**: - Factor A, Factor B: - M = 20 - M = 10 - Overall for Factor B: - M = 20 - M = 10 - Overall for Factor A: - M = 15 - **Graph**: - Line representing two levels of Factor A is parallel, indicating no interaction. - The overall mean increases from 10 to 20, showing a main effect for Factor A. #### (b) Data showing main effects for both factor A and factor B but no interaction - **Data Table**: - Factor A, Factor B: - M = 10 - M = 30 - Overall for Factor B: - M = 20 - M = 40 - Overall for Factor A: - M = 15 - M = 35 - **Graph**: - Two lines, each representing levels of Factor A, slope upwards with parallel alignment, indicating no interaction but main effects for both factors. #### (c) Data showing no main effect for either factor, but an interaction - **Data Table**: - Factor A, Factor B: - M = 10 - M = 20 - Overall for Factor B: - M = 10 - M = 20 - Overall for Factor A: - M = 15 - **Graph**: - The lines, representing the two levels of Factor A, intersect indicating an interaction effect. No main effect for either factor is evident as the overall means remain constant across the levels. This figure is helpful in understanding how different effects present visually and statistically in two-factor experiments.
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