Two-way ANOVA

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# Two-way ANOVA - PowerPoint PPT Presentation

Two-way ANOVA. Chapter 14. Factorial Designs. Simple one-way designs don’t capture the complexity of human behavior; our behavior is the result of many different influences The variables can have unique effects or can combine with other variables to have a combined effect

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### Two-way ANOVA

Chapter 14

Factorial Designs
• Simple one-way designs don’t capture the complexity of human behavior; our behavior is the result of many different influences
• The variables can have unique effects or can combine with other variables to have a combined effect
• Allow for greater generalizability of results
• Efficient and cost-effective
• Move beyond the one-way ANOVA which has 1 IV, to a two-way design which as 2IVs
Get information about the main effect of each IV as well as the interaction effect
• Will be computing multiple F-ratios
• Can be both between-subjects, both within subjects, or mixed design
• 2 (levels of A) X 2 (levels of B)
• 3 X 2, 2 X 4, ETC.
• Each combination of factor A and factor B creates a cell (what we are comparing is the means of each cell)
Two-way Between-subjects ANOVA
• Assumptions:
• The cells contain independent samples
• DV measures of interval or ratio scores are approximately normally distributed
• The populations all have homogeneous variance
• 2-way ANOVA – two main effects and an interaction
Main Effects
• The main effect refers to the effect of that factor (I.e., the levels) collapsing across other factors (averaging across those levels)
• For factor A compute the means for each column, ignoring factor B, which is represented by the rows
• Essentially perform a one-way ANOVA for each main effect
Main Effects
• For each main effect (determined by the number of IVs) you have a null hypothesis and alternative hypothesis
• Compute Fobt called FA
• If significant then graph the main effect means, perform post hoc comparisons, and determine the proportion of variance accounted for by factor A
• Do the same for factor B, collapsing across factor A
• May have different values for k and n for each factor
Interaction
• Two-way interaction effect is the combined effects of the levels of factor A with the levels of factor B
• Treat each cell in the study as a level of the interaction and compare the cell means
• Assess the extent to which the cell means differ AFTER removing those differences between scores that are due to the main effects of factor A and B
• Thus, differences due to the combination of A and B, not each separately
Interaction effect
• The relationship between one factor and the DV change with, or depends on, the level of the other factor that is present
• The influence of changing one factor is NOT the same for each level of the other factor
• If the pattern is the same or the relationship is the same between the scores and one factor for each level of the other factor there is NOT an interaction
Hypotheses: for Interaction
• Ho says that differences between scores due to A at one level of B equal the differences between scores due to A at the other level of B
• Compute another separate F-ratio, graph the interaction, perform post hoc comparisons on cell means and compute the proportion of variance accounted for
Eysenck Study
• Level-of processing (5 levels) and age differences (elderly may not process as deeply)
• Thus, a 2 X 5 factorial design
• 10 different groups of participants
• Can assess interaction between age and encoding condition
Computations
• The one-way ANOVA is the basis – a little more tedious because you have to compute a lot more
• Compute MS total
• MS within (average variability in the cells), still a reflection of the error variance; used as the denominator for all three F-ratios
• Three sources of between-groups variance; three separate MS (factor A, factor B, and the interaction)
Computations continued
• Compute appropriate SS then divide by appropriate df to get the MS