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Two-way ANOVA

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

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  1. Two-way ANOVA Chapter 14

  2. 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

  3. 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)

  4. 2 X 2

  5. 3 X 2

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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)

  14. Computations continued • Compute appropriate SS then divide by appropriate df to get the MS

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