Conducting 2x3 ANOVA: Main Effects and Interactions Explained
School
University of Waterloo**We aren't endorsed by this school
Course
PSYCH 391
Subject
Statistics
Date
Dec 12, 2024
Pages
3
Uploaded by CorporalFire15272
1. Generate a data set including 5 participants per cell in a 2 x 3 design that produces (i) a significantmain effect of Factor ‘A’, (ii) a significant main effect of Factor ‘B’, and (iii) a significant interactionbetween Factor ‘A’ and Factor ‘B’.a1a2a3b110, 14, 13, 12, 16x̄ = 1312, 14, 13, 15, 16X̄=1414, 15, 15, 16, 15X̄= 15b211, 15, 14, 13, 17x̄ =1417, 19, 18, 20, 21X̄= 1922,26,28,23,25X̄= 24(i) Conduct the 2x3 ANOVA testing for the two main effects and the interaction. Include Partial h2(calculated in SPSS) for the two main effects and the interaction.As seen in figure 1 , there is a significant main effect of Factor B where b1 (M = 13) has a greatereffect than b2 (M = 14), F(1,24) = 53.73, MSE = 3.58, p < .001, η2 = .69. There is a significant maineffect of Factor B, F(2,24) = 25.07, MSE = 3.58, p < .001, η2 = .69. There is also a significantinteraction between Factor A on Factor B, F(2,24) = 15.41, MSE = 3.58, p < .001, η2 = .56.(ii) Imagine that you a prior predicted that a1 was significantly different than the combination of a2and a3 for both levels of Factor B (i.e., b1 and b2 separately). Split the file on Factor B and conductthese linear contrasts. Conduct another linear contrast comparing specific levels of Factor A for bothlevels of Factor B that is orthogonal to the first one. Prove that the linear contrasts are orthogonalmathematically (note that this is done by hand).
As seen in Figure 1, in Linear Contrast 1, a1 does not differ from a2 and a3 in b1, t(12) = -.988, SE =1.82, p = .343, and in as seen b2 a1 is significantly different from a2 and a3 , t(12) = -6.88, SE = 2.30,p < .001. In Figure 1, in Linear Contrast 2, it can also be seen that a2 is not significantly different thana3 for b1, t(12) = 0.951, SE = 1.05, p = 0.361, but it does for b2, t(12) = 4.37, SE = 1.33, p <.001.(iii)Imagine that you also wanted to do exploratory post hoc tests comparing compare b1 versus b2 foreach level of Factor A. Using t-tests (with a Bonferroni correction) conduct these statisticalcomparisons (note that the Bonferroni correction is done by hand but use software to do the t-tests).As seen in this figure, at Factor B level 2(b2), all groups were significantly differentfrom each other, a1 was significantlydifferent from a2, SE = 1.33, p = .003, andfrom Group a3, SE = 1.33, p < .001, a2 wassignificantly different from a3, SE = 1.33,p = .003.
3.4. Write ups are beside results.5. Orthogonal contrasts are important because they are statistically independent, which means thateach contrast tests a unique hypothesis without needing to overlap with others. This independencemakes sure there is no redundancy and that each contrast provides distinct information about the data.To add on, orthogonal contrasts help control the overall Type I error rate, avoiding inflated error risksthat could come up from non-orthogonal comparisons. They also make results more easier byattributing significant effects to specific patterns rather than shared variance. Overall, orthogonalcontrasts allow for a more efficient and clear analysis, maximising the use of available variance in thedata.