Shavelson Chapter 14 S14-1. Know the purpose of a two-way factorial design and what type of information it will supply (e.g. main effects and interaction effects) ( ) General purpose of two-way factorial design: Used when you have 4 or more groups, in a factorial design Provides information on main effects (the effect each IV might have on the DV) Provides information on interaction effects (the effect one IV has on the other - i.e. the effect both conditions have together)

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Shavelson Chapter 14 S14-2. What are the three reasons why factorial designs might be used over one-way research studies? (419) Reasons to use a factorial design: 1.Economical, time and money wise! 2.Provides more information (main and interaction effects) 3.Can get a better estimate of error variance (within variance) in factorial design (can add suspected Extraneous Variable as a factor)

Shavelson Chapter 14 S14-3. Be able to create a graph of the interactions in a study and know the difference between a disordinal interaction and an ordinal interaction. (420) and figure 14-3). Given a graph of an interaction, you should be able to explain what they mean in terms of an interaction. (as is done on the top of 420, 2)

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Shavelson Chapter 14 S14-3 continued No exer. B1 Exer. B2 Vit. A A1 Vit. B A2 B Exercise A 10 DV A1A2 Vit. AVit. B DV = Performance on a test (2) (6) (4) B2 Exercise B1 No exercise

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Shavelson Chapter 14 DisordinalOrdinal No Interaction S14-3 continued

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S14-4. Know in general terms how to calculate the F for the main and interaction effects in a factorial design ( ). To aid in this, you should be familiar with the breakdown of the total variability as illustrated in formula 14-1 on page 425. Given a partially completed table, (e.g. 14-2, p 422) be able to complete it. I will not ask you to calculate or to know how to calculate the sum of squares, but you should be able to calculate the degrees of freedom, the mean squares and the F observed. Calculating the Fs for factorial designs: For main effects: MS a MS within F = variance of factor A variance within Variance within + Trtmnt Effects Variance within = MS b MS within Variance within + Trtmnt Effects Variance within = variance of factor B variance within F = For interaction effects: MS a  B(interaction) MS within F = variance of AxB variance within = (Variance A  B) - (Var A) - (Var B) + (Variance Within Variance within

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S14-5. For the Two-way ANOVA you should know: A.The design requirements and assumptions ( ). B.Be able to recognize or generate hypotheses ( ). C.Know the decision rules for rejecting the null hypothesis and be able to interpret the results of a two-way ANOVA. In interpreting you need to look at the interaction effects first. Note the points on page 431 regarding interpreting the main effects. S14-5(a) 2 Way ANOVA Design Requirements: A.2 IV’s each with 2 or more levels (completely crossed) B.Levels can differ Qualitatively or Quantitatively C.Participant only appears in one cell of design, and is randomly selected from the population Shavelson Chapter 14

S14-5(a) continued Assumptions of the 2 way ANOVA A.All scores are independent of each other B.The population from which each group was drawn should be normally distributed (but not usually a problem) C.Homogeneity of variance (that is, each group’s population should have equal variances) But if group sizes are equal, no problem) Shavelson Chapter 14

S14-5(b) Hypotheses for the 2 way ANOVA Null Hypotheses used: (For each factor) H o :  1 =  2 =  3… (All means are equal) (For each Factor) H 1 :  i ≠  i' (At least one of the pairs of means differ from one another) Interaction: H o : interaction effect = 0 H 1 : interaction effect ≠ 0 1.Examine the interaction first. If null is rejected, then main effects of A & B are not straightforward. Should plot interaction and examine. 2.If no interaction effect exists, main effects can be interpreted in straightforward manner. Shavelson Chapter 14

S14-6. Given a value for the omega statistic (and for what it was calculated), be able to explain what that number means (I.e. given and omega value of.64 for interaction, what does this mean?) ( ) Omega-Squared Provides information on the strength of the association between each factor (e.g. factor A & B), as well as the interaction (A  B) and the DV. e.g. Omega (A) =.08 (accounts for 8 % of DV variability) Omega (B) =.21 (accounts for 21% of DV variability) Omega (A  B) =.64 (accounts for 64% of DV variability) Shavelson Chapter 14

14-7. ANOVA Source Table – be able to complete it and interpret it! SourceSSDFMsF obs Verbal Ability Question Type AxB Within Group (error or residual) 36.5 Total

Tukey posthocs for the factorial ANOVA (2-way)