3-way Factorial Designs Expanding factorial designs Effects in a 3-way design Defining a 3-way interaction BG & WG comparisons Experimental & Non-experimental.

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3-way Factorial Designs Expanding factorial designs Effects in a 3-way design Defining a 3-way interaction BG & WG comparisons Experimental & Non-experimental comparisons Causal Interpretations “Descriptive” & “Misleading” effects Identifying “the replication”

3-way Factorial Designs The simplest factorial design is a 2x2, which can be expanded in two ways: 1) Adding conditions to one, the other, or both IVs

2) Add a 3rd IV (making a 3-way factorial design) Learning Psyc Methods Learning Psyc Content Ugrads Grads Ugrads Grads Computer Instruction Lecture Instruction Identify the three IVs in this design... Specify the properties of each condition/cell of this design...

3-Way Factorial Designs There are 7 effects involved in a 3-way factorial 3 main effects (one for each IV) 3 2-way interactions (one for each pair of IVs) 1 3-way interaction For the example name the... main effects 2-way interactions 3-way interaction 1. Topic 2. Instruction Method 3. Ed. level 1. Topic X Inst. Method 2.Topic X Ed. Level 3. Inst. Method X Ed. Level Topic X Instruction Method X Ed. level

What does a 3-way interaction look like? Remember that a 2-way interaction is, “when the effect of one IV is different for different levels of a 2nd IV” Extending this to a design with 3 IVs, a 3-way interaction is, “when the interaction of two IVs is different for different levels of a 3rd IV” Practice Difficulty 1 10 Easy Hard SE of Practice is different for Easy and Hard Tasks Familiar Task Practice Difficulty 1 10 Easy Hard Unfamiliar Task Practice Difficulty 1 10 Easy Hard The 2-way interaction of Practice and Difficulty is different for Familiar and Unfamiliar Tasks

Considering BG and WG comparisons… … there are four different kinds of 3-way designs. Completely Between Groups 3-way Completely Within-Groups 3-way (each either repeated measures of matched-groups) Mixed 3-way with 2 BG and 1 WG (either repeated measures of matched-groups) Mixed 3-way with 1 BG and 2 WG (each either repeated measures of matched-groups)

Considering Experimental & Nonexperimental comparisons … … there are four different kinds of 3-way designs. All 3 IVs are RA & Manip, etc. All 3 “IVs” are measured (subject) variables 1 IV is RA & Manip, etc. -- other two “IVs” are measured (subject) variables 2 IVs are RA & Manip, etc. -- other “IV” is a measured (subject) variables

Causal Interpretations of 3-way Designs When can a main effect be causally interpreted ? When can a 2-way interaction be causally interpreted ? When can a 3-way interaction be causally interpreted ? When the conditions of that IV are RA, Manip, Etc. When the conditions of both the involved IVs are RA, Manip, Etc. When the conditions of all three IVs are RA, Manip, Etc.

“Descriptive” effects in a 3-way The 3-way -- significant or not -- is always descriptive ! If the 3-way is significant, all 2-way & main effects are “suspect” If the 3-way is significant, a 2-way is only descriptive if that 2-way has the same pattern for each condition of the 3 rd IV If the 3-way is significant, a main effect is only descriptive if that main effect has the same pattern for each combination of the other two IVs If the 3-way is non-significant, all three 2-ways are significant

“Descriptive” effects in a 3-way If a 2-way is significant, the main effects of those IVs are “suspect” If a 2-way is significant, the main effect of an IV involved in that interaction is only descriptive if that main effect has the same pattern for each condition of the other IV The main effect of an IV that is not involved in any 2-way or 3-way interaction is always descriptive

Identifying “the replication” With 7 main effects and interactions (and myriad simple effects) you have to be careful to get the correct part of the design that is “the replication” of an earlier study. Example: You want to check if your recent 3-way study replicated an earlier effect that people who had 10 practices did about 40 points better than those who had only one practice (same DV). Familiar Task Practice Difficulty 1 10 Easy Hard Unfamiliar Task Practice Difficulty 1 10 Easy Hard As you can see, there is much variability in the effect of practice -- depending upon the conditions of the other IVs