Other Ways of Thinking About Interactions Ways of
Other Ways of Thinking About Interactions • Ways of Describing Interactions other than “Simple Effects” • Interactions as “other kinds of” cell mean difference patterns • Interactions as “non-additive combinations” of IV effects • augmenting vs. interfering interactions • Describing “interactions” vs. “data patterns” • isolating the interaction effect
Generally folks define, identify, and describe interactions in terms of “different differences” or “different simple effects, ” as we have done so far… Task Difficulty Easy Hard Task Presentation Paper Computer 90 = 90 40 < 70 one simple effect “null” one simple effect However, that’s not the only way to define, indentify or describe interactions…
The IVs are “Training Modality” and “Testing Modality” leading to this 2 x 2 factorial design… Training Modality Visual Touch Testing Modality Touch Visual Sometimes our hypotheses aren’t about patterns of simple effects, but … are about other kinds of mean difference patterns… VV TV VT TT Among these conditions, 2 are “intramodal” (VV & TT) & 2 are “cross-modal” (VT & TV). RH: s for the study were… RH 1: VV > TT hypothesized dif among intramodal conditions RH 2: VT > TV hypothesized dif among cross-modal conditions Neither of which corresponds to a “simple effect” !! REM! LSDmmd can be used to compare among any of the cells!
Training Modality Visual Touch Testing Modality Cross Intra At the time, using LSDmmd hadn’t “caught on” yet, and since neither RH: corresponds to a SE, folks would use separate t-tests to compare each cell pair – leading several to make Type II errors because of the lowered power… VV TT VT TV The “significant interaction that isn’t anywhere” we’ve discussed! In this case there is an “organizational” solution… Just re-label the IVs… “Training Modality” Vision vs. Touch & “Testing Modality” Intramodal vs. Cross-modal then… RH 1: VV > TT SE of Training Modality for Intramodal tests RH 2: VT > TV SE of Training Modality for Cross-modal tests
Another Example – same research area… This was the common design for studying intra- and cross-modal memory with the usual RH: VV > VT = TV = TT Performance … which can be directly & completely tested using the 6 pairwise comparisons among the 4 conditions. VT TV TT After several studies, someone noticed that these conditions define a factorial… Training Modality Visual Touch Testing Modality Touch Visual VV 99. 6% 24. 8 % 26. 2 % 25. 6 %
There was an interaction! There was a (misleading) main effect of Testing Modality Touch Visual There was a (misleading) main effect of Training Modality Visual Touch 99. 6% 24. 8 % 26. 2 % 25. 6 % Notice how the very large VV cell mean “drives” both main effects (while ensuring they will each be misleading) as well as driving the interaction!? ! However interesting and informative was the idea from the significant interaction, that “performance is the joint effect of Training and Testing Modalities” – none of these “effect tests” give a direct test of the RH: The set of pairwise comparisons gives the most direct RH test!!!
Here’s yet another way of thinking about interactions… we’ll need an example!! Brownies – great things… worthy of serious theory & research!!! The usual brownie is made with 4 blocks of chocolate and 2 cups of sugar. Replicated research tells us that the average rating of brownies made with this recipe is about 3 on a 10 point scale. My theory? People don’t really like brownies! What they really like is fudge! So, goes my theory, making brownies more “fudge-like” will make them better liked. How to make them more fudge-like, you ask? Add more sugar & more chocolate!!!
So, we made up several batches of brownies and asked people to taste a standardized amount of brownie after rinsing their mouth with water, eating an unsalted saltine cracker and rinsing their mouth a second time. We used the same 10 -point rating scale; 1 = this is the worst plain brownie I’ve ever had, 10=this is the best plain brownie I’ve ever had. Our first study: 2 -cups of sugar 3 So, far so good! 4 -cups of sugar 5
Our second study: What? ? 4 blocks of choc. 3 8 blocks of choc. 2 Oh – yeah! Unsweetened chocolate… Then the argument started. . One side: We have partial support for theory – adding sugar helps, but adding chocolate hurts!!! Other side: We have not tested theory!!! What was our theory? Add more sugar & more chocolate!!! We need a better design!
4 blocks of choc. 2 -cups of sugar 3 4 -cups of sugar 5 8 blocks of choc. 2 What do we expect for the 4 -cup & 8 -block brownies? standard brownie 3 + sugar effect + 2 + chocolate effect - 1 expected additive effect of choc & sugar 1 expected score for 4&8 brownies 4
4 blocks of choc. 8 blocks of choc. 2 -cups of sugar 3 2 4 -cups of sugar 5 9 The effect of adding both simultaneously is 6 … not 4? ? ? How do we account for this ? There is a non-additive joint effect of chocolate and sugar!!!! The joint effect of adding chocolate and sugar is not predictable as the sum of the effects of adding each!!! Said differently, there is an interaction of chocolate and sugar that emerges when they are added simultaneously.
This leads to the distinction between two “kinds” of interactions… “Augmenting” Interaction “Interfering” Interaction # practices 10 30 ~Rew ~FB 10 15 ~Aud 10 20 FB 20 45 Aud 25 15 The combined effect is greater than would be expected as the additive effect! The combined effect is less than would be expected as the additive effect! Practice effect = 5 Feedback effect = 10 Expected additive effect = 15 Joint effect = 35 Reward effect = 10 Audience effect = 15 Expected additive effect = 25 Joint effect = 5
“Describing a pattern of data that includes an interaction” vs. “Describing the Interaction in a pattern of data” 90 91 70 50 30 Easy Hard Paper Computer Task Presentation The pattern of data shown the figure demonstrate that while Task Presentation has no effect for Easy tasks, for Hard tasks, those using Computer did better than when using Paper. This is “a description of a pattern of data that includes an interaction” Technically, it would be wrong to say that “The interaction shown in the figure demonstrates that while Task Presentation has no effect for Easy tasks, for Hard tasks, those using Computer did better than when using Paper. In order to “describe the interaction effect” we have to isolate the “interaction effect” from the main effects…
The process, called “mean polishing, ” involves residulaizing the data for the main effects, leaving the interaction effect… Presentation Paper Comp Easy Hard means col effect 90 50 70 -5 90 70 80 +5 means 90 60 75 Correcting for row effects (subtract +/- 15) row effect +15 -15 grand mean Correcting for column effects (subtract +/- 5) Presentation Paper Comp Easy Hard 75 65 75 85 Presentation Paper Comp Easy Hard 80 70 70 80
Correcting for Grand Mean (subtract 75) Presentation Paper Comp Easy Hard 5 -5 -5 5 1. 10 2. 5 0 -5 -10 Hard Easy Paper Computer Task Presentation The proper description of “the interaction effect” is The interaction shown in the figure demonstrates that for Easy tasks those using Paper performed better than those using Computer, however, for Hard tasks, those using Computer performed better than those using Paper.
Looked at in this way, interactions differ in only 2 ways… Which group has “increase” and which had “decrease” Hard Easy vs. Easy Hard The “strength” of the interaction effect… Hard Easy null Easy small Hard Easy medium Easy large
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