# Factorial Practice Answers

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Factorial Practice -- Answers

 Study #1 The purpose of the study was to explore object discrimination accuracy, with a focus on the joint effects of modality (visual vs. touch) and stimulus type (shape vs. texture). Participants were randomly assigned to work with either the shape or texture stimuli, and, based on a second coin-flip, it was decided that all participants would complete first the more familiar visual and then the less familiar touch conditions with the randomly chosen stimulus type. a. Draw & Label the Boxes depicting this design Stimulus Type Shape Texture Modality Visual Touch 1 2 7 3 4 8 5 6 b. List each ME, SE & Int and tell whether or not the design provides for initial equivalence and the hope of causal interpretation (if ongoing equivalence was maintained). Effect? BG/WG/MG Init Eq (why)? ME Stimulus Type BG yep – RA SE Stim Type for Visual BG yep – RA SE Stim Type for Touch BG yep – RA ME Modality WG no – no CB SE Modality for Shape WG no – no CB SE Modality for Texture WG no – no CB INT Stim Type * Modality MG no – Mod There is never a “good enough” reason to prescribe the order (unless it is a seriated variable that can only occur in a particular order, like age or # practices). For each RH: below (Hint: There’s more than one are interaction RH:)… tell which means are involved -- using the #s 1-8 from above on left tell the specific ME, SE or set of SEs (if an interaction) used to test each RH: RH: Which means? ME, SE or Int? Touch performance will be better than visual performance. Visual & touch accuracy are the same for shape, but vision is poorer than touch for texture stimuli. Visual performance with shape will be about the same as visual performance with texture Touch texture perception will be better than visual. The modality effect is greater for texture than shape stimuli. For shape stimuli, visual and touch performance will be equivalent. Accuracy will be better with texture than shape stimuli. When using touch, textures are perceived more accurately than shapes. Textures are perceived more accurately than shapes by touch, but there is no such visual effect. 7 vs. 8 vs. 2-4 1 vs. 2 2 vs. 4 1-3 vs. 2-4 1 vs. 3 5 vs. 6 2 vs. 4 1-2 vs. 3-4 ME Modality Int – SE of Mod for @ Stim SE of Stim Type for Vision SE of Mod for Texture Int – SE of Mod for @ Stim SE of Mod for Shape ME Stim Type SE of Stim Type for Touch Int – SE of Stim Type for @ Mod

Answer the questions about each set of results below.

 Results Set #1 Stimulus Type F = 5.32, p = .008 Modality F = 2.12, p = .213 Interaction F = 4.43, p = .021, LSDmmd = 8.23 What is LSDmmd used for? Test if cell means are significantly different Why do we need to be able to do this? Describe pattern of significant interaction Check if MEs are descriptive/misleading How do we tell if there is an interaction effect? p-value of Interaction F-test Can the interaction effect possibly be misleading? Nope – highest-order effect is always descriptive Do we need the LSDmmd to test the interaction RH:? Yes, interaction is significant How do we know if the Modality SEs are different for Shape & Texture? p-value of Interaction F-test (int is different SEs) How do we tell if there is a Stimulus main effect? p-value of Stimulus main effect F-test Can the Stimulus Type effect possibly be misleading? Yes – because interaction is significant Do we need LSDmmd to describe Stim Type marginal mean pattern if ME is significant? No – ME only has 2 conditions/means Do we need LSDmmd to tell if the Stim Type main effect is misleading? Yes – must compare ME pattern to SE patterns & need LSDmmd to describe SE patterns Do we need LSDmmd to test Stim Type ME RH:? Yes – ME RH only fully supported if ME is descriptive & need LSDmmd to describe SE patterns How do we tell if there is a Modality main effect? p-value of Modality main effect F-test Can the Modality effect possibly be misleading? Yes – because the interaction is significant Do we need LSDmmd to describe Modality marginal mean pattern if ME is significant? No – ME only has 2 conditions/means Do we need LSDmmd to tell if the Modality main effect is misleading? Yes – must compare ME pattern to SE patterns & need LSDmmd to describe SE patterns Do we need LSDmmd to test Modality RH:? Yes – ME RH only fully supported if ME is descriptive & need LSDmmd to describe SE patterns Results Set #2 Stimulus Type F = 1.32, p = .48 Modality F = 7.12, p = .002 Interaction F = .43, p = .921, LSDmmd = 12.23 What is LSDmmd used for? Not needed – interaction is nonsig Why do we need to be able to do this? We don’t – interaction is nonsig How do we tell if there is an interaction effect? p-value of Interaction F-test Can the interaction effect possibly be misleading? Nope – highest-order effect is always descriptive Do we need the LSDmmd to test the interaction RH:? No, interaction is nonsignificant How do we know if the Stimulus Type SEs are different for Visual and Touch? p-value of Interaction F-test (int is different SEs) How do we tell if there is a Stimulus main effect? p-value of Stimulus main effect F-test Can the Stimulus Type effect possibly be misleading? No – the interaction is nonsignificant Do we need LSDmmd to describe Stim Type marginal mean pattern if ME is significant? No – ME only has 2 conditions/means Do we need LSDmmd to tell if the Stim Type main effect is misleading? No – the interaction is nonsig, so the SEs must match ME Do we need LSDmmd to test Stim Type ME RH:? No – ME must be descriptive because no interaction How do we tell if there is a Modality main effect? p-value of Modality main effect F-test Can the Modality effect possibly be misleading? No – the interaction is nonsignificant Do we need LSDmmd to describe Modality marginal mean pattern if ME is significant? No – ME only has 2 conditions/means Do we need LSDmmd to tell if the Modality main effect is misleading? No – the interaction is nonsig, so the SEs must match ME Do we need LSDmmd to test Modality RH:? No – ME must be descriptive because no interaction

 Study #2 The purpose of the study was to test whether the differences commonly found between Individual and Group treatments in laboratory studies would generalize to a clinical setting. Based on a thorough evaluation, each participant was assigned to the treatment type that would most like lead to the greatest improvement. Participants were randomly assigned receive their treatment in the laboratory or clinical setting, except for those who were already receiving treatment in a clinical setting, who all received the treatment in the clinical setting. a. Draw & Label the Boxes depicting this design Treatment Type Individual Group Location Laboratory Clinic 1 2 7 3 4 8 5 6 b. List each ME, SE & Int and tell whether or not the design provides for initial equivalence and the hope of causal interpretation (if ongoing equivalence was maintained). Effect? BG/WG/MG Init Eq (why)? ME Treatment Type BG No – no RA SE Tx type for Individual BG No – no RA SE Tx type for Group BG No – no RA ME Location BG No – no RA SE Location for Ind BG No – no RA SE Location for Grp BG No – no RA INT Tx Type * Location BG No However well meaning, ethical, etc. not RAing means there’s no initial equivalence!!! For each RH: below (Hint: There’s more than one are interaction RH:) … tell which means are involved -- using the #s 1-8 from above on left tell the specific ME, SE or set of SEs (if an interaction) used to test each RH: RH: Which means? ME, SE or Int? Individual performance will be better than Group performance. Individual performance is better than Group performance in both the lab and clinic settings, but with a smaller effect in the clinic. Results from Individual treatment in the clinic will be about the same as from Individual treatment in the laboratory Group treatment will not work as well as Individual treatment in the Clinical setting. The Location effect is greater group than for Individual treatment. In the Laboratory setting, Individual and Group treatment will be equivalent. Results will be better in the Laboratory than in the Clinic When using Group therapy, better results are expected in the Laboratory than in the clinic. Better results are found in the Lab than in the Clinic when using Group Tx, but there is no such effect for Individual Tx. 5 vs. 6 1-2 vs. 3-4 1 vs. 3 3 vs. 4 1-3 vs. 2-4 1 vs. 2 7 vs. 8 2 vs. 4 2-4 vs. 3-4 ME of Treatment Type Int – SE of Tx for @ Location SE of Location for Indiv Tx SE of Tx Type for Clinic setting Int – SE of Location for @ Tx SE of Tx for Laboratory setting ME of Location SE of Location for Group Tx Int – SE of Location for @ Tx

Answer the questions about each set of results below.

 Results Set #1 Treatment Type F = 1.32, p = .48 Location F = 7.12, p = .02 Interaction F = 1 .43, p = .321, LSDmmd = 12.23 What is LSDmmd used for? Not needed – interaction is nonsig Why do we need to be able to do this? We don’t – interaction is nonsig How do we tell if there is an interaction effect? p-value of Interaction F-test Can the interaction effect possibly be misleading? Nope – highest-order effect is always descriptive Do we need the LSDmmd to test the interaction RH:? No – the interaction is nonsignificant How do we know if the Treatment SEs are different for different Locations? p-value of Interaction F-test (int is different SEs) How do we tell if there is a Treatment main effect? p-value of Treatment main effect F-test Can the Treatment effect possibly be misleading? No – the interaction is nonsignificant Do we need LSDmmd to describe Treatment marginal mean pattern if ME is significant? No – ME only has 2 conditions/means Do we need LSDmmd to tell if the Treatment main effect is misleading? No – the interaction is nonsig, so the SEs must match ME Do we need LSDmmd to test Treatment ME RH:? No – ME must be descriptive because no interaction How do we tell if there is a Location main effect? p-value of Modality main effect F-test Can the Location effect possibly be misleading? No – the interaction is nonsignificant Do we need LSDmmd to describe Location marginal mean pattern if ME is significant? No – ME only has 2 conditions/means Do we need LSDmmd to tell if the Location main effect is misleading? No – the interaction is nonsig, so the SEs must match ME Do we need LSDmmd to test Location RH:? No – ME must be descriptive because no interaction Results Set #2 Treatment Type F = 5.32, p = .008 Location F = 2.12, p = .213 Interaction F = 4.43, p = .021, LSDmmd = 8.23 What is LSDmmd used for? Test if cell means are significantly different What are two reasons we want to be able to do this? Describe pattern of significant interaction If sig int – check if MEs are descriptive/misleading How do we tell if there is an interaction effect? p-value of Interaction F-test Can the interaction effect possibly be misleading? Nope – highest-order effect is always descriptive Do we need the LSDmmd to test the interaction RH:? Yes – the interaction is significant How do we know if the Location SEs are different for Group & Individual treatments? p-value of Interaction F-test (int is different SEs) How do we tell if there is a Treatment main effect? p-value of Treatment main effect F-test Can the Treatment effect possibly be misleading? Yes – because interaction is significant Do we need LSDmmd to describe Treatment marginal mean pattern if ME is significant? No – ME only has 2 conditions/means Do we need LSDmmd to tell if the Treatment main effect is misleading? Yes – must compare ME pattern to SE patterns & need LSDmmd to describe SE patterns Do we need LSDmmd to test Treatment ME RH:? Yes – ME RH only fully supported if ME is descriptive & need LSDmmd to describe SE patterns How do we tell if there is a Location main effect? p-value of Modality main effect F-test Can the Location effect possibly be misleading? Yes – because the interaction is significant Do we need LSDmmd to describe Location marginal mean pattern if ME is significant? No – ME only has 2 conditions/means Do we need LSDmmd to tell if the Location main effect is misleading? Yes – must compare ME pattern to SE patterns & need LSDmmd to describe SE patterns Do we need LSDmmd to test Location RH:? Yes – ME RH only fully supported if ME is descriptive & need LSDmmd to describe SE patterns

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