PS 295 Week 11 2024 Post Exam Information PDF

Summary

This document is for PS 295 Week 11 of 2024 and contains exam information. It covers the topics of factorial designs, hypotheses, data, and how to interpret results. This is an exam paper that asks about main effects and interactions, using data and examples of 2x2, 2x3, and other designs to demonstrate different interactions.

Full Transcript

Final Exam Information (also see Final Exam Information document on MyLS)  Saturday, December 7, 8:30-10:30am  Multiple locations in BA – see Exam Information document  2.0 hours  Format  100 Points in total  80 Multiple Choice  20 Short Answer – 10 questions wo...

Final Exam Information (also see Final Exam Information document on MyLS)  Saturday, December 7, 8:30-10:30am  Multiple locations in BA – see Exam Information document  2.0 hours  Format  100 Points in total  80 Multiple Choice  20 Short Answer – 10 questions worth 2 points each  Format of questions similar to Midterm  No aids permitted – no calculators  Material covered  Lecture weeks 1-14  Chapters: 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13 p. 401-418, 14, Stats module p. 467-479  Price Text: Chapter 3 (pdf is in course information folder)  Emphasis on material after the midterm (approximately 60%)  Lecture weeks 9-14  Text chapters: 9-14  Emphasis on material covered in class  Lecture & Text shared material (approximately 80%) – tested by MC or SA questions  Lecture only material (approximately 10%) – tested by MC or SA questions  Textbook only material (approximately 10%) – tested by MC questions only  Lab only Material (approximately 2%) – tested by MC questions only Week 11 Outline Simple vs. more complex hypotheses and designs  Testing interaction hypotheses  Factorial designs Describing features of factorial designs  Terminology: variables, levels, conditions  Independent-groups, within-groups, mixed  Manipulated IVs vs. Participant Variables Interpreting results of a 2 x 2 factorial design  Example experiment  Types of effects: main effects, interaction  A note on statistical significance  The possible patterns of results  Identifying effects in tables and graphs Extensions and variations  Increasing the number of levels of an IV  Increasing the number of IVs Week 11 Outline (continued) More on interpreting main effects and interactions  Follow-up tests  Interaction effects are more important  Describing in words Combining IVs and PVs  Uses of IV x PV designs  Cautions in interpreting results Assignment to conditions in factorial design  Independent-groups designs (between)  Within-groups designs (within)  Mixed designs (between-within) Advantages and uses of factorial designs  Advantages – compared to one-way designs  Uses of factorial designs Identifying factorial designs in your reading Week 11 Factorial designs Simple causal hypotheses  State the effect that one IV will have on a DV  Tested in “one-way” designs that have one IV  Conclusions yielded are “general” or “unqualified”  Prompts research aimed at specifying the conditions under which the effect might disappear or grow stronger  “Boundary conditions” More complex causal hypotheses  State how two (or more) IVs affect a DV  Called “interaction hypotheses” because they specify how two independent variables “interact” to influence a dependent variable  Can lead to more “qualified” conclusions about behaviour Interaction hypothesis: example  The effect that X has on Y depends on Z.  The effect that anxiety has on performance depends on task difficulty.  When tasks are easy, increases in anxiety produce increases in performance.  When tasks are difficult, increases in anxiety produce decreases in performance. Interaction hypothesis: example  The effect that X has on Y depends on Z.  The effect that violent media has on aggression in children depends on their parents’ reactions.  When parents react favourably, the more violence watched, the more aggressive the child will be.  When parents react unfavourably, the more violence watched, the less aggressive the child will be. Interaction hypotheses: Testing for moderators  Recall that a moderator is a variable that changes the strength of association between two other variables  Inexperiments, a moderator is an independent variable that changes the strength of the effect that another IV has on the DV.  The effect that anxiety has on performance is moderated by task difficulty.  The effect that media violence has on aggression is moderated by the parents’ reactions. Describing Factorial Designs Factorial designs  A research design that tests the effect of two or more factors (IVs) simultaneously  Each factor is “crossed” with each other factor  Creates all possible combinations  The number of conditions (or “cells”) is the product of the number of levels of each factor  2 x 2 = 4 conditions  3 x 2 x 4 = 24 conditions  The simplest type of factorial design is the 2 x 2 (said two-by-two) factorial design 2 x 2 Factorial Design IVA IVA Level 1 Level 2 IVB A1-B1 A2-B1 Level 1 IVB A1-B2 A2-B2 Level 2 2 x 2 factorial design 2 x 2 Factorial Design Nonviolent Violent Media Media Positive parental response Negative parental response 2 x 4 Factorial Design Nonviolent Slightly Moderately Extremely violent violent violent Positive parental response Negative parental response Describing factorial designs: Variables, levels, and conditions 2 x3 There are 2 IVs (or factors) First factor has 2 levels Second factor has 3 levels There are 6 conditions Describing factorial designs: Variables, levels, and conditions 2 x 2 4 x 4 3 x 3 2 x 2x2 2 x 4x3 Exercise: Describing Factorial Designs 1. In 2 x 2 x 2 design, how many factors are there? 2. In a 2 x 4 x 2 design, how many conditions are there? 3. In a 2 x 3 x 2 design, how many independent variables are there? 4. In a 2 x 2 x 2 design, how many cells are there? 5. In a 3 x 4 design, how many levels does each IV have? 6. In a 3 x 3 design, how many conditions are there? 7. A study includes 2 IVs that both have 3 levels, and one DV. What is the factorial notation? 8. A study has the lowest number of conditions possible for a factorial design. What is the factorial notation? 9. A study includes 3 factors that all have 2 different levels. What is the factorial notation? Exercise: Describing Factorial Designs 1. In 2 x 2 x 2 design, how many factors are there? [3 factors] 2. In a 2 x 4 x 2 design, how many conditions are there? [16 conditions] 3. In a 2 x 3 x 2 design, how many independent variables are there? [3 IVs] 4. In a 2 x 2 x 2 design, how many cells are there? [8 cells] 5. In a 3 x 4 design, how many levels does each IV have? [first IV has 3 levels, second IV has 4 levels] 6. In a 3 x 3 design, how many conditions are there? [9 conditions] 7. A study includes 2 IVs that both have 3 levels, and one DV. What is the factorial notation? [3 x 3] 8. A study has the lowest number of conditions possible for a factorial design. What is the factorial notation? [2 x 2] 9. A study includes 3 factors that all have 2 different levels. What is the factorial notation? [2 x 2 x 2] Describing factorial designs: Independent-groups vs. Within-groups  Each factor can be independent-groups (between-subjects) or within-groups (within-subjects)  Independent-groups = different participants receive each level of the IV  Within-groups = same participants receive each level of the IV  Factorial designs can be:  Completely independent-groups design  Completely within-groups design  Mixed factorial design (between-within) Describing factorial designs: Independent variables and participant variables  Each factor can be either an independent variable (IV) or a participant variable (PV)  IV = manipulated variable  PV = measured variable  Factorial designs can be:  IV x IV  IV x PV  This distinction matters for conclusions about causation  A PV is correlational (measured)  But might still be called an “IV” by researchers Describing factorial designs: Written descriptions  The study used a 2 (media violence: violent, nonviolent) x 2 (parental response: positive, negative) independent- groups design. The dependent variable was the level of aggression displayed during a free play period.  The hypothesis was tested in a 2 (type of task: naming patches, naming words) x 2 (age: 4 years, 12 years) mixed-factorial design in which the type of task was a within-groups factor and age was an independent-groups factor. The dependent variable was the time it took to complete the second task in seconds. Interpreting Results of the 2 x 2 Design Example experiment  Hypothesis: The effect of performance level (success vs. failure) on feelings of self- esteem differs depending on the importance of the task.  On important tasks, people feel better about themselves after success than failure  On unimportant tasks, people’s feelings about themselves are not affected by their performance level Example experiment  Procedure: Participants solve puzzles and are given 1 of 4 kinds of feedback  Score 85/100; test measures important skills  Score 85/100; test measures unimportant skills  Score 40/100; test measures important skills  Score 40/100; tests measures unimportant skills  DV: Self-esteem – rate how good you feel about yourself from 1 (not at all good) to 20 (extremely good) Example experiment Performance Level Success Failure p1 - 15 p5 - 17 p8 - 8 p12 - 7 Important p2 - 16 p6 - 18 p9 - 7 p13 - 5 p10 Task p3 - 14 p7 - 16 - 6 p14- 6 Importance p4 - 13 p11 - 5 p15 - 12 p19 - 8 p22 - 8 p26 - 10 Unimportant p16 - 11 p20 - 10 p23 - 11 p27 - 10 p17 - 10 p21 - 11 p24 - 9 p28 - 12 p18 - 9 p25 - 10 Raw Data Performance Level Success Failure p1 - 15 p5 - 17 p8 - 8 p12 - 7 Important p2 - 16 p6 - 18 p9 - 7 p13 - 5 p10 Task p3 - 14 p7 - 16 - 6 p14- 6 Importance p4 - 13 p11 - 5 p15 - 12 p19 - 8 p22 - 8 p26 - 10 Unimportant p16 - 11 p20 - 10 p23 - 11 p27 - 10 p17 - 10 p21 - 11 p24 - 9 p28 - 12 p18 - 9 p25 - 10 Raw data Performance Level Success Failure p1 - 15 p5 - 17 p8 - 8 p12 - 7 Important p2 - 16 p6 - 18 p9 - 7 p13 - 5 p10 Task p3 - 14 p7 - 16 - 6 p14- 6 Importance p4 - 13 p11 - 5 M = 10.9 M = 15.6 M = 6.3 p15 - 12 p19 - 8 p22 - 8 p26 - 10 Unimporta p16 - 11 p20 - 10 p23 - 11 p27 - 10 nt p17 - 10 p21 - 11 p24 - 9 p28 - 12 M = 10.1 p18 - 9 p25 - 10 M = 10.4 M = 10.0 M = 12.9 M = 8.14 Interpreting Factorial Designs: Types of Effects  Main effects – Can assess whether each IV has an “overall effect” on the DV  Main effect of performance level: Success produces different self-feelings than failure  Main effect of task performance: Important tasks produce different feelings than unimportant tasks  Interaction effect – Can assess whether the effect of an IV on the DV differs depending on the other IV  The effect that performance has on self-feelings differs depending on task importance Interpreting factorial designs  With 2 IVs, there are 3 possible “effects”:  Main effect of the first IV  Main effect of the second IV  Interaction of the 2 IVs  To evaluate each main effect  Compare the “marginal means”  Marginal mean = average of the DV at one level of an IV (disregarding the other IVs)  To evaluate an interaction effect  Compare the “cell means”  Does the effect of one IV depend on the level of the other IV?  “Are the differences between cell means different”? Interpreting Factorial Designs: Which Means are Compared for Each Type of Effect? Success Failure Important Unimportant Interpreting Factorial Designs: Which Means are Compared for Each Type of Effect? Success Failure Important M= 16 M= 12 M = 14 Unimportant M = 10 M = 10 M = 10 M = 13 M = 11 Examining Means on a Figure (Line Graph) A Note on Statistical Tests  As in one-way designs, would need to perform a statistical test to determine whether each effect is significant (p <.05, or 95% CI does not include zero)  Test used for factorial designs is the Analysis of Variance (ANOVA)  Identifies systematic variance coming from:  Main effect of A  Main effect of B  A x B interaction  Get an “F-value” for each effect that represents the amount of systematic variance/unsystematic variance  For this course, though, treat any difference between means as significant Possible patterns of results (8 patterns)  No interaction effect 1. No main effects 2. Main effect of A; no main effect B 3. No main effect of A; main effect of B 4. Main effect of B; main effect of A o Interaction effect 1. No main effects 2. Main effect of A; no main effect of B 3. No main effect of A; main effect of B 4. Main effect of A; main effect of B Pattern #1 Success Failure Important 11 11 11 Unimportant 11 11 11 11 11 - No main effect of performance level - No main effect of task importance - No interaction effect Pattern #1 Pattern #2 Success Failure Important 18 10 14 Unimportant 18 10 14 18 10 - Main effect of performance level - No main effect of task importance - No interaction effect Pattern #2 Pattern #3 Success Failure Important 18 18 18 Unimportant 10 10 10 18 18 - No main effect of performance level - Main effect of task importance - No interaction effect Pattern #3 Pattern #4 Success Failure Important 18 10 14 Unimportant 13 5 9 15.5 7.5 - Main effect of performance level - Main effect of task importance - No interaction effect Pattern #4 Pattern #5 Success Failure Important 15 10 12.5 Unimportant 10 15 12.5 12.5 12.5 - No main effect of performance level - No main effect of task importance - Interaction effect Pattern #5 Pattern #6 Success Failure Important 18 10 14 Unimportant 14 14 14 16 12 - Main effect of performance level - No main effect of task importance - Interaction effect Pattern #6 Pattern #6 Pattern #7 Success Failure Important 18 14 16 Unimportant 10 14 12 14 14 - No main effect of performance level - Main effect of task importance - Interaction effect Pattern #7 Pattern #7 Pattern #8 Success Failure Important 18 13 15.5 Unimportant 13 13 13 15.5 13 - Main effect of performance level - Main effect of task importance - Interaction effect Pattern #8 Pattern #8 Possible Main Effects and Interactions in a 2 x 2 Factorial Possible Main Effects and Interactions in a 2 x 2 Factorial Practice Question 1: What effects are there? A1 A2 B1 6 3 B2 4 1 a. Main effect of A b. Main effect of B c. A x B interaction d. Both a & b e. All of the above Practice Question 2: What effects are there? A1 A2 B1 8 8 B2 6 6 a. Main effect of A b. Main effect of B c. A x B interaction d. Both a & b e. All of the above Practice Question 3: B1 What effects are there? B2 20 15 DV 10 5 0 A1 A2 a. Main effect of A b. Main effect of B c. A x B interaction d. Both a & b e. All of the above Practice Question 4: What effects are there? A1 A2 B1 7 7 B2 7 1 a. Main effect of A b. Main effect of B c. A x B interaction d. Both a & b e. All of the above Practice Question 5: What effects are there? A1 A2 B1 5 7 B2 7 5 a. Main effect of A b. Main effect of B c. A x B interaction d. Both a & b e. All of the above Practice Question 6: What effects are there? a. Main effect of A b. Main effect of B c. A x B interaction d. Both a & b e. All of the above Extension Factors with more than two levels 2 x 3 Design: Example #1 Success Neutral Failure Important 20 15 10 15 Unimportant 18 13 5 12 19 14 7.5 - Main effect of task importance - Main effect of performance level - Interaction effect 2 x 3 Design: Example #1 2 x 3 Design: Example #1 2 x 3 Design: Example #2 Success Neutral Failure Important 16 12 8 12 Unimportant 12 12 12 12 14 12 10 - No main effect of task importance - Main effect of performance level - Interaction effect 2 x 3 Design: Example #2 2 x 3 Design: Example #2 2 x 4 Design Example Success Failure Extremely 18 12 15 important Moderately 14 6 10 important Slightly 10 6 8 important Unimportant 8 5 6.5 10 7.3 2 x 4 Design Example 3 x 3 Design Example Success Neutral Failure Extremely 22 16 10 16 important Moderately 20 14 8 14 important Slightly 12 10 8 10 important 18 13.3 8.7 Example of 3 x 3 design 25 20 Extremely 15 important Moderately 10 important Slightly important 5 0 Success Neutral Failure Practice Question: What effects are there? A1 A2 A3 B1 10 10 6 B2 8 8 4 a. Main effect of A b. Main effect of B c. A x B interaction d. Both a & b e. All of the above Practice Question: What effects are there? A1 A2 A3 B1 6 4 10 B2 4 2 8 a. Main effect of A b. Main effect of B c. A x B interaction d. Both a & b e. All of the above Practice Question: What effects are there? A1 A2 A3 B1 7 5 3 B2 3 5 7 a. Main effect of A b. Main effect of B c. A x B interaction d. Both a & b e. All of the above Practice Question: What effects are there? A1 A2 B1 18 16 B2 14 12 B3 12 7 B4 10 5 a. Main effect of A b. Main effect of B c. A x B interaction d. Both a & b e. All of the above Extension Higher order designs: Designs with more than two factors 2 x 2 x 2 Design Example Success Failure Alone Important Unimportant With Important Others Unimportant Interpreting higher order factorial designs  With 3 factors, we can examine the following main effects and interactions:  Three main effects (A, B, C)  Main effect of performance level  Main effect of task importance  Main effect of the presence of others  Three 2-way interactions (AB, BC, AC)  Performance level x Task importance  Performance level x Presence of others  Task Importance x Presence of others  One 3-way interaction (ABC)  Performance level x Task importance x Presence of others 2 x 2 x 2 Design Example Success Failure Alone Important 18 14 Unimportant 16 16 With Important 18 12 Others Unimportant 18 18 2 x 2 x 2 Design Example Success Failure Alone Important 18 14 Unimportant 16 16 With Important 18 12 Others Unimportant 18 18 17.5 15 Main effect of Success vs. Failure compares: (18+16+18+18)/4=17.5 (14+16+12+18)/4=15 2 x 2 x 2 Design Example Success Failure Alone Important 18 14 Unimportant 16 16 With Important 18 12 Others Unimportant 18 18 Main effect of Alone vs. With Others compares: (18+14+16+16)/4=16 (18+18+12+18)/4=16.5 2 x 2 x 2 Design Example Success Failure Alone Important 18 14 Unimportant 16 16 With Important 18 12 Others Unimportant 18 18 17.5 15 Main effect of Important vs. Unimportant compares: (18+14+18+12)/4=15.5 (16+16+18+18)/4=17 Examining 2-way interactions in a higher order design  Examine each 2-way interaction by ignoring or “collapsing across” the remaining factors  E.g., To examine the performance level x presence of others interaction, look at a 2x2 table that ignores importance factor Success Failure Alone 17 15 16 With 18 15 16.5 Others (e.g., Success/Alone = [18+16/2] = 17.5) 17.5 15 Examining 2-way interactions in a higher order design  E.g., To examine the performance level x task importance interaction, look at a 2x2 table that ignores presence of others factor Success Failure Important 18 13 15.5 Unimportant 17 17 17 17.5 15 (e.g., Success/Important = [18+18/2] = 18) Examining the 3-way interaction in a 3-way design  A 3-way design can provide information about the combined effects of all three factors  There will be a 3-way interaction if the 2-way interaction between two factors differs depending on the remaining factor  Asking: Does a 2-way interaction differ across the levels of the remaining factor?  Examine the 2-way interaction pattern at each level of the remaining factor Examining the 3-way interaction Alone: Success Failure Important 18 14 Unimportant 16 16 With others: Success Failure Important 18 12 Unimportant 18 18 When alone, interaction is: difference = 4 vs. difference = 0. With others, interaction is: difference = 6 vs. difference = 0. These 2-way interactions are not the same so there is a 3-way interaction. Follow-up Tests Follow-up tests: After a significant main effect  If the IV has only 2 levels, no further tests are needed  If the IV has more than 2 levels, further tests are needed to interpret the findings  Called “post-hoc tests” or “multiple comparisons”  Want to determine precisely which of the marginal means differ significantly from each other Post hoc tests Success Neutral Failure Important 20 15 10 15 Unimportant 18 13 5 12 19 14 7.5 - Main effect of task importance - Main effect of performance level - Interaction effect Post hoc tests Success Neutral Failure Important 20 20 10 16.6 Unimportant 18 18 5 13.6 19 19 7.5 - Main effect of task importance - Main effect of performance level - Interaction effect Follow-up tests: After a significant interaction  If an interaction effect is significant, further tests are needed to determine the precise nature of the interaction  Want to determine precisely which of the condition means within the interaction differ from each other  We conduct tests of simple effects  Simple effect = the effect of one IV at a particular level of another IV  In a 2 x 2 interaction we could examine 4 simple effects  Note: The interaction effect tells us that the “differences are different”; simple effects tests tell us whether there is a difference or not between two conditions Tests of Simple Effects  Simple effect of A at B1 A1 A2 B1 x x B2  Simple effect of A at B2 A1 A2 B1 B2 x x Tests of Simple Effects  Simple effect of B at A1 A1 A2 B1 x B2 x  Simple effect of B at A2 A1 A2 B1 x B2 x Test of Simple Effects: Example Using Pattern #6 Success Failure Important 18 10 14 Unimportant 14 14 14 16 12 Test of Simple Effects: Alternative Example Success Failure Important 18 10 14 Unimportant 18 14 16 18 12 Describing Main Effects and Interactions in Words Describing Main Effects and Interactions  Main effects  Without an interaction  With an interaction  Interaction effects Pattern #2 Success Failure Important 18 10 10 Unimportant 18 10 10 18 10 - Main effect of performance level - No main effect of task importance - No interaction effect Example: One main effect without an interaction (Example Using Pattern #2)  There was no significant main effect of task importance, F (1, 37) = 1.56, ns. Participants who performed important tasks did not report different levels of self-esteem than those who performed unimportant tasks.  There was a significant main effect of performance level, F (1, 37) = 4.23, p <.05. Participants reported higher levels of self-esteem when they succeeded on a task than when they failed.  The interaction between performance level and task importance was not significant, F (1, 37) = 5.26, ns. Pattern #6 Success Failure Important 18 10 14 Unimportant 14 14 14 16 12 - Main effect of performance level - No main effect of task importance - Interaction effect Example: One main effect with an interaction (Example Using Pattern #6)  There was no significant main effect of task importance, F (1, 37) = 1.56, ns. Participants who performed important tasks did not report different levels of self-esteem than those who performed unimportant tasks.  There was a significant main effect of performance level, F (1, 37) = 4.23, p <.05. Participants reported higher levels of self-esteem when they succeeded on a task than when they failed.  The effect of performance level was qualified by a significant interaction between performance level and task importance F (1, 37) = 5.26, p <.05. For important tasks, participants reported higher self-esteem when they succeeded than when they failed. For unimportant tasks, participants reported the same level of self-esteem whether they succeeded or failed. Interactions are more important than main effects  When a study shows both a main effect and an interaction, the interaction is almost always more important.  The interaction qualifies the main effect.  There may be real differences in marginal means, but the more interesting part is the interaction. Describing an interaction: Generic templates  There was an interaction between Factor A and B. The interaction indicates that the effect of Factor A on DV differs across the levels of Factor B. Specifically, when [first level of Factor B], increases in Factor A result in higher scores on the DV. In contrast, when [second level of Factor B], increases in Factor A result in lower scores in DV.  There was an interaction between Factor A and B. The interaction indicates that the effect of Factor A on DV depends on Factor B. Specifically, when [first level of Factor B], participants scored higher on DV in the A1 condition than in the A2 condition. In contrast, when [second level of Factor B], participants’ scores on DV did not differ across the A1 condition and A2 condition. Pattern #6b – alternate example Success Failure Important 18 8 13 Unimportant 16 10 13 17 9 - Main effect of performance level - No main effect of task importance - Interaction effect Describing Interactions in Words: Textbook Examples [Recall] Interaction hypothesis: example  The effect that X has on Y depends on Z.  The effect that anxiety has on performance depends on task difficulty.  When tasks are easy, increases in anxiety produce increases in performance.  When tasks are difficult, increases in anxiety produce decreases in performance. [Recall] Interaction hypothesis: example  The effect that X has on Y depends on Z.  The effect that violent media has on aggression in children depends on their parents’ reactions.  When parents react favourably, the more violence watched, the more aggressive the child will be.  When parents react unfavourably, the more violence watched, the less aggressive the child will be. Combining IVs and PVs Combining true IVs and PVs Sometimes called IV x PV designs Uses: Test the generality of an IV’s effect on the DV for different kinds of people Test the association between a PV and the DV in different situations Cautions in Interpreting Results: Cannot draw causal conclusion for effects involving the participant variable If there is an interaction, we would say the participant variable “moderated” the effect of the IV – i.e., the participant variable is a “moderator ” Example: IV - Performance Level PV – Depression DV – Feelings of Self Esteem Success Failure Depression Diagnosis No Depression Diagnosis Example: IV - Performance Level PV – Experience with Task DV – Feelings of Self Esteem Success Failure Experience d No experience Combining true IVs and PVs Sometimes called IV x PV designs Uses: Test the generality of an IV’s effect on the DV for different kinds of people Test the association between a PV and the DV in different situations Cautions in Interpreting Results: Cannot draw causal conclusion for effects involving the participant variable If there is an interaction, we would say the participant variable “moderated” the effect of the IV – i.e., the participant variable is a “moderator ” Assignment to Conditions and Orders Assignment to conditions in factorial designs  1. Independent-Groups (Between- subjects)  2. Within-Groups (Repeated measures)  3. Mixed-factorial design Independent-groups design Success, Important Success, Unimportant Random Assignment Failure, Important Failure, Unimportant Within-groups design  Each participant is in each factorial condition  Each condition still represents a combination of two factors  Would require counterbalancing Success, Success, Failure, Failure, Important Unimportant Important Unimportant Mixed-factorial designs (between-within)  A study with at least one independent-groups and one within-groups factor Success, Failure, Important Important Random Success, Failure, Assignment Unimportant Unimportant Independent-Groups (Between-subjects n = 40) Success Failure Important P1, P2, P3, P4, P5, P6, P7, P8, P9, P11, P12, P13, P14, P15, P16, P17, P18, P10 P19, P20 Unimportant P21, P22, P23, P24, P25, P26, P31, P32, P33, P34, P35, P36, P37, P38, P27, P28, P29, P39, P40 P30 Within-Groups (Repeated Measures n = 10) Success Failure Important P1, P2, P3, P4, P5, P6, P7, P8, P1, P2, P3, P4, P5, P6, P7, P8, P9, P9, P10 P10 Unimporta P1, P2, P3, P4, P5, P6, P7, P8, P1, P2, P3, P4, P5, P6, P7, P8, P9, nt P9, P10 P10 Mixed-Factorial (Between-within n = 20) Success Failure Important P1, P2, P3, P4, P5, P6, P7, P8, P1, P2, P3, P4, P5, P6, P7, P8, P9, P9, P10 P10 Unimporta P11, P12, P13, P14, P15, P16, P11, P12, P13, P14, P15, P16, nt P17, P18, P19, P20 P17, P18, P19, P20 Assignment to conditions: Independent-Groups  Only issue is how to randomly assign participants to conditions  Design tells you how many conditions  Example: 2 x 3 has 6 conditions  Number the conditions from 1-6 as though there were 6 levels of a single IV  Use random assignment  Each participant gets randomly assigned to one of the six conditions Assignment to Orders: Within-Groups  Only issue is how to assign participants to the order in which they will receive the conditions  Design tells you how many conditions  Example: 2 x 3 has 6 conditions  Number or letter the conditions as if there were 6 levels of a single IV  Use counterbalancing procedures discussed previously for single-factor designs Example: 2 x 3 design Counterbalancing (using Latin square)  Participant 1 A B F C E D  Participant 2 B C A D F E  Participant 3 C D B E A F  Participant 4 D E C F B A  Participant 5 E F D A C B  Participant 6 F A E B D C Assignment to Conditions & Order: Mixed-Factorial (between-within)  Example: 2(between) x 3(within) design  Must address both the assignment of participants to conditions (between-factor) and the order in which they will receive conditions (within-factor)  A 2-step process:  First, deal with the between-subjects factor by using random assignment of participants to groups  E.g., assign participants randomly to the 2 groups  Second, deal with the repeated-measures factor.  Need to do this for each group separately  E.g., for each group, randomly assign participants to the 6 possible orders (full counterbalancing). Example: 2 (Between) x 3 (Within) Mixed-Factorial Design Group 1  Order 1A B C  Order 2A C B  Order 3B A C  Order 4B C A  Order 5C A B  Order 6C B A Group 2  Order 1A B C  Order 2A C B  Order 3B A C  Order 4B C A  Order 5C A B  Order 6C B A Advantages and Uses of Factorial Designs Advantages of Factorial Designs  Ability to detect interactions  Can learn about factors “acting together”  Find effects that could not be detected in one-way designs  E.g., synergistic effects that are “more than the sum of the parts”  If there are interactions, more specific conclusions about the effect of a factor can be made  Ability to demonstrate generality  If there are no interactions, that suggests an effect generalizes across other factors – evidence of external validity Interactions tell us about effects of the factors “acting together” Example: 2 (Alcohol: control, alcohol) x 2(Sleep deprivation: control, deprived) DV = driving problems (number of mistakes in driving simulator) No Alcohol Alcohol Not sleep deprived 3 7 Sleep deprived 5 14 Uses of Factorial Designs  Testing limits – see text  A way to test external validity (generalization)  Identifying moderators  Testing theories – see text  Many theories suggest variables should interact  Replication plus extension of an existing finding  Evaluating order effects in within-subject designs Replication plus extension Initial single factor Negative Positive experiment Mood Mood Negative Positive Adding a second Mood Mood factor Young Adults Seniors Uses of Factorial Designs  Testing limits – see text  A way to test external validity (generalization)  Identifying moderators  Testing theories – see text  Many theories suggest variables should interact  Replication plus extension of an existing finding  Evaluating order effects in within-subject designs Order Effect Assertive Liking Submissive Liking Tape M=8 Tape M=4 Sample Submissive Liking Assertive Liking Random Tape M=6 Tape M=6 Assignment Including order as a factor in a within-groups design Example – Job Candidate Experiment 2 (candidate behavior: assertive, submissive) x 2(position: first, second) DV = rating of candidate Assertive Submissi Candidate ve Candidat e First Position 8 6 7 Second 6 2 4 Position 7 4 Carryover Effect (differential order effect) Assertive Liking Submissive Liking Tape M=8 Tape M=2 Sample Submissive Liking Assertive Liking Random Tape M=8 Tape M=6 Assignment Including order as a factor in a within-groups design Example – Job Candidate Experiment 2 (candidate behavior: assertive, submissive) x 2(position: first, second) DV = rating of candidate Assertive Submissi Candidate ve Candidat e First Position 8 8 8 Second 6 2 4 Position 7 5 Identifying Factorial Designs in Your Readings Identifying Factorial Designs in Empirical Journal Articles  The Method section will describe the design of the study.  Factorial notation: ___ x ____ x ____  The Results section will examine whether the main effects and interactions were significant.  May report 95% CI, refer to “significance” or report a p value (p <.05) for each effect Identifying Factorial Designs in Popular Press Articles  Look for “it depends” or “only when” to highlight an interaction.  Look for participant variables (e.g., age, gender, ethnicity).

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