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Factorial Design Two Way ANOVAs

Factorial Design Two Way ANOVAs. 2 Independent Variables Examples IV#1 IV#2 DV Drug Level Age of Patient Anxiety Level Type of Therapy Length of Therapy Anxiety Level Type of Exercise Type of Diet Weight Change Toy Color Gender Satisf. with Toy Key Advantages

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Factorial Design Two Way ANOVAs

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  1. Factorial Design Two Way ANOVAs • 2 Independent Variables • Examples • IV#1IV#2DV • Drug Level Age of Patient Anxiety Level • Type of Therapy Length of Therapy Anxiety Level • Type of Exercise Type of Diet Weight Change • Toy Color Gender Satisf. with Toy • Key Advantages • Compare relative influences on DV • Examine interactions between IV 2 Way ANOVA

  2. Toy Study IV: Toy Color (Blue, Pink) IV: Gender (Boy, Girl) DV: Satisfaction with Toy Terms Factors: __ * ___ * ___ Levels (a,b) Design: ___ x ___ Main Effect, collapsing Interaction Example Two Way ANOVAs 2 Way ANOVA

  3. M=4.5 M=8.0 M=5.5 M=7.0 Main Effects Two Way ANOVAs • Main Effect for Toy Color? • Compare Column Means • Main Effect for Gender? • Compare Row Means 2 Way ANOVA

  4. Interactions- Cell Means Two Way ANOVAs Graph cell means to examine possibility of interaction M=6 M=3 M=5 M=11 2 Way ANOVA

  5. Interactions-Graph Two Way ANOVAs • General rule of life: • If two lines cross, it probably means something. Non-parallel lines suggests interaction. 2 Way ANOVA

  6. SPSS: Data Input #1 Two Way ANOVAs 2 Way ANOVA

  7. SPSS: Data Input #2 Two Way ANOVAs 2 Way ANOVA

  8. SPSS: Analysis, Step #1 Two Way ANOVAs • Go to Analyze, General Linear Model, Univariate • Move DV to Dependent Variable • Move 2 IVs to Fixed Faxtors Step #1 Step #2 Step #3 Step #4 2 Way ANOVA

  9. SPSS: Analysis, Step #2 Two Way ANOVAs • Select Plots; Graph sample means with two IVs • If one IV has more levels, put on Horizontal Axis 2 Way ANOVA

  10. SPSS: Analysis, Step #3 Two Way ANOVAs • Select Options • Ask for Descriptive Statistics 2 Way ANOVA

  11. SPSS: Analysis, Step #4 Two Way ANOVAs • Select Post Hoc • Do Post Hoc (SNK) for IVs with 3+ levels • Not required in this example; both IVs have only 2 levels: color (blue & pink), sex (boy & girl) 2 Way ANOVA

  12. SPSS Output #1 Two Way ANOVAs 2 Way ANOVA

  13. SPSS Output #2: Two Way ANOVAs BG WG 2 Way ANOVA

  14. SPSS Output #3: Two Way ANOVAs Note: post-hoc tests are needed only when you have 3+ levels of an IV (here we don’t). 2 Way ANOVA

  15. Write-up Two Way ANOVAs • The hypotheses were supported. [1] There was a main effect for toy color. Pink toys (M=7.00) elicited significantly more satisfaction than blue toys (M=5.5), F(1,8) = 6.750, p≤ .05. [2]There was also a main effect for sex. Girls were significantly more satisfied (M=8.00) than boys (M=4.50), F(1,8)=36.750, p≤ .05. 2 Way ANOVA

  16. Write-up (cont.)Two Way ANOVAs • [3] Additionally, there was a significant interaction between color and sex, F(1,8) = 60.75, p≤.05. Boys and girls appear equally satisfied with blue toys. Switching to pink toys, however, raised satisfaction for girls but decreased satisfaction for boys. Sex accounted for only a small amount of variance in satisfaction (η2= .0601), but color (η2= .3274) and the interaction (η2= .5412) accounted for a large amount of variance. 2 Way ANOVA

  17. Two-Way ANOVA Cont. • Announcements • Review Study Guide for Final • Homework: Influence Study • Homework: Teamwork & Feedback Study, write-ups • Explain Purpose of 2nd ANOVA Lab • Studying for Final • Computational Review for Final • Review Name That Stat Exercises • Practice SPSS on computer • Review Old Computations 2 Way ANOVA

  18. Source of Variation Table for 2-way ANOVA • Three possible influences on DV -- factors • A: IV #1 • B: IV #2 • C: Interaction • Sum of Squares (SS) always given • Calculating Degrees of Freedom by hand • dfA = a-1 • dfB = b-1 • dfA*B = (a-1)*(b-1) • dfwg = a * b * (n-1) • dfTotal = N – 1 2 Way ANOVA

  19. Table Reading Keys • Three F’s use same formula • MSBG / MSWG = MSSpecific Factor / MSError • For example: MSA / MSError • Factor significant if p ≤ .05 • MS = SS/df for each factor and error 2 Way ANOVA

  20. Source of Variation Table from Toy Study BG WG 2 Way ANOVA

  21. Age & Intelligence (2-way ANOVA) 2 Way ANOVA

  22. Important Means • Main effect for Task? • Main effect for Age? • Graph it 2 Way ANOVA

  23. Calculate degrees of freedom by hand: • dfA • dfB • dfA*B • dfError • dfTotal 2 Way ANOVA

  24. Complete Table with these SS • SSTask = 759.375 • SSAge = 452.083 • SSTask*Age = 356.250 • SSError = 406.250 2 Way ANOVA

  25. SPSS Data Entry 2 Way ANOVA

  26. Check Output • What means pertain to… • Effect of Task • Effect of Age • Effect of interaction • Is there a …. • Main effect for Task • Main effect for Age • Interaction • Is Post Hoc Required? • Explain graph • Do complete Write-up 2 Way ANOVA

  27. 2-way ANOVA: Age & Intelligence • First, I’d like to thank my statistics teacher for devising such a creative, exciting, and enriching exercise. My life will never be the same. 2 Way ANOVA

  28. 2-way ANOVA: Age & Intelligence I’m still smarter than you are, missy. • The hypotheses were supported. • Participants scored significantly lower on tasks using fluid (M=89.58) rather than crystallized intelligence (M=100.83), F(1,18) = 33.46, p<=.05. • In addition, participants aged 85 years scored lower (M=90.00) than those aged 75 years (M=95.00), who in turn scored lower than those aged 65 years (M=100.63), F(2,18)=10.015, p<=.05. • Additionally, age interacted with type of task, F(2,18)=7.812, p<=.05. Although scores on crystallized tasks remain relatively constant, scores on fluid tasks decline with age. 2 Way ANOVA

  29. Interpreting 2-way Outcomes 2 Way ANOVA

  30. Interpreting 2-way Outcomes (cont.) 2 Way ANOVA

  31. Bogus Winthrop Data – 2-way ANOVA • Some of the hypotheses were supported. • There was a main effect for residence. On-campus students earned higher GPAs (M=3.2545) than off-campus students (M=1.9667), F(1,14)=21.625,p<=.05. • However, there was no main effect for program. GPAs for students in the control (M=2.5857), mentoring (M=2.5286), and study hall condition (M=2.9500) did not differ significantly, F(2,14)=.069, n.s. • There was no interaction, F(2,14)=.205, n.s. • Residence accounted for a moderate amount of variance in GPA, eta2 = .5132. • Overall, it appears residence, but not type of program, affects GPA. 2 Way ANOVA

  32. Is there a sig. difference in funniness?Yet another excuse for a 1-way Anova #2 #1 Rate each video on the following scale: Not funny 1 2 3 4 5 6 7 Funny #3 2 Way ANOVA

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