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 Compare relative influences on DV Examine interactions between IV Dr. Sinn, PSYC 301 2 Way ANOVA

Example Two Way ANOVAs 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 Dr. Sinn, PSYC 301 2 Way ANOVA

Main Effects Two Way ANOVAs Toy Color Blue (1) Pink (2) Sex Boy (1) 7 6 5 2 3 4 Girl (2) 12 10 11 Main Effect for Toy Color? Compare Column Means M=5.5 M=7.0 M=8.0 M=4.5 Main Effect for Gender? Compare Row Means Dr. Sinn, PSYC 301 2 Way ANOVA

Interactions- Cell Means Two Way ANOVAs Toy Color Blue (1) Pink (2) Sex Boy (1) 7 6 5 2 3 4 Girl (2) 12 10 11 Graph cell means to examine possibility of interaction M=6 M=3 M=5 M=11 Dr. Sinn, PSYC 301 2 Way ANOVA

Interactions-Graph Two Way ANOVAs General rule of life: If two lines cross, it probably means something. Non-parallel lines suggests interaction. Dr. Sinn, PSYC 301 2 Way ANOVA

SPSS: Data Input #1 Two Way ANOVAs Dr. Sinn, PSYC 301 2 Way ANOVA

SPSS: Data Input #2 Two Way ANOVAs Dr. Sinn, PSYC 301 2 Way ANOVA

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 Dr. Sinn, PSYC 301 2 Way ANOVA

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 Dr. Sinn, PSYC 301 2 Way ANOVA

SPSS: Analysis, Step #3 Two Way ANOVAs Select Options Ask for Descriptive Statistics Dr. Sinn, PSYC 301 2 Way ANOVA

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) Dr. Sinn, PSYC 301 2 Way ANOVA

SPSS Output #1 Two Way ANOVAs   SPSS Output #1 Two Way ANOVAs Dr. Sinn, PSYC 301 2 Way ANOVA

SPSS Output #2: Two Way ANOVAs BG WG Dr. Sinn, PSYC 301 2 Way ANOVA

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). Dr. Sinn, PSYC 301 2 Way ANOVA

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. Dr. Sinn, PSYC 301 2 Way ANOVA

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. Dr. Sinn, PSYC 301 2 Way ANOVA

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 Dr. Sinn, PSYC 301 2 Way ANOVA

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 Dr. Sinn, PSYC 301 2 Way ANOVA

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 Dr. Sinn, PSYC 301 2 Way ANOVA

Source of Variation Table from Toy Study BG WG Dr. Sinn, PSYC 301 2 Way ANOVA

Age & Intelligence (2-way ANOVA) Task Fluid Crystalized Age 65 105 100 95 110 75 85 90 80 Age & Intelligence (2-way ANOVA) Dr. Sinn, PSYC 301 2 Way ANOVA

Important Means Main effect for Task? Main effect for Age? Graph it Dr. Sinn, PSYC 301 2 Way ANOVA

Calculate degrees of freedom by hand: dfA dfB dfA*B dfError dfTotal Dr. Sinn, PSYC 301 2 Way ANOVA

Complete Table with these SS SSTask = 759.375 SSAge = 452.083 SSTask*Age = 356.250 SSError = 406.250 Dr. Sinn, PSYC 301 2 Way ANOVA

SPSS Data Entry Dr. Sinn, PSYC 301 2 Way ANOVA

Check Output What means pertain to… Is there a …. 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 Dr. Sinn, PSYC 301 2 Way ANOVA

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. Dr. Sinn, PSYC 301 2 Way ANOVA

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. Dr. Sinn, PSYC 301 2 Way ANOVA

Interpreting 2-way Outcomes Dr. Sinn, PSYC 301 2 Way ANOVA

Interpreting 2-way Outcomes (cont.) Dr. Sinn, PSYC 301 2 Way ANOVA

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. Dr. Sinn, PSYC 301 2 Way ANOVA

Is there a sig. difference in funniness 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 Dr. Sinn, PSYC 301 2 Way ANOVA