Practice These are sample data from Diener et. al (1999). Participants were asked their marital status and how often they engaged in religious behavior. They also indicated how happy they were on a scale of 1 to 10. Examine the data

NeverOccasionallyOften Married Unmarried Frequency of religious behavior

Practice Participants were asked about their current romantic relationship (dating, married, or cohabitating) and the number of children they have (none, one, or two). They also indicated how many arguments they had with their romantic partner during the past year. Use the data on the next page to complete the incomplete ANOVA table.

SourcedfSSMSF Children Relationship AB Within Total

NoneOneTwo Dating Married Cohabitating Number of children

SourcedfSSMSF Children Relationship * AB * Within Total F critical A (2, 36) = 3.27 F critical B (2, 36) = 3.27 F critical AB (4, 36) = 2.64

Remember You were asked to determine the effects of both college major (psychology, sociology, and biology) and gender (male and female) on class attendance

Sociology Psychology Biology

Simple Effects The effect of one factor at one level on the other factor. –Use to “tease apart” a significant interaction You wonder if college major has an effect on class attendance for just females? You wonder if male and female psychology students differ in their class attendance?

Sociology Psychology Biology

Simple Effects Why not just do 5 new analyses –2 ANOVAs –3 Independent Samples t-tests You will lose df! Type I error problem still exists

Sociology Psychology Biology

SociologyPsychologyBiologyMean Female Mean 1j Males Mean 2j Mean.j Are these means different?

Simple Effects SS Major at Female –Represents the SS deviations of the treatment means around the Female mean –Its multiplied by n to give an estimate of the population variance (Central limit theorem) –Same formula as SS between in the one-way

SociologyPsychologyBiologyMean Female Mean 1j Males Mean 2j Mean.j SS M at Female = 3*((2.67 – 1.78) 2 + (1.00 – 1.78) 2 + (1.67 – 1.78) 2 = 4.23

Note

Sociology Psychology Biology

SociologyPsychologyBiologyMean Female Mean 1j Males Mean 2j Mean.j Are these means different?

Simple Effects SS Major at Male –Same formula as SS between in the one-way

SociologyPsychologyBiologyMean Female Mean 1j Males Mean 2j Mean.j SS M at Male = 3*((3.67 – 2.33) 2 + (3.00 – 2.33) 2 + (0.33 – 2.33) 2 = 18.71

Sociology Psychology Biology

SociologyPsychologyBiologyMean Female Mean 1j Males Mean 2j Mean.j Are these means different?

Simple Effects SS Gender at Socio –Same formula as SS between in the one-way

SociologyPsychologyBiologyMean Female Mean 1j Males Mean 2j Mean.j SS G at Socio = 3*((2.67 – 3.17) 2 + (3.67 – 3.17) 2 = 1.5

Sociology Psychology Biology

SociologyPsychologyBiologyMean Female Mean 1j Males Mean 2j Mean.j Are these means different?

Simple Effects SS Gender at Psych –Same formula as SS between in the one-way

SociologyPsychologyBiologyMean Female Mean 1j Males Mean 2j Mean.j SS G at Psych = 3*((1.00 – 2.00) 2 + (3.00 – 2.00) 2 = 6.00

Sociology Psychology Biology

SociologyPsychologyBiologyMean Female Mean 1j Males Mean 2j Mean.j Are these means different?

Simple Effects SS Gender at Bio –Same formula as SS between in the one-way

SociologyPsychologyBiologyMean Female Mean 1j Males Mean 2j Mean.j SS G at Bio = 3*((1.67 – 1.00) 2 + (0.33 – 1.00) 2 = 2.69

Overall ANOVA SourcedfSSMSF Gender Major * G x M * Within Total

Simple Effects SourcedfSSMSF Gender G at Socio G at Psych G at Bio Major M at Female M at Male Within

Simple Effects SourcedfSSMSF Gender G at Socio G at Psych G at Bio Major M at Female M at Male Within

Simple Effects SourcedfSSMSF Gender G at Socio G at Psych G at Bio Major M at Female M at Male Within dfA (Gender) = a – 1 dfB (Major) = b – 1

Simple Effects SourcedfSSMSF Gender G at Socio G at Psych G at Bio Major M at Female M at Male Within Compute MS

Simple Effects SourcedfSSMSF Gender G at Socio G at Psych G at Bio Major M at Female M at Male Within Compute F

Simple Effects SourcedfSSMSF Gender G at Socio G at Psych G at Bio * 4.89* Major M at Female M at Male * Within F critical (1, 12) = 4.75 F critical B (2, 12) = 3.89

Sociology Psychology Biology

Practice ANOVA is from exercise ) Interpret the ANOVA results 2) Plot the cell means 3) Compute an entire set of simple effects

SourcedfSSMSF Delay D at Neutral D at Area A D at Area B * 5.19* Area A at D 50 A at D 100 A at D * 6.19*.12 Within

Handout

SPSS Problem 13.1 Compute a factorial ANOVA Conduct a complete set of simple effects (you can do this by hand)