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.

Source df SS MS F Children 188.58 Relationship 356.04 AB 371.96 Within Total 1971.78

None One Two Dating 25 30 28 31 27 26 40 35 20 23 Married 11 18 22 15 Number of children None One Two Dating 25 30 28 31 27 26 40 35 20 23 Married 11 18 22 15 14 19 21 Cohabitating 24 9 16 13

Source df SS MS F Children 2 188.58 94.29 3.22 Relationship 356.04 178.02 6.07* AB 4 371.96 92.99 3.17* Within 36 1055.20 29.31 Total 44 1971.78 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

Sociology Psychology Biology

Sociology Psychology Biology

Sociology Psychology Biology

Sociology Psychology Biology

Sociology Psychology Biology

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

Sociology Psychology Biology

Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j 2.67 1.67 1.78 Males 4.00 Mean2j Mean.j 3.67 3.17 0.33 2.33 2.06 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 SSbetween in the one-way

Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j 2.67 1.67 1.78 Males 4.00 Mean2j Mean.j 3.67 3.17 0.33 2.33 2.06 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

Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j 2.67 1.67 1.78 Males 4.00 Mean2j Mean.j 3.67 3.17 0.33 2.33 2.06 Are these means different?

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

Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j 2.67 1.67 1.78 Males 4.00 Mean2j Mean.j 3.67 3.17 0.33 2.33 2.06 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

Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j 2.67 1.67 1.78 Males 4.00 Mean2j Mean.j 3.67 3.17 0.33 2.33 2.06 Are these means different?

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

Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j 2.67 1.67 1.78 Males 4.00 Mean2j Mean.j 3.67 3.17 0.33 2.33 2.06 SS G at Socio = 3*((2.67 – 3.17)2 + (3.67 – 3.17)2 = 1.5

Sociology Psychology Biology

Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j 2.67 1.67 1.78 Males 4.00 Mean2j Mean.j 3.67 3.17 0.33 2.33 2.06 Are these means different?

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

Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j 2.67 1.67 1.78 Males 4.00 Mean2j Mean.j 3.67 3.17 0.33 2.33 2.06 SS G at Psych = 3*((1.00 – 2.00)2 + (3.00 – 2.00)2 = 6.00

Sociology Psychology Biology

Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j 2.67 1.67 1.78 Males 4.00 Mean2j Mean.j 3.67 3.17 0.33 2.33 2.06 Are these means different?

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

Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j 2.67 1.67 1.78 Males 4.00 Mean2j Mean.j 3.67 3.17 0.33 2.33 2.06 SS G at Bio = 3*((1.67 – 1.00)2 + (0.33 – 1.00)2 = 2.69

Overall ANOVA Source df SS MS F Gender 1 1.36 2.47 Major 2 14.16 7.08 12.87* G x M 8.83 4.42 8.03* Within 12 6.59 .55 Total 17 30.94

Simple Effects Source df SS MS F Gender G at Socio G at Psych G at Bio Major M at Female M at Male Within 12 6.59 .55

Simple Effects Source df SS MS F Gender G at Socio G at Psych G at Bio 1.50 6.00 2.69 Major M at Female M at Male 4.23 18.71 Within 12 6.59 .55

Simple Effects Source df SS MS F Gender G at Socio G at Psych G at Bio dfA (Gender) = a – 1 dfB (Major) = b – 1 Simple Effects Source df SS MS F Gender G at Socio G at Psych G at Bio 1 1.50 6.00 2.69 Major M at Female M at Male 2 4.23 18.71 Within 12 6.59 .55

Simple Effects Source df SS MS F Gender G at Socio G at Psych G at Bio Compute MS Simple Effects Source df SS MS F Gender G at Socio G at Psych G at Bio 1 1.50 6.00 2.69 Major M at Female M at Male 2 4.23 18.71 2.12 9.36 Within 12 6.59 .55

Simple Effects Source df SS MS F Gender G at Socio G at Psych G at Bio Compute F Simple Effects Source df SS MS F Gender G at Socio G at Psych G at Bio 1 1.50 6.00 2.69 2.72 10.91 4.89 Major M at Female M at Male 2 4.23 18.71 2.12 9.36 3.85 17.02 Within 12 6.59 .55

Simple Effects Source df SS MS F Gender G at Socio G at Psych G at Bio F critical (1, 12) = 4.75 F critical B (2, 12) = 3.89 Simple Effects Source df SS MS F Gender G at Socio G at Psych G at Bio 1 1.50 6.00 2.69 2.72 10.91* 4.89* Major M at Female M at Male 2 4.23 18.71 2.12 9.36 3.85 17.02* Within 12 6.59 .55

Sociology Psychology Biology

Practice ANOVA is from exercise 13.5 1) Interpret the ANOVA results 2) Plot the cell means 3) Compute an entire set of simple effects

Source df SS MS F Delay D at Neutral D at Area A D at Area B 2 1.20 254.80 304.53 0.60 127.40 152.26 .02 4.34* 5.19* Area A at D 50 A at D 100 A at D 150 357.74 363.33 6.93 178.87 181.67 3.47 6.10* 6.19* .12 Within 36 1055.20 29.31

Handout

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

Bring computers to class!