Practice Questions for ANOVA #9.2 a, b, c (2/3e) #8.2 a, b, c (1e)

#9.2 a (8.2 a) Involvement by Education Does involvement vary by education? Step 1: Independent Random Samples, Interval-Ratio Populations normally distributed, variances are equal Step 2: H0: μ1 = μ2= μ3 H1: At least one mean is different Step 3: Sampling Distribution = F distribution Alpha = 0.05 dfw = (n – k) = 15-3 = 12 dfb = k – 1 = 2 F(critical) = 3.88

#9.2 a (8.2 a) Involvement by Education cont. Computational Table: Grand Mean = 2.73 nt=15 < high school n=5 High school Coll./University ∑Xi 10 16 15 ∑X2 30 60 57 Group Means 2 3.2 3

#9.2 a (8.2 a) Involvement by Education cont. Step 4: SSW = SST-SSB = 35.021-4.135 = 30.886 MSB = SSB/dfb = 4.135/2 = 2.068 MSW = MSB/dfw = 30.886/12 = 2.574 Fobt = MSB/MSW = 2.068/2.574 = .803 Step 5: Fobt<Fcr. Fail to reject H0. Involvement does not vary by education.

#9.2 b (8.2 b) Involvement by Residence Does involvement vary by length of residence? Step 1: Independent Random Samples, Interval-Ratio Populations normally distributed, variances are equal Step 2: H0: μ1 = μ2= μ3 H1: At least one mean is different Step 3: Sampling Distribution = F distribution Alpha = 0.05 dfw = (n – k) = 15-3 = 12 dfb = k – 1 = 2 F(critical) = 3.88

#9.2 b (8.2 b) Involvement by Residence cont. Computational Table: Grand Mean = 2.73 nt=15 < 2 years n=5 2 – 5 years > 5 years ∑Xi 12 14 15 ∑X2 42 54 51 Group Means 2.4 2.8 3

#9.2 b (8.2 b) Involvement by Residence cont. Step 4: SSW = SST-SSB = 35.207-.935 = 34.272 MSB = SSB/dfb = .935/2 = .467 MSW = MSB/dfw = 34.272/12 = 2.856 Fobt = MSB/MSW = .467/2.856 = .164 Step 5: Fobt<Fcr. Fail to reject H0. Involvement does not vary by length of residence.

#9.2 c (8.2 c) Involvement by TV Viewing Does involvement vary by amount of TV watched? Step 1: Independent Random Samples, Interval-Ratio Populations normally distributed, variances are equal Step 2: H0: μ1 = μ2= μ3 H1: At least one mean is different Step 3: Sampling Distribution = F distribution Alpha = 0.05 dfw = (n – k) = 15-3 = 12 dfb = k – 1 = 2 F(critical) = 3.88

#9.2 c (8.2 c) Involvement by TV Viewing cont. Computational Table: Grand Mean = 2.73 nt=15 Little or none n=5 Moderate High ∑Xi 4 16 21 ∑X2 6 52 89 Group Means 0.8 3.2 4.2

#9.2 c (8.2 c) Involvement by TV Viewing cont. Step 4: SSW = SST-SSB = 35.206-30.534 = 4.672 MSB = SSB/dfb = 30.534/2 = 15.267 MSW = MSB/dfw = 4.672/12 = .389 Fobt = MSB/MSW = 15.267/.389 = 39.247 Step 5: Fobt>Fcr. Reject H0. Involvement varies significantly by TV viewing (F=39.25, df=2,12, α=.05)

#9.2 d (8.2 d) Involvement by Number of Children Try this one yourself! (Your answer should be Fobt = 2.32)