Exam 11: One-Factor Anova: Fixed-Effects Mode

Correct Answer:

Verified

Procedure:
1) Create a data set with two variables, Prices and Retailer. The data set should have 15 cases, each case representing one store.

2) Go to Analyze $\rightarrow$ General Linear Model $\rightarrow$ Univariate. Select Prices as the Dependent Variable and Retailer as the Fixed Factor. Go to Plot and select Retailer to the Horizontal Axis, then Add, to get a profile plot. Go to Save and check Unstandardized under Residuals to save model residuals. Go to Options. Check Estimates of effect size to get effect size estimates. Check Homogeneity tests to examine the assumption of homoscedasticity.

"3) To examine the assumption of independence, go to Graphs $\rightarrow$ Legacy Dialogs $\rightarrow$ Scatter/Dot $\rightarrow$ Simple Scatter $\rightarrow$ Define. Select RES_1 as the Y Axis, and Retailer as the X Axis. To examine the assumption of normality, go to Analyze $\rightarrow$ Descriptive Statistics $\rightarrow$ Explore. Select RES_1 to Dependent List. Go to Plots and check Normality plots with tests.

Selected SPSS Output:
Tests of Between-Subjects Efects
Dependent Variable: Frices

$\begin{array}{ccccccc}\hline \text { Source } & \begin{array}{c}\text { Type III Sum of } \\\text { Squares }\end{array} & d f & \text { Mean Square } & F & \text { Sig. } & \begin{array}{c}\text { Partial Eta } \\\text { Squared }\end{array} \\\hline \text { Retailer } & 72.933 & 2 & 36.467 & 16.328 & .000 & .731 \\\text { Error } & 26.800 & 12 & 2.233 & & & \\\text { Corrected Total } & 99.733 & 14 & & & & \\\hline\end{array}$
Levene's Test of Equality of Error
Variances Dependent Variable: Prices

$\begin{array}{llll}\hline F & d f 2 & d f 2 & \text { Sig. } \\\hline 467 & 2 & 12 & .638 \\\hline\end{array}$
Profile Plot

Residual Plot by Group

Q-Q Plot of Residuals

A one-way ANOVA was conducted to determine if the prices of a certain type of toy differed in three major retail stores.
The Q-Q plot of residuals showed that the points clustered close to the diagonal line, suggesting that the assumption of normality was reasonable. According to Levene's test, the homogeneity of variance assumption was satisfied [F(2, 12) = .467, p = .638]. The scatterplot of residuals against the levels of the independent variable demonstrated a random display of points around 0, providing evidence to the assumption of independence being satisfied. From the ANOVA summary table, we see that the prices are significantly different across the three retailers (F = 16.328, df = 2, 12, p < .001), the effect size is rather large ( $\chi$ ² = .731; suggesting about 73.1% of the variance in prices is accounted for by the differences in retailers).
The profile plot suggested that the price is the lowest in W-Mart, higher in Tag, and the highest in URToy."

Correct Answer:

Verified

There are 3 different types of page layout, so J = 3. There were 15 children in each group, so n = 15.
N = 3*15 = 45.
df_betw = J - 1 = 3 - 1 = 2, df_with = N - J = 45 - 3 = 42, df_total = N - 1 = 45 - 1 = 44.
Because F = MS_betw/MS_with, MS_with = MS_betw/F = 9/1.8 = 5.

SS_betw = MS_betw*df_betw = 9*2 = 18, SS_with = MS_with*df_with = 5*42 = 210, SS_total = SS_betw + SS_with = 18 + 210 = 228.

Critical value _.05F_2,42 = 3.22. Because F = 1.8 < critical F value, we fail to reject H₀ and conclude that page layout does not have a significant effect on the speed of reading.

$\begin{array}{lrrrcc}\hline \text { Source } & S S & {\boldsymbol{d f}} & {M S} & F & \text { Critical Value and Decision } \\\hline \text { B etween } & 18 & 2 & 9 & 1.8 & .05 F_{2,42}=3.22 \\\text { Within } & 210 & 42 & 5 & & \text { Fail to reject } H 0 \\\text { Total } & 228 & 44 & & & \\\hline\end{array}$