Deck 11: One-Factor Anova: Fixed-Effects Model

Question 1

For a one-factor ANOVA comparing five groups with n = 30 in each group, the F ratio has degrees of freedom equal to

A) 4, 120
B) 4, 145
C) 5, 149
D) 5, 145

Answer 1

B

Question 2

Suppose n₁ = 15, n₂ = 13, n₃ = 17, n₄ =17. For a one-factor ANOVA, the df_with would be

A) 3
B) 4
C) 58
D) 61

Answer 2

C

Question 3

Suppose n₁ = 15, n₂ = 13, n₃ = 17, n₄ =17. For a one-factor ANOVA, the df_betw would be

A) 3
B) 4
C) 58
D) 61

Answer 3

A

Question 4

Suppose n₁ = 15, n₂ = 13, n₃ = 17, n₄ =17. For a one-factor ANOVA, the df_total would be

A) 3
B) 4
C) 58
D) 61

Question 5

In a one-factor ANOVA, if H₀ is rejected, we conclude that

A) all population means are different from one other.
B) at least one pair of population means are different.
C) all population means are equal.
D) at least one pair of population means are the same.

Question 6

In ANOVA, the variability between group means is estimated by

A) SS_betw
B) SS_with
C) MS_betw
D) MS_with

Question 7

In ANOVA, the average deviation of all the scores from their respective group means is estimated by

A) SS_total
B) SS_with
C) MS_total
D) MS_with

Question 8

In ANOVA, which of the following is used to determine the appropriate F ratio?

A) SS values
B) MS values
C) df values
D) E(MS) values

Question 9

A researcher used ANOVA to examine the effects of paper colors on reading speed. She prepared reading materials printed on three different colors of paper: white paper, yellow paper, and blue paper. She then randomly assigned 20 readers to each type of paper. How many factors are involved in this experiment and how many levels are in the factor(s)?

A) 1 factor with 3 levels
B) 1 factor with 20 levels
C) 3 factors with 20 levels
D) 3 factors with 60 levels

Question 10

Which of the following is a necessary assumption of the ANOVA model?

A) Observations come from populations with equal means.
B) Observations come from populations with equal variances.
C) Sample sizes are equal for each group.
D) Dependent variables are measured on a ratio scale.

Question 11

If you find an F ratio of 0.5 in a one-factor ANOVA ( $\alpha$ = .05), you will

A) reject the null hypothesis.
B) fail to reject the null hypothesis.
C) not be able to decide because the df and critical value are unknown.
D) conclude that a mistake has been made.

Question 12

If you find an F ratio of 2 in a one-factor ANOVA ( $\alpha$ = .05), you will

A) reject the null hypothesis.
B) fail to reject the null hypothesis.
C) not be able to decide because the df and critical value are unknown.
D) conclude that a mistake has been made.

Question 13

If you find an F ratio of -2 in a one-factor ANOVA ( $\alpha$ = .05), you will

A) reject the null hypothesis.
B) fail to reject the null hypothesis.
C) not be able to decide because the df and critical value are unknown.
D) conclude that a mistake has been made.

Question 14

For J = 2 and $\alpha$ = .05, if the result of the one-factor fixed-effects ANOVA is nonsignificant, then the result of the independent t test using the same data set and same $\alpha$ level will be

A) significant.
B) nonsignificant.
C) uncertain.
D) depend on the sample sizes.

Question 15

When analyzing mean differences between two samples, doing an independent t test instead of an ANOVA using the same  level

A) decreases the probability of a Type I error.
B) increases the probability of a Type I error.
C) does not change the probability of a Type I error.
D) cannot be determined from the information provided.

Question 16

When analyzing mean differences between three samples, doing all pairwise independent t tests instead of ANOVA using the same $\alpha$ level

A) decreases the probability of a Type I error.
B) increases the probability of a Type I error.
C) does not change the probability of a Type I error.
D) cannot be determined from the information provided.

Question 17

Suppose that for a one-factor ANOVA with J = 3 and n = 10, the three sample means are all equal to 4.5. What is the value of MS_betw?

A) 0.
B) 45.
C) 135.
D) cannot be determined from the information provided.

Question 18

Suppose that for a one-factor ANOVA with J = 3 and n = 10, two of the sample means are both equal to 4.5, but the other sample mean is 4.8. What conclusion will you make?

A) Reject the null hypothesis.
B) Fail to reject the null hypothesis.
C) Uncertain because the df and critical value are unknown.
D) Uncertain because the variances of the samples are unknown.

Question 19

The homoscedasticity assumption states that

A) the populations are normally distributed.
B) the samples are normally distributed.
C) the variances of each population are equal.
D) the variances of each sample are equal.

Question 20

Which assumption can be examined by Q-Q plots?

A) Independence
B) Homogeneity of variance
C) Normality
D) All of the above

Question 21

A researcher wanted to compare the average home prices in three different school districts. For each district, he recorded the average annual prices over the past ten years (n = 10). Then he used a one-factor ANOVA to examine if prices are different between districts. Based on the design, what assumption of ANOVA has most likely been violated?

A) Independence
B) Homogeneity of variance
C) Normality
D) Equilibrium

Question 22

In ANOVA, which of the following statements is possible?

A) SS_total < SS_with
B) df_total < df_with
C) Both a and b are possible.
D) Neither a nor b are possible.

Question 23

In ANOVA, which of the following statements occurs when H₀ is true?

A) E(MS_betw) = E(MS_with)
B) E(MS_betw) > E(MS_with)
C) E(F) > 1
D) none of the above.

Question 24

Which of the following statements about $\alpha$ level is true?

A) As $\alpha$ level decreases, the critical F value will decrease as well.
B) As $\alpha$ level decreases, the computed F value will increase.
C) If $\alpha$ level is smaller than the p value, then the null hypothesis is rejected.
D) $\alpha$ level describes the highest risk of Type I error we are willing to take.

Question 25

Using the same data with SPSS, Jamie and John found out that the p value of an ANOVA F test is 0.004. They both rejected the null hypothesis. However, Jamie used $\alpha$ = 0.05, whereas John used $\alpha$ = 0.01. Who has a higher probability of actually making a Type I error?

A) Jamie
B) John
C) Both have the same probability.
D) Uncertain.

Question 26

A consumer testing lab wants to compare the mean life of AA batteries produced by different manufacturers. Five brands of batteries are selected, and for each brand, 20 batteries are randomly sampled. The lab then tests for the life time of each battery (in hours), and compares the average battery life of different brands using ANOVA. Complete the following one-factor ANOVA summary table using $\alpha$ = .05. Based on the results, do batteries of different brands have different life times?
$\begin{array}{llllll}\hline \text { Source } & S S & d f & M S & F & \text { Critical Value and Decision } \\\hline \begin{array}{l}\text { Between } \\\text { Within }\end{array} & & & 10 & & \\\text { Total } & 1110 & & & & \\\hline\end{array}$

Question 27

A reading specialist would like to know whether the page layout has any consistent effect on children's reading speed. He printed the same story in three types of page layout (one-column, two-column, and three-column), and then randomly assigned 15 children to each group. The time each child took to finish reading is recorded and compared using the one-factor ANOVA model. Complete the following ANOVA summary table using $\alpha$ = .05. Based on the results, does page layout have an effect on the speed of reading?
$\begin{array}{lccccc}\hline \text { Source } & S S & d f & M S & F & \text { Critical Value and Decision } \\\hline \text { Between } & & & 9 & 1.8 & \\\text { Within } & & & & & \\\text { Total } & & & & & \\\hline\end{array}$

Question 28

A consumer group wanted to determine if there was a difference in prices for a specific type of toy depending on where the toy was purchased. In the local area there are three main retailers: W-Mart, Tag, and URToy. For each retailer, the consumer group randomly selected five stores located in different parts of the city, and collected their listed prices of that specific type of toy (in dollars). Assume that all stores priced their merchandise independently.
$\begin{array}{ccc}\text { W-Mart } & \text { Tag } & \text { URToy } \\\hline 23 & 24 & 30 \\22 & 27 & 30 \\25 & 28 & 26 \\24 & 25 & 29 \\23 & 27 & 29 \\\hline\end{array}$ Use SPSS to conduct a one-factor ANOVA to determine if the prices are different across different retailers using $\alpha$ = .05. Test the assumptions, plot the group means, consider an effect size, interpret the results, and write an APA-style summary.

Question 29

A stock analyst wanted to compare the long-term return of stocks from different industries. She randomly selected eight stocks in each of the three industries of interest (financial, energy, utilities) and compiled the 10-year rate of return for each stock (assume the return for one stock is not dependent on the return for any other stock). Below are the data that were collected.
$\begin{array}{rrr}\hline \text { Financial } & \text { Energy } & \text { Utilities } \\\hline 10.76 & 12.72 & 10.88 \\15.05 & 14.91 & 5.86 \\17.01 & 6.43 & 12.46 \\5.07 & 11.19 & 9.90 \\19.50 & 18.79 & 3.95 \\8.16 & 20.73 & 3.44 \\10.38 & 9.60 & 7.11 \\6.76 & 17.40 & 15.70 \\\hline\end{array}$ Use SPSS to conduct a one-factor ANOVA to determine if the returns are equal across industries ( $\alpha$ = .05). Test the assumptions, plot the group means, consider an effect size, interpret the results, and write an APA-style summary.

Question 30

A researcher was interested in comparing rental rates in four different parts of the city. She randomly selected a block from each part of the city. For each block, she collected the rental rates of different neighboring apartments. She then used one-factor ANOVA to analyze her data. The ANOVA table below summarized the results she obtained.

a. There are two mistakes in the ANOVA table. Identify the mistakes and correct them.
b. Based on the research design, do you think any assumption of ANOVA may have been violated in this study? If so, what assumption is being violated? What might be the consequences of the violation?