Deck 9: Analysis of Variance Anova: One-Factor Completely Randomized Design

Question 1

If a three-group experiment is performed and the means for the three groups are analyzed with three t tests (Group 1 vs.Group 2, Group 2 vs.Group 3, Group 1 vs.Group 3), what is the probability of committing the Type I error?

A).05
B).10
C).14
D).15

Answer 1

.14

Question 2

A psychologist wishes to determine which of four diet plans works best. The psychologist randomly assigns 32 overweight clients to one of four diet plans: Life on Herbs (LOH), E-mail-A-Meal (EAM), Weight-Lookers (WLK), and Low-Carbs (LOC). The numbers represent weight loss in pounds for 3 months for each client. $\begin{array} { c c c c } \hline \text { LOH } & \text { EAM } & \text { WLK } & \text { LOC } \\\hline 14 & 11 & 10 & 25 \\19 & 15 & 5 & 18 \\12 & 9 & 6 & 24 \\9 & 19 & 11 & 29 \\14 & 12 & 4 & 17 \\15 & 10 & 5 & 20 \\18 & 20 & 4 & 23 \\8 & 8 & 3 & 27 \\\hline\end{array}$

-The F value for this problem is

A)1150.75
B)436.75
C)1587.50
D)24.591

Answer 2

24.591

Question 3

A psychologist wishes to determine which of four diet plans works best. The psychologist randomly assigns 32 overweight clients to one of four diet plans: Life on Herbs (LOH), E-mail-A-Meal (EAM), Weight-Lookers (WLK), and Low-Carbs (LOC). The numbers represent weight loss in pounds for 3 months for each client. $\begin{array} { c c c c } \hline \text { LOH } & \text { EAM } & \text { WLK } & \text { LOC } \\\hline 14 & 11 & 10 & 25 \\19 & 15 & 5 & 18 \\12 & 9 & 6 & 24 \\9 & 19 & 11 & 29 \\14 & 12 & 4 & 17 \\15 & 10 & 5 & 20 \\18 & 20 & 4 & 23 \\8 & 8 & 3 & 27 \\\hline\end{array}$

-The null hypothesis for this problem should be

A)rejected
B)not rejected
C)retained
D)none of the above

Answer 3

rejected

Question 4

A psychologist wishes to determine which of four diet plans works best. The psychologist randomly assigns 32 overweight clients to one of four diet plans: Life on Herbs (LOH), E-mail-A-Meal (EAM), Weight-Lookers (WLK), and Low-Carbs (LOC). The numbers represent weight loss in pounds for 3 months for each client. $\begin{array} { c c c c } \hline \text { LOH } & \text { EAM } & \text { WLK } & \text { LOC } \\\hline 14 & 11 & 10 & 25 \\19 & 15 & 5 & 18 \\12 & 9 & 6 & 24 \\9 & 19 & 11 & 29 \\14 & 12 & 4 & 17 \\15 & 10 & 5 & 20 \\18 & 20 & 4 & 23 \\8 & 8 & 3 & 27 \\\hline\end{array}$

-The sum of squares within groups (SSW) for this problem is

A)1150.75
B)436.75
C)1587.50
D)24.591

Question 5

A standard deviation derived from a finite sample of means from a population of scores is known as the

A)standard deviation
B)sampling deviation
C)standard error of the mean
D)power of a test

Question 6

An omnibus hypothesis means that

A)there are many different possible outcomes
B)there is a single outcome
C)there are two outcomes but three alternatives
D)there are two null hypotheses

Question 7

A psychologist wishes to determine which of four diet plans works best. The psychologist randomly assigns 32 overweight clients to one of four diet plans: Life on Herbs (LOH), E-mail-A-Meal (EAM), Weight-Lookers (WLK), and Low-Carbs (LOC). The numbers represent weight loss in pounds for 3 months for each client. $\begin{array} { c c c c } \hline \text { LOH } & \text { EAM } & \text { WLK } & \text { LOC } \\\hline 14 & 11 & 10 & 25 \\19 & 15 & 5 & 18 \\12 & 9 & 6 & 24 \\9 & 19 & 11 & 29 \\14 & 12 & 4 & 17 \\15 & 10 & 5 & 20 \\18 & 20 & 4 & 23 \\8 & 8 & 3 & 27 \\\hline\end{array}$

-The mean squares within groups (MSW) is

A)436.750
B)15.598
C)383.583
D)24.591

Question 8

A psychologist wishes to determine which of four diet plans works best. The psychologist randomly assigns 32 overweight clients to one of four diet plans: Life on Herbs (LOH), E-mail-A-Meal (EAM), Weight-Lookers (WLK), and Low-Carbs (LOC). The numbers represent weight loss in pounds for 3 months for each client. $\begin{array} { c c c c } \hline \text { LOH } & \text { EAM } & \text { WLK } & \text { LOC } \\\hline 14 & 11 & 10 & 25 \\19 & 15 & 5 & 18 \\12 & 9 & 6 & 24 \\9 & 19 & 11 & 29 \\14 & 12 & 4 & 17 \\15 & 10 & 5 & 20 \\18 & 20 & 4 & 23 \\8 & 8 & 3 & 27 \\\hline\end{array}$

-The degrees of freedom for the denominator (df₂) is

A)3
B)28
C)31
D)1

Question 9

When an ANOVA is significant,

A)a multiple comparison test must be performed
B)an a posteriori test must be performed
C)a post hoc test must be performed
D)all of the above

Question 10

A psychologist wishes to determine which of four diet plans works best. The psychologist randomly assigns 32 overweight clients to one of four diet plans: Life on Herbs (LOH), E-mail-A-Meal (EAM), Weight-Lookers (WLK), and Low-Carbs (LOC). The numbers represent weight loss in pounds for 3 months for each client. $\begin{array} { c c c c } \hline \text { LOH } & \text { EAM } & \text { WLK } & \text { LOC } \\\hline 14 & 11 & 10 & 25 \\19 & 15 & 5 & 18 \\12 & 9 & 6 & 24 \\9 & 19 & 11 & 29 \\14 & 12 & 4 & 17 \\15 & 10 & 5 & 20 \\18 & 20 & 4 & 23 \\8 & 8 & 3 & 27 \\\hline\end{array}$

-The sum of squares between groups (SSB) for this problem is

A)1150.75
B)436.75
C)1587.50
D)24.591

Question 11

A psychologist wishes to determine which of four diet plans works best. The psychologist randomly assigns 32 overweight clients to one of four diet plans: Life on Herbs (LOH), E-mail-A-Meal (EAM), Weight-Lookers (WLK), and Low-Carbs (LOC). The numbers represent weight loss in pounds for 3 months for each client. $\begin{array} { c c c c } \hline \text { LOH } & \text { EAM } & \text { WLK } & \text { LOC } \\\hline 14 & 11 & 10 & 25 \\19 & 15 & 5 & 18 \\12 & 9 & 6 & 24 \\9 & 19 & 11 & 29 \\14 & 12 & 4 & 17 \\15 & 10 & 5 & 20 \\18 & 20 & 4 & 23 \\8 & 8 & 3 & 27 \\\hline\end{array}$

-Which of the following can be concluded about this experiment?

A)There are differences in weight loss among the groups.
B)There are no differences in weight loss among the groups.
C)One group was superior to the other groups in weight loss.
D)Two of the groups were better than the other groups in weight loss.

Question 12

The original Bonferroni correction for three multiple t tests would have the conventional level of significance change to

A).05
B).01
C).001
D).017

Question 13

The problem with the original Bonferroni correction is that

A)one is more likely to commit the Type I error
B)the probability of the Type II error increases dramatically
C)Type I and Type II errors increase dramatically
D)the power of the test is increased

Question 14

Which of the following is not an assumption of ANOVA?

A)the dependent variable is drawn from a normally distributed population of scores
B)the participants are randomly assigned to each group, and the scores are independent
C)the variances about each group mean are not too different from each other
D)the independent variable has an infinite number of levels

Question 15

The derived F value in ANOVA is a _______ of variances.

A)collection
B)group
C)ratio
D)matrix

Question 16

The procedures of ANOVA were primarily developed by

A)Galton
B)Pearson
C)Fisher
D)Gosset

Question 17

A psychologist wishes to determine which of four diet plans works best. The psychologist randomly assigns 32 overweight clients to one of four diet plans: Life on Herbs (LOH), E-mail-A-Meal (EAM), Weight-Lookers (WLK), and Low-Carbs (LOC). The numbers represent weight loss in pounds for 3 months for each client. $\begin{array} { c c c c } \hline \text { LOH } & \text { EAM } & \text { WLK } & \text { LOC } \\\hline 14 & 11 & 10 & 25 \\19 & 15 & 5 & 18 \\12 & 9 & 6 & 24 \\9 & 19 & 11 & 29 \\14 & 12 & 4 & 17 \\15 & 10 & 5 & 20 \\18 & 20 & 4 & 23 \\8 & 8 & 3 & 27 \\\hline\end{array}$

-The sum of squares total (SST) for this problem is

A)1150.75
B)436.75
C)1587.50
D)24.591

Question 18

Theoretically, in ANOVA, if there were virtually no group mean differences, then the value of the derived F would be

A)0.00
B)0.05
C)1.00
D)0.01

Question 19

A psychologist wishes to determine which of four diet plans works best. The psychologist randomly assigns 32 overweight clients to one of four diet plans: Life on Herbs (LOH), E-mail-A-Meal (EAM), Weight-Lookers (WLK), and Low-Carbs (LOC). The numbers represent weight loss in pounds for 3 months for each client. $\begin{array} { c c c c } \hline \text { LOH } & \text { EAM } & \text { WLK } & \text { LOC } \\\hline 14 & 11 & 10 & 25 \\19 & 15 & 5 & 18 \\12 & 9 & 6 & 24 \\9 & 19 & 11 & 29 \\14 & 12 & 4 & 17 \\15 & 10 & 5 & 20 \\18 & 20 & 4 & 23 \\8 & 8 & 3 & 27 \\\hline\end{array}$

-The degrees of freedom for the numerator (df₁) is

A)3
B)28
C)31
D)1

Question 20

A psychologist wishes to determine which of four diet plans works best. The psychologist randomly assigns 32 overweight clients to one of four diet plans: Life on Herbs (LOH), E-mail-A-Meal (EAM), Weight-Lookers (WLK), and Low-Carbs (LOC). The numbers represent weight loss in pounds for 3 months for each client. $\begin{array} { c c c c } \hline \text { LOH } & \text { EAM } & \text { WLK } & \text { LOC } \\\hline 14 & 11 & 10 & 25 \\19 & 15 & 5 & 18 \\12 & 9 & 6 & 24 \\9 & 19 & 11 & 29 \\14 & 12 & 4 & 17 \\15 & 10 & 5 & 20 \\18 & 20 & 4 & 23 \\8 & 8 & 3 & 27 \\\hline\end{array}$

-One way to determine the effect size in ANOVA is

A)omega-squared
B)F squared
C)alpha-squared
D)beta-squared

Question 21

A consumer psychologist wishes to determine whether playing music increases sales. The owner plays no music, soft rock, classical, or jazz and notes the sales for 28 people under these conditions. The following numbers are in dollar amounts per shopper. $\begin{array} { c c c c } \hline \text { No Music } & \text { Soft Rock } & \text { Classical } & \text { Jazz } \\\hline 128 & 57 & 87 & 55 \\101 & 32 & 40 & 24 \\157 & 93 & 21 & 95 \\196 & 35 & 92 & 19 \\163 & 58 & 55 & 60 \\144 & 61 & 59 & 85 \\170 & 82 & 39 & 54 \\\hline\end{array}$

-The F value for this problem is

A)17,451.714
B)63,902.714
C)21.293
D)46,451.000

Question 22

A consumer psychologist wishes to determine whether playing music increases sales. The owner plays no music, soft rock, classical, or jazz and notes the sales for 28 people under these conditions. The following numbers are in dollar amounts per shopper. $\begin{array} { c c c c } \hline \text { No Music } & \text { Soft Rock } & \text { Classical } & \text { Jazz } \\\hline 128 & 57 & 87 & 55 \\101 & 32 & 40 & 24 \\157 & 93 & 21 & 95 \\196 & 35 & 92 & 19 \\163 & 58 & 55 & 60 \\144 & 61 & 59 & 85 \\170 & 82 & 39 & 54 \\\hline\end{array}$

-The sum of squares total (SST) for this problem is

A)17,451.714
B)63,902.714
C)21.293
D)46,451.000

Question 23

A consumer psychologist wishes to determine whether playing music increases sales. The owner plays no music, soft rock, classical, or jazz and notes the sales for 28 people under these conditions. The following numbers are in dollar amounts per shopper. $\begin{array} { c c c c } \hline \text { No Music } & \text { Soft Rock } & \text { Classical } & \text { Jazz } \\\hline 128 & 57 & 87 & 55 \\101 & 32 & 40 & 24 \\157 & 93 & 21 & 95 \\196 & 35 & 92 & 19 \\163 & 58 & 55 & 60 \\144 & 61 & 59 & 85 \\170 & 82 & 39 & 54 \\\hline\end{array}$

-The sum of squares between groups (SSB) for this problem is

A)17,451.714
B)63,902.714
C)21.293
D)46,451.000

Question 24

A consumer psychologist wishes to determine whether playing music increases sales. The owner plays no music, soft rock, classical, or jazz and notes the sales for 28 people under these conditions. The following numbers are in dollar amounts per shopper. $\begin{array} { c c c c } \hline \text { No Music } & \text { Soft Rock } & \text { Classical } & \text { Jazz } \\\hline 128 & 57 & 87 & 55 \\101 & 32 & 40 & 24 \\157 & 93 & 21 & 95 \\196 & 35 & 92 & 19 \\163 & 58 & 55 & 60 \\144 & 61 & 59 & 85 \\170 & 82 & 39 & 54 \\\hline\end{array}$

-The mean squares within groups (MSW) is

A)727.155
B)15,483.667
C)21.293
D)46,451.000

Question 25

A consumer psychologist wishes to determine whether playing music increases sales. The owner plays no music, soft rock, classical, or jazz and notes the sales for 28 people under these conditions. The following numbers are in dollar amounts per shopper. $\begin{array} { c c c c } \hline \text { No Music } & \text { Soft Rock } & \text { Classical } & \text { Jazz } \\\hline 128 & 57 & 87 & 55 \\101 & 32 & 40 & 24 \\157 & 93 & 21 & 95 \\196 & 35 & 92 & 19 \\163 & 58 & 55 & 60 \\144 & 61 & 59 & 85 \\170 & 82 & 39 & 54 \\\hline\end{array}$

-The degrees of freedom for the denominator (df₂) is

A)3
B)24
C)27
D)28

Question 26

A consumer psychologist wishes to determine whether playing music increases sales. The owner plays no music, soft rock, classical, or jazz and notes the sales for 28 people under these conditions. The following numbers are in dollar amounts per shopper. $\begin{array} { c c c c } \hline \text { No Music } & \text { Soft Rock } & \text { Classical } & \text { Jazz } \\\hline 128 & 57 & 87 & 55 \\101 & 32 & 40 & 24 \\157 & 93 & 21 & 95 \\196 & 35 & 92 & 19 \\163 & 58 & 55 & 60 \\144 & 61 & 59 & 85 \\170 & 82 & 39 & 54 \\\hline\end{array}$

-The null hypothesis for this problem should be

A)rejected
B)not rejected
C)retained
D)neither rejected nor not rejected

Question 27

A consumer psychologist wishes to determine whether playing music increases sales. The owner plays no music, soft rock, classical, or jazz and notes the sales for 28 people under these conditions. The following numbers are in dollar amounts per shopper. $\begin{array} { c c c c } \hline \text { No Music } & \text { Soft Rock } & \text { Classical } & \text { Jazz } \\\hline 128 & 57 & 87 & 55 \\101 & 32 & 40 & 24 \\157 & 93 & 21 & 95 \\196 & 35 & 92 & 19 \\163 & 58 & 55 & 60 \\144 & 61 & 59 & 85 \\170 & 82 & 39 & 54 \\\hline\end{array}$

-Which of the following can be concluded about this experiment?

A)There are differences in sales among the groups.
B)There are no differences in sales among the groups.
C)One group was superior to the other groups in sales.
D)Two of the groups were better than the other groups in sales.

Question 28

A consumer psychologist wishes to determine whether playing music increases sales. The owner plays no music, soft rock, classical, or jazz and notes the sales for 28 people under these conditions. The following numbers are in dollar amounts per shopper. $\begin{array} { c c c c } \hline \text { No Music } & \text { Soft Rock } & \text { Classical } & \text { Jazz } \\\hline 128 & 57 & 87 & 55 \\101 & 32 & 40 & 24 \\157 & 93 & 21 & 95 \\196 & 35 & 92 & 19 \\163 & 58 & 55 & 60 \\144 & 61 & 59 & 85 \\170 & 82 & 39 & 54 \\\hline\end{array}$

-The degrees of freedom for the numerator (df₁) is

A)3
B)24
C)27
D)28

Question 29

A consumer psychologist wishes to determine whether playing music increases sales. The owner plays no music, soft rock, classical, or jazz and notes the sales for 28 people under these conditions. The following numbers are in dollar amounts per shopper. $\begin{array} { c c c c } \hline \text { No Music } & \text { Soft Rock } & \text { Classical } & \text { Jazz } \\\hline 128 & 57 & 87 & 55 \\101 & 32 & 40 & 24 \\157 & 93 & 21 & 95 \\196 & 35 & 92 & 19 \\163 & 58 & 55 & 60 \\144 & 61 & 59 & 85 \\170 & 82 & 39 & 54 \\\hline\end{array}$

-The significance level for this problem is

A)p < .01
B)p < .10
C)p > .05
D)p > .001

Question 30

A consumer psychologist wishes to determine whether playing music increases sales. The owner plays no music, soft rock, classical, or jazz and notes the sales for 28 people under these conditions. The following numbers are in dollar amounts per shopper. $\begin{array} { c c c c } \hline \text { No Music } & \text { Soft Rock } & \text { Classical } & \text { Jazz } \\\hline 128 & 57 & 87 & 55 \\101 & 32 & 40 & 24 \\157 & 93 & 21 & 95 \\196 & 35 & 92 & 19 \\163 & 58 & 55 & 60 \\144 & 61 & 59 & 85 \\170 & 82 & 39 & 54 \\\hline\end{array}$

-The sum of squares within groups (SSW) for this problem is

A)17,451.714
B)63,902.714
C)21.293
D)46,451.000