Deck 12: Analysis of Variance

Question 1

For a disordinal interaction, the main effects can be interpreted independently of each other.

Answer 1

False

Question 2

In a two-way ANOVA procedure, variable A has four levels and variable B has two levels.The d.f.N.for
factor would be 3.

Answer 2

True

Question 3

Complete the formula for the sum of squares between groups:

A)
B)
C)
D)

Answer 3

Question 4

In order to conduct the Scheffé test, one must compare the means two at a time, using all possible
combinations of means.

Question 5

If the means of four different groups were compared at and the critical value of the F-test was 3.96, the critical value for the Scheffé test would be 15.84.

Question 6

When the absolute value of q is less than the critical value for the Tukey test, there is a significant
difference between the two means being compared.

Question 7

When finding the degrees of freedom for the F-distribution, d.f.N is equal to one less than the number of
groups.

Question 8

If a researcher wanted to use the t-test to compare 10 means, two at a time, 45 tests would need to be
performed.

Question 9

If one tested at the 1% level of significance, one would declare that averaging over the 3 diets, weight
gains were significantly different between males and females (i.e., that the main effect of gender is
significant).

Question 10

For three groups, the F-test can show whether or not a difference exists among three or more means and
where the difference lies.

Question 11

The ANOVA technique is an abbreviation for the following term:

A)analysis of variance
B)variance
C)Scheffé test
D)Tukey test

Question 12

When performing an F-test, if the means differ significantly, the between-group variance will be much
smaller than the within-group variance.

Question 13

The F-test for comparing means is always right-tailed.

Question 14

An F-test can be used to compare the variances of three or more means.

Question 15

The value of the F-distribution can be negative.

Question 16

To find the critical value for the Tukey test, the number of means, k, and the degrees of freedom
associated with the between-group variance, n, are needed.

Question 17

If there are 3 means to be compared, how many different comparisons are possible?

A)2
B)3
C)5
D)6

Question 18

Which of the following assumptions is not made for the F-test for comparing three or more means?

A)The populations from which the samples were obtained must be normally distributed.
B)The samples must be independent of each other.
C)The sample sizes must be equal.
D)The variances of the populations must be equal.

Question 19

To compare 7 means, which of the following techniques would be applicable?

A)Analysis of Variance
B)ANOVA
C)Both (A) and (B)
D)Neither (A) nor (B)

Question 20

A researcher can use the Scheffé or the Tukey test to determine where the difference in the means lies
once the null hypothesis for the F-test has been rejected.

Question 21

A vending machine company wants to check three of its machines to determine if they are properly
dispensing 12 ounces of coffee.The data are given below.
What is the within-group variance for the three coffee machines?

A)0.017
B)0.0136
C)0.13
D)0.029

Question 22

A researcher is comparing three groups of the same size.The sample mean of the first group is 12, the sample mean of the second group is 16, and the sample mean of the third group is 20.If the Scheffé F-test
Value for comparing group 1 with group 2 is 7.4, then the Scheffé F-test value for comparing group 2 with
Group 3 will be:

A)3.7
B)7.4
C)14.8
D)Cannot be determined with the information given

Question 23

Complete the formula for the Tukey test: q =

A)
B)
C)
D)

Question 24

Is there a significant difference between the means for vending machines A, B, and C?

A)Yes, there is a significant difference between the means.
B)No, there is no significant difference between the means.
C)The F-test cannot be used to answer whether or not there is a significant difference between the means.
D)The Scheffé test needs to be performed in order to determine whether or not there is a significant difference between the means.

Question 25

A researcher calculated the ANOVA summary table for an experiment, but accidentally spilled grape juice over the first line of the output.From the data below, calculate the F test
Value.

A)F = 0.91
B)F = 1.28
C)F = 2.01
D)F = 2.74

Question 26

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected; in other words, the 4 population means are not all equal.We should expect that:

A)all 6 of the comparisons of means ould be significant using the Scheffé test.
B)at least 4 of the comparisons of mean ould be significant using the Scheffé test.
C)at least 2 of the comparisons of means ould be significant using the Scheffé test.
D)at least 1 of the comparisons of mean ould be significant using the Scheffé test.

Question 27

In the Scheffé test, if = 6 for a group of size n2 = 7, = 14 for a group of size n4 = 7, and the within-group variance = 14, then the FS test value for comparing these two groups is equal to:

A)-2.00
B)16.00
C)4.57
D)10.29

Question 28

A vending machine company wants to check three of its machines to determine if they are properly
dispensing 12 ounces of coffee.The data are given below.
What is the grand mean for the data given above?

A)12.08
B)11.96
C)11.82
D)11.85

Question 29

A researcher is comparing 3 groups to test if they have the same means.There are 51 data values altogether.The degrees of freedom for the Between (dfB) and the degrees of freedom for the Within
(dfW) are:

A)dfB = 48, dfW = 50
B)dfB = 2, dfW = 48
C)dfB = 2, dfW = 50
D)dfB = 3, dfW = 50

Question 30

In an Analysis of Variance Summary Table, if the Mean Square Between = 33 and the Mean Square Within = 29, then the null hypothesis of the groups having the same mean is

A)Accepted because
B)Rejected because
C)Cannot be determined without knowing the Sums of Squares (between and within)
D)Cannot be determined without knowing the Degrees of Freedom (between and within)

Question 31

A researcher is comparing three groups of the same size.The sample mean of the first group is 12, the sample mean of the second group is 14, and the sample mean of the third group is 16.If the Tukey q-test
Value for comparing group 1 with group 2 is 2.6, then the Tukey q-test value for comparing group 2 with
Group 3 will be:

A)2.6
B)5.2
C)10.4
D)Cannot be determined with the information given

Question 32

A portion of an ANOVA summary table is shown below. The critical value for this problem should have dfN (degrees of freedom in the numerator) ___ and dfD
(degrees of freedom in the denominator) of ___:

A)dfN = 2, dfD = 27
B)dfN = 27, dfD = 2
C)dfN = 22, dfD = 39
D)dfN = 39, dfD = 22

Question 33

In the Tukey test, if = 6 for a group of siz = 7, = 14 for a group of size = 7, and the within-group variance = 28, then the q test value for comparing group 2 to group 4 is:

A)-0.01
B)-0.29
C)-1.51
D)-4.00

Question 34

A vending machine company wants to check three of its machines to determine if they are properly
dispensing 12 ounces of coffee.The data are given below.
What is the between-group variance for the three coffee machines?

A)0.017
B)0.098
C)0.057
D)0.086

Question 35

If a researcher wanted to compare the F-value with the critical value for F at , what would that critical F be?

A)3.70
B)3.08
C)3.89
D)3.73

Question 36

A vending machine company wants to check three of its machines to determine if they are properly
dispensing 12 ounces of coffee.The data are given below.
What is the F-value for the coffee machines?

A)2.25
B)5.06
C)6.62
D)4.86

Question 37

In an Analysis of Variance Summary Table, if the Mean Square Between = 16 and the Mean Square Within = 27, then the null hypothesis of the groups having the same mean is

A)Accepted because
B)Rejected because
C)Cannot be determined without knowing the Sums of Squares (between and within)
D)Cannot be determined without knowing the Degrees of Freedom (between and within)

Question 38

What would the Tukey test value be for comparing the means of machine B and machine C at ?

A)-1.61
B)-1.17
C)-7.72
D)-4.46

Question 39

The between-group variance and the error variance are sometimes referred to as:

A)ANOVA summary table
B)mean squares
C)main effects
D)interaction effects

Question 40

A portion of an ANOVA summary table is shown below.What is the F-test value?

A)0.15
B)0.47
C)6.59
D)2.13

Question 41

The degrees of freedom for the interaction between diet and gender are:

A)1
B)2
C)3
D)4

Question 42

When there is one independent variable, the analysis of variance is called a __________ ANOVA.
________________________________________

Question 43

A Two-Way ANOVA Summary Table is shown below.
The critical value for the F test using d.f.N.= 2, and d.f.D = 36 is 3.26.Then:

A)Only the null hypothesis concerning Factor A should be rejected
B)Only the null hypothesis concerning Factor B should be rejected
C)Only the null hypothesis concerning Factor A and the Interaction (AxB) effect should be rejected
D)All of the null hypotheses should be accepted

Question 44

an English course differs depending upon the time of day that the course is being offered.
Is there a significant difference between the mean attendance for the classes given ?

A)Yes, there is a significant difference between the means.
B)No, there is no significant difference between the means.
C)The F-test cannot be used to answer whether or not there is a significant difference between the means.
D)The Scheffé test needs to be performed in order to find whether or not there is a significant difference between the means.

Question 45

A researcher is performing a two-way ANOVA using two factors.The first factor has 4 levels and the second factor also has 4 levels.In the ANOVA Summary Table, the degrees of freedom for the first and
Second factors will be:

A)4 d.f.for the first factor and 4 d.f.for the second factor
B)3 d.f.for the first factor and 3 d.f.for the second factor
C)5 d.f.for the first factor and 5 d.f.for the second factor
D)16 d.f.for the first factor and 16 d.f.for the second factor

Question 46

A researcher is comparing three groups of the same size.The sample mean of the first group is 11, the sample mean of the second group is 13, and the sample mean of the third group is 15.If the Tukey q-test
Value for comparing group 1 with group 2 is -2.1, then the Tukey q-test value for comparing group 1 with
Group 3 will be:

A)-2.1
B)-4.2
C)-8.4
D)Cannot be determined with the information given

Question 47

The figure below is an example of what type of interaction?

A)disordinal interaction
B)ordinal interaction
C)polar interaction
D)cardinal interaction

Question 48

The figure below is an example of what type of interaction?

A)disordinal interaction
B)ordinal interaction
C)There is no interaction because the lines do not cross.

Question 49

The degrees of freedom for error are:

A)14
B)24
C)29
D)30

Question 50

If the figure below is the result of a two-way ANOVA, which of the following statements would apply?

A)There is no significant interaction effect.
B)There is a significant interaction effect.
C)The main effects should not be interpreted without considering the interaction effect.
D)The graph does not give any indication of whether or not there is an interaction effect.An experiment has been designed to study the effectiveness of a new diet on weight gain for use with anorexic individuals.The diet is available in both a solid and a liquid form.The two new diets and a standard control diet were randomly assigned to 15 women and 15 men.Thus,
Each of the 3 diets was assigned to 5 men and 5 women.The weight gains attained after 12 weeks were
Recorded for each of the participants and the corresponding averages are summarized in the following
Table.
ANOVA

Question 51

A Two-Way ANOVA Summary Table is shown below.
The critical value for the F test using d.f.N.= 2, and d.f.D = 45 is 3.20.Then:

A)The null hypothesis concerning Factor A should be rejected
B)The null hypothesis concerning Factor B should be rejected
C)The null hypothesis concerning Factor A and the Interaction (AxB) effect should be rejected
D)All of the null hypotheses should be accepted

Question 52

A researcher is performing a two-way ANOVA using two factors.The first factor has 4 levels and the second factor has 10 levels.In the ANOVA Summary Table, the degrees of freedom for the interaction
Between the first and second factors will be:

A)27
B)30
C)36
D)40

Question 53

This experiment is best described as a(n):

A)randomized survey.
B)completely randomized design.
C)factorial treatment design carried out in a completely randomized experimental design.
D)observational study.

Question 54

an English course differs depending upon the time of day that the course is being offered.
Given the between-group variance (determined in the previous question) and the fact that the F-test value is 6.00, what is the within-group variance for the three class times?

A)23.40
B)46.80
C)3.90
D)7.18

Question 55

an English course differs depending upon the time of day that the course is being offered.
What is the between-group variance for the data given above.

A)23.40
B)46.80
C)3.90
D)7.18

Question 56

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected; in other words, the 7 population means (from samples of the same size) are not all equal.We should expect that:

A)all 21 of the comparisons of means ould be significant using the Tukey test.
B)at least 7 of the comparisons of mean ould be significant using the Tukey test.
C)at least 4 of the comparisons of means ould be significant using the Tukey test.
D)at least 1 of the comparisons of means ould be significant using the Tukey test.

Question 57

A Two-Way ANOVA Summary Table is shown below. The critical value for the F-test using , d.f.N.= 2, and d.f.D = 27 is 3.35.Then:

A)Only the null hypothesis concerning Factor A should be rejected
B)Only the null hypothesis concerning Factor B should be rejected
C)Only the null hypothesis concerning Factor A and the Interaction (AxB) effect should be rejected
D)All of the null hypotheses should be accepted

Question 58

The total number of degrees of freedom for a two-way ANOVA is equal to one less than the total number
of samples.

Question 59

A researcher is comparing three groups of the same size.The sample mean of the first group is 14, the sample mean of the second group is 17, and the sample mean of the third group is 20.If the Scheffé F-test
Value for comparing group 1 with group 2 is 5.4, then the Scheffé F-test value for comparing group 1 with
Group 3 will be:

A)5.4
B)10.8
C)21.6
D)Cannot be determined with the information given

Question 60

Which of the following assumptions does not apply to the two-way ANOVA?

A)The populations from which the samples are obtained must be normally or approximately normally distributed.
B)The samples must be independent of each other.
C)The means of the populations must be equal.
D)The groups must be equal in sample size.

Question 61

The ______________ test can be used even if the sample sizes are not equal.
________________________________________

Question 62

In a two-way ANOVA design, variable A has four levels and variable B has two levels.There are eight
data values in each cell.What is the d.f.N.for factor B?

Question 63

Two methods for teaching Introductory Statistics are to be compared.Ten students are randomly assigned
to one of two groups and their midterm averages are recorded.Analyze the data using a two-way
ANOVA at α = 0.05.

Question 64

The manager of a grocery store wants to determine if there is a difference in the amount of money that
the store brings in at different times of day for different days of the week.The amount of money spent
by five randomly selected customers is listed below.Analyze the data using a two-way ANOVA at α =0.05.

Question 65

Qualitative independent variables can also be called ______________.
________________________________________

Question 66

If there is no difference in the means, the _____________ variance will be approximately equal to the
within-group variance.
________________________________________

Question 67

A researcher wants to investigate whether there is a significant difference in the average age of
instructors, assistant professors, associate professors, and full professors at a university.The faculty
members were selected at random and their ages were recorded.Use the collected data to complete the ANOVA chart given below.

Question 68

The ________________ variance is made by computing the variance using all the data and is not affected
by differences in the means.
________________________________________

Question 69

A diet centre wants to test three different methods for losing weight to determine if the average
weight loss (reported in pounds/week) for each method is the same.The results for the three methods
are given below.Assuming that there is a significant difference between the three methods, use the
Tukey test to determine if there is a significant difference between each pair of methods.Let 0.05.

Question 70

The ____________ test can be used after the analysis of variance has been completed to make pairwise
comparisons between means when groups have the same sample size.
________________________________________

Question 71

Each independent variable investigated could have two or more different treatments or
______________.
________________________________________