Deck 12: Analysis of Variance

Question 1

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

Answer 1

within-group

Question 2

In an Analysis of Variance Summary Table, if the Mean Square Between = 13 and the Mean Square Within = 21, then the null hypothesis of the groups having the same mean is

A) acepted because 13 < 21.
B) rejected because 13 < 21.
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).

Answer 2

A

Question 3

In an Analysis of Variance Summary Table, if the Mean Square Between = 34 and the Mean Square Within = 24, then the null hypothesis of the groups having the same mean is

A) accepted because 34 > 24.
B) rejected because 34 > 24.
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).

Answer 3

D

Question 4

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

Question 5

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

Question 6

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 = 3, dfD = 26
B) dfN = 26, dfD = 3
C) dfN = 19, dfD = 34
D) dfN = 34, dfD = 19

Question 7

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 8

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

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

Question 9

Complete the formula for the sum of squares between groups:

A)
B)
C)
D)

Question 10

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 = 0.87
B) F = 1.33
C) F = 1.81
D) F = 2.29

Question 11

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

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

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

Question 14

ANOVA is an abbreviation for the following term:

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

Question 15

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

Question 16

A portion of an ANOVA summary table is shown below. Calculate the F test value.

A) 0.16
B) 0.48
C) 6.20
D) 27.24

Question 17

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

Question 18

The value of the F-distribution can be negative.

Question 19

If there are 4 means to be compared, then how many possible different comparisons (such as compared to ) are there altogether?

A) 4
B) 6
C) 12
D) 16

Question 20

A researcher is comparing 6 groups to test if they have the same means. There are 53 data values altogether. The degrees of freedom for the Between (dfB) and the degrees of freedom for the Within (dfW) are

A) dfB = 47, dfW = 52
B) dfB = 5, dfW = 47
C) dfB = 5, dfW = 52
D) dfB = 6, dfW = 52

Question 21

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, V, are needed.

Question 22

A researcher is performing a two-way ANOVA using two factors. The first factor has 5 levels and the second factor has 9 levels. In the ANOVA Summary Table, the degrees of freedom for the interaction between the first and second factors will be

A) 32
B) 36
C) 40
D) 45

Question 23

The data consist of the weights in ounces of three different types of digital camera. Use to see if the means are equal.

Question 24

A diet center wanted 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 tabulated below. Given 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 .

Question 25

In the Tukey test, if = 8 for a group size = 7, = 13 for a group size = 7, and the within-group variance = 21, then the q test value for comparing group 2 to group 4 is

A) -0.01
B) -0.24
C) -1.09
D) -2.89

Question 26

Independent variables can also be called ______________.

Question 27

The ______________ test to detect where the difference is among the means can be used even if the sample sizes are not equal.

Question 28

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 7 population means are not all equal. We should expect that

A) all 21 of the comparisons of means versus would be significant using the Scheffe test.
B) at least 7 of the comparisons of means versus would be significant using the Scheffe test.
C) at least 4 of the comparisons of means versus would be significant using the Scheffe test.
D) at least 1 of the comparisons of means versus would be significant using the Scheffe test.

Question 29

Use the following to answer questions :
A vending machine company wants to check three of its machines to determine if they are properly dispensing 12 ounces of coffee. Their data is given below.
Compute the test value for the coffee machines.

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

Question 30

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

A) The populations from which the samples were 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 31

A researcher is performing a two-way ANOVA using two factors. The first factor has 4 levels and the second factor has 5 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 5 d.f. for the second factor
B) 3 d.f. for the first factor and 4 d.f. for the second factor
C) 5 d.f. for the first factor and 6 d.f. for the second factor
D) 20 d.f. for the first factor and 20 d.f. for the second factor

Question 32

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 33

Use the following to answer question:
The head of the English department wants to determine if the average number of students taking 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 for ?

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.

Question 34

Complete the formula for the Tukey test: q =

A)
B)
C)
D)

Question 35

Use the following to answer questions :
A vending machine company wants to check three of its machines to determine if they are properly dispensing 12 ounces of coffee. Their data is given below.
Is there a significant difference between the vending machines A, B, and C? Use .

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.

Question 36

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 9 population means (from equal sized samples) are not all equal. We should expect that

A) all 36 of the comparisons of means versus would be significant using the Tukey test.
B) at least 9 of the comparisons of means versus would be significant using the Tukey test.
C) at least 5 of the comparisons of means versus would be significant using the Tukey test.
D) at least 1 of the comparisons of means versus would be significant using the Tukey test.

Question 37

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

Question 38

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

Question 39

In the Scheffe test, if = 8 for a group size = 7, = 11 for a group size = 7, and the within-group variance = 14, then the test value for comparing these two groups is equal to

A) -0.75
B) 2.25
C) 0.64
D) 1.44

Question 40

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 41

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.
D) cardinal interaction

Question 42

The figure below is a 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.

Question 43

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 .

Question 44

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

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

Question 45

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 46

A Two-Way ANOVA Summary Table is shown below. The critical value for the F test using = 0.05, 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 (A $\times$ B) effect should be rejected.
D) all of the null hypotheses should be accepted.

Question 47

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 the 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 .

Question 48

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

Question 49

A Two-Way ANOVA Summary Table is shown below. The critical value for the F test using = 0.05, d.f.N. = 2, and d.f.D = 54 is 3.17. 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 50

In 2-way ANOVA, each independent variable investigated could have two or more different treatments or ______________.

Question 51

In 2-way ANOVA, effects of the independent variables are also referred to as the ________________.

Question 52

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 (A $\times$ B) effect should be rejected.
D) all of the null hypotheses should be accepted.

Question 53

A Two-Way ANOVA Summary Table is shown below. The critical value for the F test using = 0.05, 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 54

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.