Deck 8: Analysis of Variance

Question 1

The formula for dfwithin is:

A)
B)
C)
D)

Answer 1

Question 2

In an analysis of variance with three groups, the research hypothesis is:

A)
B)
C)
D)

Answer 2

Question 3

The question below refers to the following situation:
In an analysis of variance with 4 groups, each containing 12 respondents:
Calculate the within-group degrees of freedom.

A)60
B)3
C)44
D)45

Answer 3

44

Question 4

Using the F ratio requires:

A)interval data.
B)ordinal data.
C)nominal data.
D)all of the above.

Question 5

The larger the value of the calculated F ratio:

A)the more likely an observed difference is due to chance.
B)the larger the mean square within groups is compared to the mean square between groups.
C)the less likely an observed difference is due to chance.
D)the larger the sum of squares within groups is compared to the sum of squares between groups.

Question 6

The distance or deviation of raw scores from their group mean is known as:

A)between-group variation.
B)variation within groups.
C)total variation.
D)none of the above

Question 7

The formula for the total sum of squares, SStotal , is:

A)
B)
C)
D)

Question 8

The sum of squares is the method for measuring variation:

A)within groups.
B)between groups.
C)for the total sample.
D)all of the above

Question 9

In an analysis of variance with three groups, the null hypothesis states:

A)
B)
C)
D)

Question 10

Which of the following is a requirement for computing the F ratio?

A)comparing two or more independent means
B)a normal distribution
C)random sampling
D)all of the above

Question 11

The normality assumption required for using an F ratio holds if

A)we draw small enough samples from each group.
B)the characteristic we are comparing between and within groups is biased.
C)we draw large enough samples from each group.
D)none of the above.

Question 12

The question below refers to the following situation:
In an analysis of variance with 4 groups, each containing 12 respondents:
Calculate the between-group degrees of freedom.

A)20
B)44
C)3
D)47

Question 13

The distance or deviation of group means from one another is known as:

A)variation between groups.
B)within-group variation.
C)total variation.
D)none of the above

Question 14

The formula for dfbetween is:

A)
B)
C)
D)

Question 15

Which is NOT true of an analysis of variance?

A)The population variances are all assumed to be equal.
B)All samples must be selected randomly.
C)All data must be ordinal level data.
D )All of the above are untrue.

Question 16

The mean square is:

A)calculated by dividing the sum of squares within groups by the degrees of freedom within groups.
B)calculated by dividing the sum of squares between groups by the degrees of freedom between groups.
C)a method for assessing variation in conjunction with the sums of squares measures.
D)all of the above

Question 17

The F ratio is calculated by:

A)dividing the degrees of freedom within by degrees of freedom between.
B)dividing the mean square between by the mean square within.
C)dividing the mean square within by the mean square between.
D)none of the above

Question 18

The question below refers to the following situation:
In an analysis of variance with 4 groups, each containing 12 respondents:
Calculate the total degrees of freedom.

A)47
B)60
C)48
D)42

Question 19

In a one-way analysis of variance, the total variation is divisible into __________
Component(s).

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

Question 20

We use the analysis of variance rather than the t ratio when more than two groups are Involved because:

A)it is less time consuming to make the necessary calculations.
B)it decreases the likelihood of making a Type 1 error.
C)the more statistical tests conducted, the more likely sampling error may cause statistically Significant findings.
D)all of the above

Question 21

The question below refers to the following situation:
A researcher is interested in the effects of family size on leisure time. He questions 16 families on the number of "free hours per week." He polls 4 families at each size, from 1 to 4 children. The data are as follows:
Calculate the total sum of squares.

Question 22

The question below refers to the following situation:
A social researcher is interested in studying the relationship between religious affiliation
and years of education. Here is the data she is working with:
Calculate the total sum of squares.

Question 23

The __________ sum of squares is defined as

Question 24

Analysis of Variance is generally used to compare three or fewer groups.

Question 25

The question below refers to the following situation:
A social researcher is interested in studying the relationship between religious affiliation and years of education. Here is the data she is working with:
Calculate the mean square within groups (MSwithin).

Question 26

In ANOVA, the dependent variable is measured at the interval level.

Question 27

Analysis of variance should only be used on the __________ level of data.

Question 28

The question below refers to the following situation:
A social researcher is interested in studying the relationship between religious affiliation and years of education. Here is the data she is working with:
What are your conclusions about the null hypothesis?

Question 29

The __________ sum of squares is defined as

Question 30

The question below refers to the following situation:
A social researcher is interested in studying the relationship between religious affiliation and years of education. Here is the data she is working with:
Calculate the within-group sum of squares.

Question 31

Analysis of variance should be used on __________ or more independent means.

Question 32

In Analysis of Variance if the F ratio is larger than the critical value the groups are the Same in the population.

Question 33

The question below refers to the following situation:
A social researcher is interested in studying the relationship between religious affiliation and years of education. Here is the data she is working with:
Calculate the mean square between groups (MSbetween).

Question 34

In Analysis of Variance, the dependent variable is measured at the nominal level.

Question 35

The __________ sum of squares is defined as

Question 36

The question below refers to the following situation:
A social researcher is interested in studying the relationship between religious affiliation and years of education. Here is the data she is working with:
Calculate the between-group sum of squares.

Question 37

Groups in an analysis of variance are typically formed based on a __________ measure.

Question 38

The question below refers to the following situation:
A social researcher is interested in studying the relationship between religious affiliation and years of education. Here is the data she is working with:
Calculate the F ratio.

Question 39

Analysis of variance yields a(n) __________ whose numerator represents variation between
groups being compared, and whose denominator contains an estimate of variation within
those groups.

Question 40

The question below refers to the following situation:
A social researcher is interested in studying the relationship between religious affiliation and years of education. Here is the data she is working with:
Are your results statistically significant, and if so, at what level?

Question 41

The question below refers to the following situation:
A valet parking attendant is interested in whether daytime temperature affects the size of
tips. To study this question, she records the size of the tip given by her customers on 3
extremely hot summer days, 3 warm spring days, and 3 cold winter days. Complete an
analysis of variance to test the differences between mean tips with significance (α = .05), to
determine if the groups differ from each other.
Calculate mean square within.

Question 42

The question below refers to the following situation:
A valet parking attendant is interested in whether daytime temperature affects the size of
tips. To study this question, she records the size of the tip given by her customers on 3
extremely hot summer days, 3 warm spring days, and 3 cold winter days. Complete an
analysis of variance to test the differences between mean tips with significance (α = .05), to
determine if the groups differ from each other.
Calculate F.

Question 43

The question below refers to the following situation:
A valet parking attendant is interested in whether daytime temperature affects the size of tips. To study this question, she records the size of the tip given by her customers on 3 extremely hot summer days, 3 warm spring days, and 3 cold winter days. Complete an analysis of variance to test the differences between mean tips with significance (α = .05), to determine if the groups differ from each other.
What are your conclusions about the null hypothesis?

Question 44

The question below refers to the following situation:
A valet parking attendant is interested in whether daytime temperature affects the size of
tips. To study this question, she records the size of the tip given by her customers on 3
extremely hot summer days, 3 warm spring days, and 3 cold winter days. Complete an
analysis of variance to test the differences between mean tips with significance (α = .05), to
determine if the groups differ from each other.
Calculate mean square between.

Question 45

The question below refers to the following situation:
A valet parking attendant is interested in whether daytime temperature affects the size of
tips. To study this question, she records the size of the tip given by her customers on 3
extremely hot summer days, 3 warm spring days, and 3 cold winter days. Complete an
analysis of variance to test the differences between mean tips with significance (α = .05), to
determine if the groups differ from each other.
Calculate the within-group sum of squares.

Question 46

The question below refers to the following situation:
A valet parking attendant is interested in whether daytime temperature affects the size of tips. To study this question, she records the size of the tip given by her customers on 3 extremely hot summer days, 3 warm spring days, and 3 cold winter days. Complete an analysis of variance to test the differences between mean tips with significance (α = .05), to determine if the groups differ from each other.
Calculate the between-group sum of squares.

Question 47

The question below refers to the following situation:
A valet parking attendant is interested in whether daytime temperature affects the size of tips. To study this question, she records the size of the tip given by her customers on 3 extremely hot summer days, 3 warm spring days, and 3 cold winter days. Complete an analysis of variance to test the differences between mean tips with significance (α = .05), to determine if the groups differ from each other.
What is the research hypothesis?

Question 48

The question below refers to the following situation:
A valet parking attendant is interested in whether daytime temperature affects the size of tips. To study this question, she records the size of the tip given by her customers on 3 extremely hot summer days, 3 warm spring days, and 3 cold winter days. Complete an analysis of variance to test the differences between mean tips with significance (α = .05), to determine if the groups differ from each other.
Calculate the total sum of squares.

Question 49

The question below refers to the following situation:
A valet parking attendant is interested in whether daytime temperature affects the size of tips. To study this question, she records the size of the tip given by her customers on 3 extremely hot summer days, 3 warm spring days, and 3 cold winter days. Complete an analysis of variance to test the differences between mean tips with significance (α = .05), to determine if the groups differ from each other.
Are the results statistically significant and, if so, at what level?

Question 50

The question below refers to the following situation:
A researcher is interested in the effects of family size on leisure time. He questions 16 families on the number of "free hours per week." He polls 4 families at each size, from 1 to 4 children. The data are as follows:
Calculate the mean square between groups.

Question 51

The question below refers to the following situation:
A valet parking attendant is interested in whether daytime temperature affects the size of tips. To study this question, she records the size of the tip given by her customers on 3 extremely hot summer days, 3 warm spring days, and 3 cold winter days. Complete an analysis of variance to test the differences between mean tips with significance (α = .05), to determine if the groups differ from each other.
What is the null hypothesis?