Deck 9: Analysis of Variance

Question 1

If the sum of squares between is equal to 20 and the sum of squares within is equal to 10, what is the value of the total sum of squares?

A) 10
B) 20
C) 30
D) 200

Answer 1

30

Question 2

If the sum of squares between is equal to 20 and the sum of squares within is equal to 10, what is the value of eta²?

A) .2
B) .46
C) .67
D) 1.5

Answer 2

.67

Question 3

If the sum of squares between is equal to 7 and the sum of squares within is equal to 3, what is the value of the total sum of squares?

A) 7
B) 10
C) 13
D) 21

Answer 3

10

Question 4

If the sum of squares between is equal to 7 and the sum of squares within is equal to 3, what is the value of eta²?

A) .2
B) .43
C) .70
D) 1.4

Question 5

Eta² should be used when the independent variable is categorical and the dependent variable is -----------.

A) nominal
B) ordinal
C) categorical
D) interval/ratio

Question 6

What is the strength of the association represented by an eta² of .87?

A) weak
B) moderate
C) strong
D) the measure does not reflect strength

Question 7

Use the table below to answer questions :
Number of Years Respondent Worked across Employers

$\begin{array}{l}\text { } \\\begin{array}{|l|l|ll|} \hline \text {Employer A ~~~~ ~~~~~~ } & \text { Employer B ~~~ ~~~~~~ ~~~~ } & \text { Employer C ~~~~ ~~~~ } \\\hline \text { 3 } & 5 & 6 \\\hline \text { 1 } & 2 & 4 \\\hline \text {2 } & 1 & 5 \\\hline\end{array}\end{array}$



-Determine the number of degrees of freedom between groups.

A) 1
B) 2
C) 3
D) 6

Question 8

Use the table below to answer questions :
Number of Years Respondent Worked across Employers

$\begin{array}{l}\text { } \\\begin{array}{|l|l|ll|} \hline \text {Employer A ~~~~ ~~~~~~ } & \text { Employer B ~~~ ~~~~~~ ~~~~ } & \text { Employer C ~~~~ ~~~~ } \\\hline \text { 3 } & 5 & 6 \\\hline \text { 1 } & 2 & 4 \\\hline \text {2 } & 1 & 5 \\\hline\end{array}\end{array}$



-Determine the number of degrees of freedom among the subgroups.

A) 2
B) 3
C) 6
D) 12

Question 9

Use the table below to answer questions :
Number of Years Respondent Worked across Employers

$\begin{array}{l}\text { } \\\begin{array}{|l|l|ll|} \hline \text {Employer A ~~~~ ~~~~~~ } & \text { Employer B ~~~ ~~~~~~ ~~~~ } & \text { Employer C ~~~~ ~~~~ } \\\hline \text { 3 } & 5 & 6 \\\hline \text { 1 } & 2 & 4 \\\hline \text {2 } & 1 & 5 \\\hline\end{array}\end{array}$



-What is the value of the total sum of squares (SST)?

A) 3.22
B) 4.93
C) 27.55
D) 32.14

Question 10

Use the table below to answer questions :
Number of Years Respondent Worked across Employers

$\begin{array}{l}\text { } \\\begin{array}{|l|l|ll|} \hline \text {Employer A ~~~~ ~~~~~~ } & \text { Employer B ~~~ ~~~~~~ ~~~~ } & \text { Employer C ~~~~ ~~~~ } \\\hline \text { 3 } & 5 & 6 \\\hline \text { 1 } & 2 & 4 \\\hline \text {2 } & 1 & 5 \\\hline\end{array}\end{array}$



-What is the value of the within-group sum of squares (SSW)?

A) 8.67
B) 12.67
C) 22.61
D) 32.14

Question 11

Use the table below to answer questions :
Number of Years Respondent Worked across Employers

$\begin{array}{l}\text { } \\\begin{array}{|l|l|ll|} \hline \text {Employer A ~~~~ ~~~~~~ } & \text { Employer B ~~~ ~~~~~~ ~~~~ } & \text { Employer C ~~~~ ~~~~ } \\\hline \text { 3 } & 5 & 6 \\\hline \text { 1 } & 2 & 4 \\\hline \text {2 } & 1 & 5 \\\hline\end{array}\end{array}$



-What is the value of the between-group sum of squares (SSB)?

A) 8.67
B) 12.67
C) 14.88
D) 22.61

Question 12

Use the table below to answer questions :
Number of Years Respondent Worked across Employers

$\begin{array}{l}\text { } \\\begin{array}{|l|l|ll|} \hline \text {Employer A ~~~~ ~~~~~~ } & \text { Employer B ~~~ ~~~~~~ ~~~~ } & \text { Employer C ~~~~ ~~~~ } \\\hline \text { 3 } & 5 & 6 \\\hline \text { 1 } & 2 & 4 \\\hline \text {2 } & 1 & 5 \\\hline\end{array}\end{array}$



-What is the value of the mean square between populations?

A) 7.44
B) 8.67
C) 14.88
D) 22.61

Question 13

Use the table below to answer questions :
Number of Years Respondent Worked across Employers

$\begin{array}{l}\text { } \\\begin{array}{|l|l|ll|} \hline \text {Employer A ~~~~ ~~~~~~ } & \text { Employer B ~~~ ~~~~~~ ~~~~ } & \text { Employer C ~~~~ ~~~~ } \\\hline \text { 3 } & 5 & 6 \\\hline \text { 1 } & 2 & 4 \\\hline \text {2 } & 1 & 5 \\\hline\end{array}\end{array}$



-What is the value of the mean square within populations?

A) 2.11
B) 7.44
C) 14.88
D) 22.61

Question 14

Use the table below to answer questions :
Number of Years Respondent Worked across Employers

$\begin{array}{l}\text { } \\\begin{array}{|l|l|ll|} \hline \text {Employer A ~~~~ ~~~~~~ } & \text { Employer B ~~~ ~~~~~~ ~~~~ } & \text { Employer C ~~~~ ~~~~ } \\\hline \text { 3 } & 5 & 6 \\\hline \text { 1 } & 2 & 4 \\\hline \text {2 } & 1 & 5 \\\hline\end{array}\end{array}$



-What is the value of the f-ratio?

A) 1.06
B) 3.52
C) 9.23
D) 14.88

Question 15

Use the table below to answer questions :
Number of Years Respondent Worked across Employers

$\begin{array}{l}\text { } \\\begin{array}{|l|l|ll|} \hline \text {Employer A ~~~~ ~~~~~~ } & \text { Employer B ~~~ ~~~~~~ ~~~~ } & \text { Employer C ~~~~ ~~~~ } \\\hline \text { 3 } & 5 & 6 \\\hline \text { 1 } & 2 & 4 \\\hline \text {2 } & 1 & 5 \\\hline\end{array}\end{array}$



-Is there a statistically significant difference among the means of these groups?

A) no
B) yes
C) there is not enough information to determine

Question 16

Use the table below to answer questions :
Number of Years Respondent Worked across Employers

$\begin{array}{l}\text { } \\\begin{array}{|l|l|ll|} \hline \text {Employer A ~~~~ ~~~~~~ } & \text { Employer B ~~~ ~~~~~~ ~~~~ } & \text { Employer C ~~~~ ~~~~ } \\\hline \text { 3 } & 5 & 6 \\\hline \text { 1 } & 2 & 4 \\\hline \text {2 } & 1 & 5 \\\hline\end{array}\end{array}$



-What is the value of eta²?

A) .2
B) .43
C) .54
D) .72

Question 17

Use the table below to answer questions :

$\begin{array}{l}\text { Age Respondent Across Race } \\\begin{array}{|l|l|l|ll|} \hline \text { } & \text { Sum of Squares } & \text { ~~~ ~~ df ~~~~ ~~~~ } & \text { Mean Square } \\ \text { } \\\hline \text { Between Groups } & 53652.022 & 2 &26826.011 & \\ \text { Within Groups } & 1228151.9 & 4489 & 273.591 & \\ \text { Total } & 1281803.9 & 4491 & & \\\hline\end{array}\end{array}$




-What is the value of the f-ratio?

A) .02
B) .27
C) 98.05
D) 273.59

Question 18

Use the table below to answer questions :

$\begin{array}{l}\text { Age Respondent Across Race } \\\begin{array}{|l|l|l|ll|} \hline \text { } & \text { Sum of Squares } & \text { ~~~ ~~ df ~~~~ ~~~~ } & \text { Mean Square } \\ \text { } \\\hline \text { Between Groups } & 53652.022 & 2 &26826.011 & \\ \text { Within Groups } & 1228151.9 & 4489 & 273.591 & \\ \text { Total } & 1281803.9 & 4491 & & \\\hline\end{array}\end{array}$




-Are the differences across categories statistically significant?

A) no
B) yes
C) there is not enough information to determine

Question 19

Use the table below to answer questions :

$\begin{array}{l}\text { ~~~ ~~ ~~~ ~~ ~~~ ~~ ~~~ ~~ ~~~ ~~ ~~~ ~~ ~~~ ~ ~~~ ~~ ~~~ ~~ ~~~ ~~~ ~~~ ~~ ~~~ ~~ ~~~ ~~ANOVA } \\ \text { } \\ \text { } \\ \begin{array}{|l|l|l|ll|} \hline \text { } & \text { Sum of Squares } & \text { ~~~ ~~ df ~~~~ ~~~~ } & \text { Mean Square } \\ \text { } \\\hline \text { Between Groups } & 67.078 & 1 & 67.078 & \\ \text { Within Groups } &566828.73 & 1933 & 293.238 & \\ \text { Total } & 566895.81 & 1934 & & \\\hline\end{array}\end{array}$




-What is the value of the f-ratio?

A) .001
B) .229
C) .293
D) 67.08

Question 20

Use the table below to answer questions :

$\begin{array}{l}\text { ~~~ ~~ ~~~ ~~ ~~~ ~~ ~~~ ~~ ~~~ ~~ ~~~ ~~ ~~~ ~ ~~~ ~~ ~~~ ~~ ~~~ ~~~ ~~~ ~~ ~~~ ~~ ~~~ ~~ANOVA } \\ \text { } \\ \text { } \\ \begin{array}{|l|l|l|ll|} \hline \text { } & \text { Sum of Squares } & \text { ~~~ ~~ df ~~~~ ~~~~ } & \text { Mean Square } \\ \text { } \\\hline \text { Between Groups } & 67.078 & 1 & 67.078 & \\ \text { Within Groups } &566828.73 & 1933 & 293.238 & \\ \text { Total } & 566895.81 & 1934 & & \\\hline\end{array}\end{array}$




-Are the differences across categories statistically significant?

A) no
B) yes
C) there is not enough information to determine

Question 21

ANOVA is only useful when comparing two means.

Question 22

Within-group sum of squares is the amount of variation that exists for all cases in a sample relative to their sub-group means.

Question 23

Within-group sum of squares is the amount of variation that exists for all cases in a sample relative to the overall mean.

Question 24

Eta² should be used when the independent variable is interval/ratio and the dependent variable is categorical.

Question 25

When should ANOVA be used?

Question 26

How does ANOVA improve upon t-tests?

Question 27

Use the table below to answer the following questions:

$\begin{array}{l}\text { Hypothetical Data : Attitudes across Region } \\\begin{array}{|l|l|l|ll|} \hline \text {North ~~ ~~ ~~~~~~~ ~~~~~~ ~~~~~} & \text { East ~~~ ~~~~~~~ ~ ~~~~~~ ~~~~ } & \text { South ~~~~ ~~~ ~~~~~~~ ~~ } & \text { ~ ~~~~~~~ ~ ~~~~~~~ West } \\ \hline \text { 5 } & 8 & 10 & 4 & \\\hline \text { 4 } & 6 & 6 & 6 & \\\hline \text { 3 } & 7 & 8 & 2 & \\\hline\end{array}\end{array}$



a.Determine the number of degrees of freedom between groups.
b.Determine the number of degrees of freedom among the subgroups.
c.What is the value of thetotal sum of squares (SST)?
d.What is the value of the within-group sum of squares (SSW)?
e.What is the value of the between-group sum of squares (SSB)?
f.What is the value of the mean square between populations?
g.What is the value of the mean square within populations?
h.What is the value of the f-ratio?
i.Is there a statistically significant difference among the means of these groups?
j.What is the value of Eta²?
k.oes Eta² offer any evidence that attitudes areassociated with region? Explain.