Question 1

A study examining the heights of single individuals from each of a series of families based on whether the family was vegetarian or not would be analyzed using a random-effects ANOVA.

Accepted Answer

A) True 
 B)False  False

Question 2

Consider the data table shown with values for five individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.
​
 $\begin{array}{c}
\text { Groups }\
\begin{array}{rrrr}
\text { A } & \text { B } & \text { C } & \text { D } \
6 & 7 & 9 & 11 \
8 & 10 & 11 & 14 \
10 & 11 & 12 & 15 \
12 & 12 & 13 & 16 \
14 & 15 & 15 & 19
\end{array}\end{array}$ ​
-To test the significance of the F-ratio value, what degrees of freedom would we use?

Accepted Answer

A)   df = 3 in the numerator, df = 12 in the denominator
B)   df = 3 in the numerator, df = 16 in the denominator
C)   df = 4 in the numerator, df = 12 in the denominator
D)   df = 4 in the numerator, df = 16 in the denominator  B

Question 3

An experimental mistake is always equivalent to either a Type I or Type II error.

Accepted Answer

A) True 
 B)False  False

Question 4

The ANOVA technique requires more than two groups.

Accepted Answer

A) True 
 B)False

Question 5

When studying randomly chosen groups, we don't tend to do which of the following?

Accepted Answer

A)   Create an ANOVA table.
B)   Compare the within-group variance to the between-group variance.
C)   Estimate variance components.
D)   Test a null hypothesis.

Question 6

When using the Tukey-Kramer method, the P-value is exact when the sample sizes in all groups are the same.

Accepted Answer

A) True 
 B)False

Question 7

Based on the ANOVA table shown, what is the $S_{A}^{2}$ value for this data?
?
$\begin{array}{|lcrcc|}
\hline \text { Source of } & \text { Sum of } & & {\text { Mean }} \
\text { variation } & \text { squares } & \text { df } & \text { squares } & \text { F-ratio } \
\text { Groups } & 406 & 7 & 58 & 5.27 \
\text { Error } & 704 & 64 & 11 & \
\text { Total } & 1,110 & 71 & & \
\hline
\end{array}$ ?

Accepted Answer

A)   4.55
B)   4.77
C)   4.99
D)   5.22

Question 8

Consider the data table shown with values for six individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.
​
 $\begin{array}{c}
\text { Groups }\
\begin{array}{rrrr}
\text { A } & \text { B } & \text { C } & \text { D } \
11 & 12 & 11 & 16 \
12 & 13 & 14 & 18 \
14 & 14 & 15 & 19 \
15 & 17 & 16 & 23
\end{array}\end{array}$
-What is the SSerror?

Accepted Answer

A)   64.00
B)   72.00
C)   80.00
D)   88.00

Question 9

Consider the data table shown with values for five individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.
​
 $\begin{array}{c}
\text { Groups }\
\begin{array}{rrrr}
\text { A } & \text { B } & \text { C } & \text { D } \
6 & 7 & 9 & 11 \
8 & 10 & 11 & 14 \
10 & 11 & 12 & 15 \
12 & 12 & 13 & 16 \
14 & 15 & 15 & 19
\end{array}\end{array}$ ​
-What is the SSgroups?

Accepted Answer

A)   45
B)   60
C)   70
D)   85

Question 10

Consider the data table shown with values for five individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.
​
 $\begin{array}{c}
\text { Groups }\
\begin{array}{rrrr}
\text { A } & \text { B } & \text { C } & \text { D } \
6 & 7 & 9 & 11 \
8 & 10 & 11 & 14 \
10 & 11 & 12 & 15 \
12 & 12 & 13 & 16 \
14 & 15 & 15 & 19
\end{array}\end{array}$ ​
-What is the SSerror?

Accepted Answer

A)   108
B)   128
C)   148
D)   168

Question 11

Using the data set shown, calculate all the values you need to complete an ANOVA table.
​
 $\begin{array}{c}
\text { Groups }\
\begin{array}{rrrr}
\text { A } & \text { B } & \text { C } & \text { D } \
14 & 14 & 14 & 15 \
15 & 16 & 17 & 17 \
17 & 17 & 18 & 18 \
18 & 21 & 19 & 22
\end{array}\end{array}$ $\begin{array}{|lcrcc|}
\hline \text { Source of } & \text { Sum of } & & {\text { Mean }} \
\text { variation } & \text { squares } & \text { df } & \text { squares } & \text { F-ratio } \
\text { Groups } & --- & ---  & ---  & --- \
\text { Error } & --- & ---  & --- & \
\text { Total } & ---  &  & \
\hline
\end{array}$ ​

Accepted Answer

The answer of Using the data set shown, calculate all...

Question 12

The repeatability measures the overall similarity of repeat measurements made on the same group.

Accepted Answer

A) True 
 B)False

Question 13

Consider the figure showing the results of a Tukey-Kramer procedure on the means of individuals collected from four different environments. If the bars represent 95% confidence intervals, what letter or combination of letters would the blank have?
​
 ​

Accepted Answer

A)   a
B)   ab
C)   b
D)   c

Question 14

Consider the data table shown with values for six individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.
​
 $\begin{array}{c}
\text { Groups }\
\begin{array}{rrrr}
\text { A } & \text { B } & \text { C } & \text { D } \
11 & 12 & 11 & 16 \
12 & 13 & 14 & 18 \
14 & 14 & 15 & 19 \
15 & 17 & 16 & 23
\end{array}\end{array}$
-What is the error mean square?

Accepted Answer

A)   4.66
B)   5.00
C)   5.33
D)   5.66

Question 15

Which of the following is not an assumption of the ANOVA?

Accepted Answer

A)   The populations exhibit normal distributions.
B)   The populations have equal variances.
C)   The values are randomly chosen from the populations.
D)   The values are randomly chosen from the samples.

Question 16

The ANOVA techniques is robust to violations of its assumptions when sample sizes are large.

Accepted Answer

A) True 
 B)False

Question 17

Planned comparisons are slightly more robust to violations of the assumptions of the ANOVA than the ANOVA they follow.

Accepted Answer

A) True 
 B)False

Question 18

Consider the data table shown with values for six individuals measured in each of four groups (A, B, C, and D). We will conduct an ANOVA analysis of this.
​
 $\begin{array}{c}
\text { Groups }\
\begin{array}{rrrr}
\text { A } & \text { B } & \text { C } & \text { D } \
11 & 12 & 11 & 16 \
12 & 13 & 14 & 18 \
14 & 14 & 15 & 19 \
15 & 17 & 16 & 23
\end{array}\end{array}$
-What are the means of the groups and overall mean?

Accepted Answer

A)   12, 13, 13, 19, and 15
B)   13, 13, 14, 19, and 15
C)   13, 14, 14, 19, and 15
D)   14, 14, 15, 19, and 15

Question 19

Usually for an ANOVA the variances in all the groups should be the same, but when can this assumption be relaxed?

Accepted Answer

A)   The samples are large, the same size, and the variances differ by less than tenfold.
B)   The samples are large, the same size, and the variances differ by less than threefold.
C)   The samples are small, the same size, and the variances differ by less than tenfold.
D)   The samples are small, the same size, and the variances differ by less than threefold.

Question 20

In an ANOVA analysis, the R2 is likely to be larger when the P-value is smaller and vice-versa.

Accepted Answer

A) True 
 B)False

Exam 15: Comparing Means of More Than Two Groups

A study examining the heights of single individuals from each of a series of families based on whether the family was vegetarian or not would be analyzed using a random-effects ANOVA.

An experimental mistake is always equivalent to either a Type I or Type II error.

The ANOVA technique requires more than two groups.

When studying randomly chosen groups, we don't tend to do which of the following?

When using the Tukey-Kramer method, the P-value is exact when the sample sizes in all groups are the same.

The repeatability measures the overall similarity of repeat measurements made on the same group.

Consider the figure showing the results of a Tukey-Kramer procedure on the means of individuals collected from four different environments. If the bars represent 95% confidence intervals, what letter or combination of letters would the blank have?

Which of the following is not an assumption of the ANOVA?

The ANOVA techniques is robust to violations of its assumptions when sample sizes are large.

Planned comparisons are slightly more robust to violations of the assumptions of the ANOVA than the ANOVA they follow.

Usually for an ANOVA the variances in all the groups should be the same, but when can this assumption be relaxed?

In an ANOVA analysis, the R² is likely to be larger when the P-value is smaller and vice-versa.

Exam 15: Comparing Means of More Than Two Groups

A study examining the heights of single individuals from each of a series of families based on whether the family was vegetarian or not would be analyzed using a random-effects ANOVA.

An experimental mistake is always equivalent to either a Type I or Type II error.

The ANOVA technique requires more than two groups.

When studying randomly chosen groups, we don't tend to do which of the following?

When using the Tukey-Kramer method, the P-value is exact when the sample sizes in all groups are the same.

The repeatability measures the overall similarity of repeat measurements made on the same group.

Consider the figure showing the results of a Tukey-Kramer procedure on the means of individuals collected from four different environments. If the bars represent 95% confidence intervals, what letter or combination of letters would the blank have? ​ ​

Which of the following is not an assumption of the ANOVA?

The ANOVA techniques is robust to violations of its assumptions when sample sizes are large.

Planned comparisons are slightly more robust to violations of the assumptions of the ANOVA than the ANOVA they follow.

Usually for an ANOVA the variances in all the groups should be the same, but when can this assumption be relaxed?

In an ANOVA analysis, the R2 is likely to be larger when the P-value is smaller and vice-versa.

Consider the figure showing the results of a Tukey-Kramer procedure on the means of individuals collected from four different environments. If the bars represent 95% confidence intervals, what letter or combination of letters would the blank have?

In an ANOVA analysis, the R² is likely to be larger when the P-value is smaller and vice-versa.