Question 1

The error mean square is best described by which of the following?

Accepted Answer

A)  It measures how many values there are. 
B)  It measures the variation between all values in all of the groups. 
C)  It measures the variation between the means of the groups. 
D)  It measures the variation between values within each of the groups. 
A)  It measures how many values there are. 
B)  It measures the variation between all values in all of the groups. 
C)  It measures the variation between the means of the groups. 
D)  It measures the variation between values within each of the groups.

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.
​
 $\begin{array}{c}
\text { Groups }\
\begin{array}{rrrr}
\text { A } & \text { B } & \text { C } & \text { D } \
6 & 7 & 9 & 11 \
8 & 10 & 11 & 14 \
10 & 11 & 12 & 15 \
12 & 12 & 13 & 16 \
14 & 15 & 15 & 19
\end{array}\end{array}$ ​
-What is the value of the R2 value we obtain from the analysis?

Accepted Answer

A)  0.222 
B)  0.333 
C)  0.444 
D)  0.555 
A)  0.222 
B)  0.333 
C)  0.444 
D)  0.555

Question 3

If the data intended for an ANOVA does not meet the assumptions, there are three options. Describe each of these options and what you would do to pursue each of them.

Accepted Answer

The three options for when the data inte

Question 4

Describe the reason we need a technique like the ANOVA. Illustrate the problem with an example using t-tests to study several groups. Make reference to the appropriate type of statistical error and use an example calculation to show the problem the ANOVA addresses.

Accepted Answer

The Analysis of Variance (ANOVA) techniq

Question 5

Describe the difference between ANOVA analyses examined fixed and random effects. Describe how the interpretation of the same numerical values is done differently.

Accepted Answer

ANOVA (Analysis of Variance) analyses ca

Question 6

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 value of the F-ratio we will use in the analysis?

Accepted Answer

A)  5.00 
B)  5.25 
C)  5.50 
D)  5.75 
A)  5.00 
B)  5.25 
C)  5.50 
D)  5.75

Question 7

Consider a study involving seven populations from which we draw samples of 13 values each in which the group mean square is 315 and the error mean square is 2020.
​
 $\begin{array}{|lcrcc|}
\hline \text { Source of } & \text { Sum of } & & {\text { Mean }} \
\text { variation } & \text { squares } & \text { df } & \text { squares } & \text { F-ratio } \
\text { Groups } & --- & ---  & ---  & --- \
\text { Error } & --- & ---  & --- & \
\text { Total } & ---  &  & \
\hline
\end{array}$ (a) Complete the ANOVA table.
(b) Does it appear that any of the population the samples are drawn from have means that differ from one another?
​

Accepted Answer

(a) Complete the ANOVA table:

\begin{ar

Question 8

A planned comparison is really just a t-test, but using a standard error based on the variance from all the groups.

Accepted Answer

A) True 
 B)False

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 error mean square?

Accepted Answer

A)  8 
B)  9 
C)  10 
D)  11 
A)  8 
B)  9 
C)  10 
D)  11

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 value of the F-ratio we will use in the analysis?

Accepted Answer

A)  1.83 
B)  2.92 
C)  6.34 
D)  8.75 
A)  1.83 
B)  2.92 
C)  6.34 
D)  8.75

Question 11

If the normality assumption of the single-factor ANOVA is violated, then the Kruskal-Wallis test is a good alternative as long as the sample sizes are large and the distributions are similar.

Accepted Answer

A) True 
 B)False

Question 12

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.
​
 $\begin{array}{c}
\text { Groups }\
\begin{array}{rrrr}
\text { A } & \text { B } & \text { C } & \text { D } \
11 & 12 & 11 & 16 \
12 & 13 & 14 & 18 \
14 & 14 & 15 & 19 \
15 & 17 & 16 & 23
\end{array}\end{array}$
-To test the significance of the F-ratio value, what degrees of freedom would we use?

Accepted Answer

A)  df = 2 in the numerator, df = 12 in the denominator. 
B)  df = 2 in the numerator, df = 15 in the denominator. 
C)  df = 3 in the numerator, df = 12 in the denominator. 
D)  df = 3 in the numerator, df = 15 in the denominator. 
A)  df = 2 in the numerator, df = 12 in the denominator. 
B)  df = 2 in the numerator, df = 15 in the denominator. 
C)  df = 3 in the numerator, df = 12 in the denominator. 
D)  df = 3 in the numerator, df = 15 in the denominator.

Question 13

Consider the partially completed ANOVA table shown.
​
 $\begin{array}{|lcrcc|}
\hline \text { Source of } & \text { Sum of } & & \text { Mean } & \
\text { variation } & \text { squares } & \text { df } & \text { squares } & \text { F-ratio } \
\text { Groups } & 384 & 6 & \ldots & \ldots \
\text { Error } & 676 & 98 & \ldots & \
\text { Total } & 1,060 & 104 & & \
\hline
\end{array}$ ​
-What is the F-ratio for this ANOVA table?

Accepted Answer

A)  9.28 
B)  10.28 
C)  16.33 
D)  17.33 
A)  9.28 
B)  10.28 
C)  16.33 
D)  17.33

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 group mean square?

Accepted Answer

A)  19.33 
B)  24.50 
C)  29.33 
D)  34.50 
A)  19.33 
B)  24.50 
C)  29.33 
D)  34.50

Question 15

Which of the following best describes the alternative hypothesis is an ANOVA analysis?

Accepted Answer

A)  All the population means are different from at least one other. 
B)  All the population means are different from one another. 
C)  At least one population's mean is different from all the others. 
D)  At least one population's mean is different from at least one other. 
A)  All the population means are different from at least one other. 
B)  All the population means are different from one another. 
C)  At least one population's mean is different from all the others. 
D)  At least one population's mean is different from at least one other.

Question 16

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 are the means of the groups and overall mean?

Accepted Answer

A)  8, 11, 12, 15, and 12 
B)  9, 11, 12, 15, and 12 
C)  10, 11, 12, 15, and 11 
D)  10, 11, 12, 15, and 12 
A)  8, 11, 12, 15, and 12 
B)  9, 11, 12, 15, and 12 
C)  10, 11, 12, 15, and 11 
D)  10, 11, 12, 15, and 12

Question 17

Which of the following is what we expect if the samples we use in an ANOVA come from populations with the same means?

Accepted Answer

A)  The error mean square will be identical to the group mean square. 
B)  The error mean square will be larger than the group mean square. 
C)  The error mean square will be smaller than the group mean square 
D)  The error mean square will be very close to than the group mean square. 
A)  The error mean square will be identical to the group mean square. 
B)  The error mean square will be larger than the group mean square. 
C)  The error mean square will be smaller than the group mean square 
D)  The error mean square will be very close to than the group mean square.

Question 18

Describe the difference between ANOVA analyses using planned and unplanned comparisons. Describe how the analysis is done differently.

Accepted Answer

ANOVA (Analysis of Variance) is a statis

Question 19

Based on the ANOVA table shown, what is the repeatability 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)  0.190 
B)  0.322 
C)  0.345 
D)  0.408 
A)  0.190 
B)  0.322 
C)  0.345 
D)  0.408

Question 20

A study examining the heights of multiple individuals in each of a series of families chosen at random from a population would be analyzed using a random-effects ANOVA.

Accepted Answer

A) True 
 B)False

The error mean square is best described by which of the following?

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. Groups A B C D 6 7 9 11 8 10 11 14 10 11 12 15 12 12 13 16 14 15 15 19 -What is the value of the R² value we obtain from the analysis?

If the data intended for an ANOVA does not meet the assumptions, there are three options. Describe each of these options and what you would do to pursue each of them.

Describe the reason we need a technique like the ANOVA. Illustrate the problem with an example using t-tests to study several groups. Make reference to the appropriate type of statistical error and use an example calculation to show the problem the ANOVA addresses.

Describe the difference between ANOVA analyses examined fixed and random effects. Describe how the interpretation of the same numerical values is done differently.

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. Groups A B C D 11 12 11 16 12 13 14 18 14 14 15 19 15 17 16 23 -What is the value of the F-ratio we will use in the analysis?

A planned comparison is really just a t-test, but using a standard error based on the variance from all the groups.

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. Groups A B C D 6 7 9 11 8 10 11 14 10 11 12 15 12 12 13 16 14 15 15 19 -What is the error mean square?

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. Groups A B C D 6 7 9 11 8 10 11 14 10 11 12 15 12 12 13 16 14 15 15 19 -What is the value of the F-ratio we will use in the analysis?

If the normality assumption of the single-factor ANOVA is violated, then the Kruskal-Wallis test is a good alternative as long as the sample sizes are large and the distributions are similar.

Consider the partially completed ANOVA table shown. Source of Sum of Mean variation squares df squares F-ratio Groups 384 6 \ldots \ldots Error 676 98 \ldots Total 1,060 104 -What is the F-ratio for this ANOVA table?

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. Groups A B C D 11 12 11 16 12 13 14 18 14 14 15 19 15 17 16 23 -What is the group mean square?

Which of the following best describes the alternative hypothesis is an ANOVA analysis?

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. Groups A B C D 6 7 9 11 8 10 11 14 10 11 12 15 12 12 13 16 14 15 15 19 -What are the means of the groups and overall mean?

Which of the following is what we expect if the samples we use in an ANOVA come from populations with the same means?

Describe the difference between ANOVA analyses using planned and unplanned comparisons. Describe how the analysis is done differently.

Based on the ANOVA table shown, what is the repeatability for this data? ? Source of Sum of Mean variation squares df squares F-ratio Groups 406 7 58 5.27 Error 704 64 11 Total 1,110 71 ?

A study examining the heights of multiple individuals in each of a series of families chosen at random from a population would be analyzed using a random-effects ANOVA.

Statistics and Samples

Displaying Data

Describing Data

Estimating With Uncertainty

Probability

Hypothesis Testing

Analyzing Proportions

Fitting Probability Models to Frequency Data

Contingency Analysis: Associations Between

The Normal Distribution

Inference for a Normal Population

Comparing Two Means

Handling Violations of Assumptions

Designing Experiments

Correlation Between Numerical Variables

Regression

Multiple Explanatory Variables

Computer-Intensive Methods

Likelihood

Meta-Analysis: Combining Information From

Filters

Exam 15: Comparing Means of More Than Two Groups

The error mean square is best described by which of the following?

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. ​ Groups A B C D 6 7 9 11 8 10 11 14 10 11 12 15 12 12 13 16 14 15 15 19 ​ -What is the value of the R2 value we obtain from the analysis?

If the data intended for an ANOVA does not meet the assumptions, there are three options. Describe each of these options and what you would do to pursue each of them.

Describe the reason we need a technique like the ANOVA. Illustrate the problem with an example using t-tests to study several groups. Make reference to the appropriate type of statistical error and use an example calculation to show the problem the ANOVA addresses.

Describe the difference between ANOVA analyses examined fixed and random effects. Describe how the interpretation of the same numerical values is done differently.

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. ​ Groups A B C D 11 12 11 16 12 13 14 18 14 14 15 19 15 17 16 23 -What is the value of the F-ratio we will use in the analysis?

A planned comparison is really just a t-test, but using a standard error based on the variance from all the groups.

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. ​ Groups A B C D 6 7 9 11 8 10 11 14 10 11 12 15 12 12 13 16 14 15 15 19 ​ -What is the error mean square?

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. ​ Groups A B C D 6 7 9 11 8 10 11 14 10 11 12 15 12 12 13 16 14 15 15 19 ​ -What is the value of the F-ratio we will use in the analysis?

If the normality assumption of the single-factor ANOVA is violated, then the Kruskal-Wallis test is a good alternative as long as the sample sizes are large and the distributions are similar.

Consider the partially completed ANOVA table shown. ​ Source of Sum of Mean variation squares df squares F-ratio Groups 384 6 \ldots \ldots Error 676 98 \ldots Total 1,060 104 ​ -What is the F-ratio for this ANOVA table?

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. ​ Groups A B C D 11 12 11 16 12 13 14 18 14 14 15 19 15 17 16 23 -What is the group mean square?

Which of the following best describes the alternative hypothesis is an ANOVA analysis?

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. ​ Groups A B C D 6 7 9 11 8 10 11 14 10 11 12 15 12 12 13 16 14 15 15 19 ​ -What are the means of the groups and overall mean?

Which of the following is what we expect if the samples we use in an ANOVA come from populations with the same means?

Describe the difference between ANOVA analyses using planned and unplanned comparisons. Describe how the analysis is done differently.

Based on the ANOVA table shown, what is the repeatability for this data? ? Source of Sum of Mean variation squares df squares F-ratio Groups 406 7 58 5.27 Error 704 64 11 Total 1,110 71 ?

A study examining the heights of multiple individuals in each of a series of families chosen at random from a population would be analyzed using a random-effects ANOVA.

Statistics and Samples

Displaying Data

Describing Data

Estimating With Uncertainty

Probability

Hypothesis Testing

Analyzing Proportions

Fitting Probability Models to Frequency Data

Contingency Analysis: Associations Between

The Normal Distribution

Inference for a Normal Population

Comparing Two Means

Handling Violations of Assumptions

Designing Experiments

Correlation Between Numerical Variables

Regression

Multiple Explanatory Variables

Computer-Intensive Methods

Likelihood

Meta-Analysis: Combining Information From

Filters

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. Groups A B C D 6 7 9 11 8 10 11 14 10 11 12 15 12 12 13 16 14 15 15 19 -What is the value of the R² value we obtain from the analysis?

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. Groups A B C D 11 12 11 16 12 13 14 18 14 14 15 19 15 17 16 23 -What is the value of the F-ratio we will use in the analysis?

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. Groups A B C D 6 7 9 11 8 10 11 14 10 11 12 15 12 12 13 16 14 15 15 19 -What is the error mean square?

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. Groups A B C D 6 7 9 11 8 10 11 14 10 11 12 15 12 12 13 16 14 15 15 19 -What is the value of the F-ratio we will use in the analysis?

Consider the partially completed ANOVA table shown. Source of Sum of Mean variation squares df squares F-ratio Groups 384 6 \ldots \ldots Error 676 98 \ldots Total 1,060 104 -What is the F-ratio for this ANOVA table?

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. Groups A B C D 11 12 11 16 12 13 14 18 14 14 15 19 15 17 16 23 -What is the group mean square?

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. Groups A B C D 6 7 9 11 8 10 11 14 10 11 12 15 12 12 13 16 14 15 15 19 -What are the means of the groups and overall mean?