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?

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 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

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

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

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?

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

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?

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

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?

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

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

To calculate the values needed for the A

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?

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

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?

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 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

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.

Free

(True/False)

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Question 1

Correct Answer:

Verified

False

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 -To test the significance of the F-ratio value, what degrees of freedom would we use?

Free

(Multiple Choice)

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Question 2

Correct Answer:

Verified

B

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

Free

(True/False)

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Question 3

Correct Answer:

Verified

False

The ANOVA technique requires more than two groups.

(True/False)

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Question 4

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

(Multiple Choice)

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Question 5

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

(True/False)

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Question 6

Based on the ANOVA table shown, what is the $S_{A}^{2}$ value 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 ?

(Multiple Choice)

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Question 7

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 SS_error?

(Multiple Choice)

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Question 8

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 SS_groups?

(Multiple Choice)

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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. 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 SS_error?

(Multiple Choice)

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Question 10

Using the data set shown, calculate all the values you need to complete an ANOVA table. Groups A B C D 14 14 14 15 15 16 17 17 17 17 18 18 18 21 19 22 Source of Sum of Mean variation squares df squares F-ratio Groups --- --- --- --- Error --- --- --- Total ---

(Essay)

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Question 11

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

(True/False)

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Question 12

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?

(Multiple Choice)

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Question 13

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 error mean square?

(Multiple Choice)

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Question 14

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

(Multiple Choice)

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Question 15

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

(True/False)

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Question 16

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

(True/False)

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Question 17

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 are the means of the groups and overall mean?

(Multiple Choice)

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Question 18

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

(Multiple Choice)

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Question 19

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

(True/False)

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Question 20

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.

Based on the ANOVA table shown, what is the $S_{A}^{2}$ value 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 ?

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 SS_error?

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 SS_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 SS_error?

Using the data set shown, calculate all the values you need to complete an ANOVA table. Groups A B C D 14 14 14 15 15 16 17 17 17 17 18 18 18 21 19 22 Source of Sum of Mean variation squares df squares F-ratio Groups --- --- --- --- Error --- --- --- Total ---

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?

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 error mean square?

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.

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 are the means of the groups and overall mean?

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.

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

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.

Based on the ANOVA table shown, what is the SA2S_{A}^{2}SA2​ value 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 ?

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 SSerror?

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 SSgroups?

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 SSerror?

Using the data set shown, calculate all the values you need to complete an ANOVA table. ​ Groups A B C D 14 14 14 15 15 16 17 17 17 17 18 18 18 21 19 22 Source of Sum of Mean variation squares df squares F-ratio Groups --- --- --- --- Error --- --- --- Total --- ​

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? ​ ​

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 error mean square?

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.

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 are the means of the groups and overall mean?

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.

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

Based on the ANOVA table shown, what is the $S_{A}^{2}$ value 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 ?

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 SS_error?

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 SS_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 SS_error?

Using the data set shown, calculate all the values you need to complete an ANOVA table. Groups A B C D 14 14 14 15 15 16 17 17 17 17 18 18 18 21 19 22 Source of Sum of Mean variation squares df squares F-ratio Groups --- --- --- --- Error --- --- --- Total ---

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?

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 error mean square?

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 are the means of the groups and overall mean?

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