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 group mean square?

A) 17.50 B) 19.33 C) 21.50 D) 23.33 A) 17.50 B) 19.33 C) 21.50 D) 23.33

Consider a study involving six populations from which we draw samples of 12 values each in which the group mean square is 426 and the error mean square is 1416. \(\begin{array}{|lcrcc|} \hline \text { Source of } & \text { Sum of } & & {\text { Mean }} \\ \text { variation } & \text { squares } & \text { df } & \text { squares } & \text { F-ratio } \\ \text { Groups } & --- & --- & --- & --- \\ \text { Error } & --- & --- & --- & \\ \text { Total } & --- & & \\ \hline \end{array}\) (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?

To complete the ANOVA table, we need to

Consider the partially completed ANOVA table shown. \(\begin{array}{|lcrcc|} \hline \text { Source of } & \text { Sum of } & & \text { Mean } & \\ \text { variation } & \text { squares } & \text { df } & \text { squares } & \text { F-ratio } \\ \text { Groups } & 384 & 6 & \ldots & \ldots \\ \text { Error } & 676 & 98 & \ldots & \\ \text { Total } & 1,060 & 104 & & \\ \hline \end{array}\) -How many values are in each group of the data set this is based on?

A) 5 B) 12 C) 14 D) 15 A) 5 B) 12 C) 14 D) 15

Using the data set shown, calculate all the values you need to complete the ANOVA table. \(\begin{array}{c} \text { Groups }\\ \begin{array}{rrrr} \text { A } & \text { B } & \text { C } & \text { D } \\ 13 & 10 & 12 & 14 \\ 15 & 13 & 14 & 17 \\ 17 & 14 & 15 & 18 \\ 19 & 15 & 16 & 19 \\ 21 & 18 & 18 & 22 \end{array}\end{array}\) \(\begin{array}{|lcrcc|} \hline \text { Source of } & \text { Sum of } & & {\text { Mean }} \\ \text { variation } & \text { squares } & \text { df } & \text { squares } & \text { F-ratio } \\ \text { Groups } & --- & --- & --- & --- \\ \text { Error } & --- & --- & --- & \\ \text { Total } & --- & & \\ \hline \end{array}\)

To complete the ANOVA table, we need to

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. \(\begin{array}{c} \text { Groups }\\ \begin{array}{rrrr} \text { A } & \text { B } & \text { C } & \text { D } \\ 11 & 12 & 11 & 16 \\ 12 & 13 & 14 & 18 \\ 14 & 14 & 15 & 19 \\ 15 & 17 & 16 & 23 \end{array}\end{array}\) -Use your calculated F-ratio, the degrees of freedom, and your table of critical F values to make a conclusion for this test?

A) P 0.05, none of the means seem to differ. D) P > 0.05, at least one of the means seems to differ. A) P 0.05, none of the means seem to differ. D) P > 0.05, at least one of the means seems to differ.

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 SSgroups?

A) 72 B) 80 C) 88 D) 96 A) 72 B) 80 C) 88 D) 96

Exam 15: Comparing Means of More Than Two 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 group mean square?

(Multiple Choice)

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Question 41

In an ANOVA analysis, the R² measures the total variation in the data.

(True/False)

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Question 42

Consider a study involving six populations from which we draw samples of 12 values each in which the group mean square is 426 and the error mean square is 1416. Source of Sum of Mean variation squares df squares F-ratio Groups --- --- --- --- Error --- --- --- Total --- (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?

(Short Answer)

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Question 43

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 -How many values are in each group of the data set this is based on?

(Multiple Choice)

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Question 44

Which of the following best describes when we would reject the null hypothesis when doing an ANOVA analysis?

(Multiple Choice)

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Question 45

Using the data set shown, calculate all the values you need to complete the ANOVA table. Groups A B C D 13 10 12 14 15 13 14 17 17 14 15 18 19 15 16 19 21 18 18 22 Source of Sum of Mean variation squares df squares F-ratio Groups --- --- --- --- Error --- --- --- Total ---

(Short Answer)

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Question 46

Planned comparisons after an ANOVA using the t-test procedure tend to have higher precisions than regular two-sample t-tests. Why is that?

(Multiple Choice)

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Question 47

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 -Use your calculated F-ratio, the degrees of freedom, and your table of critical F values to make a conclusion for this test?

(Multiple Choice)

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Question 48

When using the Tukey-Kramer method, the probability of making a Type I error is α for each pairwise comparison made.

(True/False)

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Question 49

A planned comparison when doing an ANOVA must be specified before the analysis, never afterwards.

(True/False)

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Question 50

If groups are predefined and of interest themselves, the explanatory variable is called a(n) effect, but if the groups are randomly sampled from a population of possible groups, the explanatory variable is called a(n) effect.

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Question 51

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 52

Use your calculated F-ratio, the degrees of freedom, and your table of critical F values to make a conclusion for this test?

(Multiple Choice)

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Question 53

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_groups?

(Multiple Choice)

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Question 54

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 group mean square?

In an ANOVA analysis, the R² measures the total variation in the data.

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 -How many values are in each group of the data set this is based on?

Which of the following best describes when we would reject the null hypothesis when doing an ANOVA analysis?

Using the data set shown, calculate all the values you need to complete the ANOVA table. Groups A B C D 13 10 12 14 15 13 14 17 17 14 15 18 19 15 16 19 21 18 18 22 Source of Sum of Mean variation squares df squares F-ratio Groups --- --- --- --- Error --- --- --- Total ---

Planned comparisons after an ANOVA using the t-test procedure tend to have higher precisions than regular two-sample t-tests. Why is that?

When using the Tukey-Kramer method, the probability of making a Type I error is α for each pairwise comparison made.

A planned comparison when doing an ANOVA must be specified before the analysis, never afterwards.

If groups are predefined and of interest themselves, the explanatory variable is called a(n) effect, but if the groups are randomly sampled from a population of possible groups, the explanatory variable is called a(n) effect.

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?

Use your calculated F-ratio, the degrees of freedom, and your table of critical F values to make a conclusion for this test?

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_groups?

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

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 group mean square?

In an ANOVA analysis, the R2 measures the total variation in the data.

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 ​ -How many values are in each group of the data set this is based on?

Which of the following best describes when we would reject the null hypothesis when doing an ANOVA analysis?

Using the data set shown, calculate all the values you need to complete the ANOVA table. ​ Groups A B C D 13 10 12 14 15 13 14 17 17 14 15 18 19 15 16 19 21 18 18 22 Source of Sum of Mean variation squares df squares F-ratio Groups --- --- --- --- Error --- --- --- Total --- ​

Planned comparisons after an ANOVA using the t-test procedure tend to have higher precisions than regular two-sample t-tests. Why is that?

When using the Tukey-Kramer method, the probability of making a Type I error is α for each pairwise comparison made.

A planned comparison when doing an ANOVA must be specified before the analysis, never afterwards.

If groups are predefined and of interest themselves, the explanatory variable is called a(n) ____ effect, but if the groups are randomly sampled from a population of possible groups, the explanatory variable is called a(n) ____ effect.

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? ​ ​

Use your calculated F-ratio, the degrees of freedom, and your table of critical F values to make a conclusion for this test?

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 SSgroups?

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 group mean square?

In an ANOVA analysis, the R² measures the total variation in the data.

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 -How many values are in each group of the data set this is based on?

Using the data set shown, calculate all the values you need to complete the ANOVA table. Groups A B C D 13 10 12 14 15 13 14 17 17 14 15 18 19 15 16 19 21 18 18 22 Source of Sum of Mean variation squares df squares F-ratio Groups --- --- --- --- Error --- --- --- Total ---

If groups are predefined and of interest themselves, the explanatory variable is called a(n) effect, but if the groups are randomly sampled from a population of possible groups, the explanatory variable is called a(n) effect.

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 SS_groups?