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The accompanying data shows a sample of pulse rates​ (beats per​ minute) that were categorized with two​ factors, age bracket​ (years) and gender. The data were used to illustrate the use of​ two-way ANOVA. How are the results affected in each of the following​ cases?   a. The same constant is added to each sample value. b. Each sample value is multiplied by the same nonzero constant. c. The format of the table is transposed so that the row and column factors are interchanged.

The accompanying data shows a sample of pulse rates​ (beats per​ minute) that were categorized with two​ factors, age bracket​ (years) and gender. The data were used to illustrate the use of​ two-way ANOVA. How are the results affected in each of the following​ cases?   a. The same constant is added to each sample value. b. Each sample value is multiplied by the same nonzero constant. c. The format of the table is transposed so that the row and column factors are interchanged.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The accompanying data shows a sample of pulse rates​ (beats per​ minute) that were categorized with two​ factors, age bracket​ (years) and gender.
The data were used to illustrate the use of​ two-way ANOVA.
How are the results affected in each of the following​ cases?
 
a. The same constant is added to each sample value.
b. Each sample value is multiplied by the same nonzero constant.
c. The format of the table is transposed so that the row and column factors are interchanged.
d. The first sample value in the first cell is changed so that it becomes an outlier.
The accompanying data shows a sample of pulse rates (beats per minute) that were categorized with two factors, age bracket (years) and gender. The data were used to illustrate the use of two-way ANOVA. How are the results affected in each of the following cases? a. The same constant is added to each sample value. b. Each sample value is multiplied by the same nonzero constant. c. The format of the table is transposed so that the row and column factors are interchanged. d. The first sample value in the first cell is changed so that it becomes outlier. E Click the icon to view the pulse rate data. a. Choose the correct answer below. O A. The test statistic and P-value will not change. O B. The test statistic will change because the mean of each group will change. The P-value will change because the test statistic will change. O C. The test statistic will change, but the P-value will not change because increasing all values by a similar amount will not change the variance of the sample. OD. The P-value will change, but the test statistic will not change because increasing all values by a similar amount will not change the variance of the sample. b. Choose the correct answer below. O A. The P-value will change because the mean will increase, but the test statistic will not change because multiplying all values by a similar amount will not change the variance of the sample. O B. The test statistic will change because both the mean and the variance of each group will change. The P-value will change because the test statistic will change. OC. The test statistic will change because the mean will increase, but the P-value will not change because multiplying all values by a similar amount will not change the variance of the sample. O D. The test statistic and P-value will not change. c. Choose the correct answer below. O A. The test statistic will be negative one times the previous test statistic. The P-value will not change because an ANOVA is two-sided and the area outside the test statistic will not change. O B. The test statistic and P-value will not change. O C. The P-value will be one minus the previous P-value. The test statistic will be negative one times the previous test statistic. O D. The test statistic will change because both the mean and the variance of each group will change. The P-value will change because the test statistic will change. d. Choose the correct answer below. O A. The P-value and mean will only change by a very small amount, because an ANOVA is robust against outliers and a single value cannot dramatically change the results. O B. The test statistic and P-value will not change. O C. Both the test statistic and P-value will most likely change because outliers can dramatically affect and change the results of an ANOVA. O D. The P-value will be approximately one minus the previous P-value. The test statistic will be approximately negative one times the previous test statistic.
Transcribed Image Text:The accompanying data shows a sample of pulse rates (beats per minute) that were categorized with two factors, age bracket (years) and gender. The data were used to illustrate the use of two-way ANOVA. How are the results affected in each of the following cases? a. The same constant is added to each sample value. b. Each sample value is multiplied by the same nonzero constant. c. The format of the table is transposed so that the row and column factors are interchanged. d. The first sample value in the first cell is changed so that it becomes outlier. E Click the icon to view the pulse rate data. a. Choose the correct answer below. O A. The test statistic and P-value will not change. O B. The test statistic will change because the mean of each group will change. The P-value will change because the test statistic will change. O C. The test statistic will change, but the P-value will not change because increasing all values by a similar amount will not change the variance of the sample. OD. The P-value will change, but the test statistic will not change because increasing all values by a similar amount will not change the variance of the sample. b. Choose the correct answer below. O A. The P-value will change because the mean will increase, but the test statistic will not change because multiplying all values by a similar amount will not change the variance of the sample. O B. The test statistic will change because both the mean and the variance of each group will change. The P-value will change because the test statistic will change. OC. The test statistic will change because the mean will increase, but the P-value will not change because multiplying all values by a similar amount will not change the variance of the sample. O D. The test statistic and P-value will not change. c. Choose the correct answer below. O A. The test statistic will be negative one times the previous test statistic. The P-value will not change because an ANOVA is two-sided and the area outside the test statistic will not change. O B. The test statistic and P-value will not change. O C. The P-value will be one minus the previous P-value. The test statistic will be negative one times the previous test statistic. O D. The test statistic will change because both the mean and the variance of each group will change. The P-value will change because the test statistic will change. d. Choose the correct answer below. O A. The P-value and mean will only change by a very small amount, because an ANOVA is robust against outliers and a single value cannot dramatically change the results. O B. The test statistic and P-value will not change. O C. Both the test statistic and P-value will most likely change because outliers can dramatically affect and change the results of an ANOVA. O D. The P-value will be approximately one minus the previous P-value. The test statistic will be approximately negative one times the previous test statistic.
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