Homework Help is Here – Start Your Trial Now!
Math
Statistics
Which one of the following statements about the appropriateness of using an F-test on this data is false?   Although the data shows some signs of non-Normality, the sample size is large enough to have no concern about the assumption of Normality. The data indicates we should be concerned with the assumption of the underlying means being the same. Because the participants were randomly assigned to an activity, there is no concern about the assumption of independence of the observations between the activity groups. The standard deviations of each activity group are not different enough for us to have concerns about the assumption of equal standard deviations of the underlying distributions. Because the participants were randomly assigned to an activity, there is no concern about the assumption of independence of the observations within each activity group.

Which one of the following statements about the appropriateness of using an F-test on this data is false?   Although the data shows some signs of non-Normality, the sample size is large enough to have no concern about the assumption of Normality. The data indicates we should be concerned with the assumption of the underlying means being the same. Because the participants were randomly assigned to an activity, there is no concern about the assumption of independence of the observations between the activity groups. The standard deviations of each activity group are not different enough for us to have concerns about the assumption of equal standard deviations of the underlying distributions. Because the participants were randomly assigned to an activity, there is no concern about the assumption of independence of the observations within each activity group.

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
See similar textbooks
icon
Related questions
Question

Which one of the following statements about the appropriateness of using an F-test on this data is false?

 
  • Although the data shows some signs of non-Normality, the sample size is large enough to have no concern about the assumption of Normality.
  • The data indicates we should be concerned with the assumption of the underlying means being the same.
  • Because the participants were randomly assigned to an activity, there is no concern about the assumption of independence of the observations between the activity groups.
  • The standard deviations of each activity group are not different enough for us to have concerns about the assumption of equal standard deviations of the underlying distributions.
  • Because the participants were randomly assigned to an activity, there is no concern about the assumption of independence of the observations within each activity group.
A one-way analysis of variance (ANOVA) F-test was conducted to investigate the relationship between Activity and BrainChange. Let "Tai be the underlying mean BrainChange when the activity is TaiChi "Soc be the underlying mean BrainChange when the activity is Social and recall that "NoInis the underlying mean BrainChange when there is no activity assigned. The plot of BrainChange by Activity is shown in Figure 2 (with each group mean being indicated by a triangle) and the output from the F-test is shown in Table 2. TaiChi Social NoIntervention 00 -2 BrainChange TaiChi Social NoIntervention Total o O BrainChange Between Groups Within Groups Total O Figure 2: BrainChange by Activity (1) Treatment TaiChi Social O N 29 27 O OOD O -1 Sum of Squares 7.820 69.556 77.376 Dependent Variable: BrainChange Tukey HSD TaiChi 00 (J) Treatment Social NoIntervention TaiChi Social Table 2: F-test ouptut Nolntervention Note that one of the values has been replaced with ++ 00 00 Nolntervention 00 Std. Mean Deviation Std. Error 4711 .85575 4056 69690 24 -2401 1.25843 80 2356 98967 00 ANOVA O Descriptives df 2 77 79 O 00 00 00 O (1-J) .06544 15891 13412 25688 .11065 Mean Square 3.910 903 .71119 -.06544 .64575 -.71119 -.64575 800000⁰ .. 0 BrainChange 0 O Minimum -1.83 -1.36 -2.03 -2.03 Multiple Comparisons F ++ Mean Difference Std. Error .25418 .26227 .25418 .26664 .26227 .26664 GOOD O OO 00 Maximum 2.20 1.80 2.01 2.20 Sig. .017 Sig. .964 .022 .964 .046 .022 .046 00 0 0 0 0 00 00 0 00 0 0 00 1 O .0844 -.6729 .0085 -1.3380 -1.2830 oo 0 2 95% Confidence Interval Lower Bound Upper Bound -.5420 .6729 1.3380 .5420 1.2830 -.0844 -.0085
Transcribed Image Text:A one-way analysis of variance (ANOVA) F-test was conducted to investigate the relationship between Activity and BrainChange. Let "Tai be the underlying mean BrainChange when the activity is TaiChi "Soc be the underlying mean BrainChange when the activity is Social and recall that "NoInis the underlying mean BrainChange when there is no activity assigned. The plot of BrainChange by Activity is shown in Figure 2 (with each group mean being indicated by a triangle) and the output from the F-test is shown in Table 2. TaiChi Social NoIntervention 00 -2 BrainChange TaiChi Social NoIntervention Total o O BrainChange Between Groups Within Groups Total O Figure 2: BrainChange by Activity (1) Treatment TaiChi Social O N 29 27 O OOD O -1 Sum of Squares 7.820 69.556 77.376 Dependent Variable: BrainChange Tukey HSD TaiChi 00 (J) Treatment Social NoIntervention TaiChi Social Table 2: F-test ouptut Nolntervention Note that one of the values has been replaced with ++ 00 00 Nolntervention 00 Std. Mean Deviation Std. Error 4711 .85575 4056 69690 24 -2401 1.25843 80 2356 98967 00 ANOVA O Descriptives df 2 77 79 O 00 00 00 O (1-J) .06544 15891 13412 25688 .11065 Mean Square 3.910 903 .71119 -.06544 .64575 -.71119 -.64575 800000⁰ .. 0 BrainChange 0 O Minimum -1.83 -1.36 -2.03 -2.03 Multiple Comparisons F ++ Mean Difference Std. Error .25418 .26227 .25418 .26664 .26227 .26664 GOOD O OO 00 Maximum 2.20 1.80 2.01 2.20 Sig. .017 Sig. .964 .022 .964 .046 .022 .046 00 0 0 0 0 00 00 0 00 0 0 00 1 O .0844 -.6729 .0085 -1.3380 -1.2830 oo 0 2 95% Confidence Interval Lower Bound Upper Bound -.5420 .6729 1.3380 .5420 1.2830 -.0844 -.0085
Brain size typically shrinks as people age and such shrinkage may be linked to dementia. A study was done in China to investigate whether different types of activity might help to prevent brain shrinkage or perhaps even lead to an increase in brain size. The 80 (non-demented) volunteers were aged between 60 and 69. Each of them had an MRI to determine brain size before the study began. They were then randomly allocated to one of three activity groups: TaiChi, Social or Nolntervention. Except for the Nolntervention group, the groups met with their leaders three times a week over a period of 40 weeks. The Nolntervention group were called four times by the study coordinator during the study period. At the end of the study, the participants had another MRI and the percentage change in size of each participant's brain was calculated. Adapted from: Mortimer, J. A., Ding, D., Borenstein, A. R., DeCarli C., Guo, Q., Wu, Y., Zhao, Q. and Chu, S. (2012), Changes in Brain Volume and Cognition in a Randomized Trial of Exercise and Social Interaction in a Community-Based Sample of Non-Demented Chinese Elders. The two variables used are defined as: Activity BrainChange Percentage change in size of participant's brain 00 The activity the participant was randomly assigned to - TaiChi (meet two Tai Chi masters to practise Tai Chi) - Social Questions 8 and 9 refer to the following additional information. -2 (meet at a community centre to discuss interesting topics) - NoIntervention (no activity assigned) A plot of BrainChange for the participants who were assigned to the Nolntervention group is shown in Figure 1. The mean is indicated by the triangle. (where a positive value means the brain increased in size) Nolntervention ooooo Nolntervention 0 BralnChange Figure 1: BrainChange for the Nolntervention group 00 8 N 24 0 0 0 One-Sample Statistics -.935 O Let uNoInt be the underlying mean BrainChange when there is no activity assigned. A one-sample t-test with hypotheses Ho: "NoInt = 0 vs H₁ : NoInt #0 was conducted to investigate whether there was an underlying mean BrainChange when there was no intervention. The output for this test is shown in Table 1. df 23 00 00 Mean Std. Deviation Std. Error Mean -2401 1.25843 25688 1 One-Sample Test Sig. (2-tailed) .360 Test Value = 0 00 2 Mean Difference - 24012 95% Confidence Interval of the Lower -.7715 Difference Upper 2913
Transcribed Image Text:Brain size typically shrinks as people age and such shrinkage may be linked to dementia. A study was done in China to investigate whether different types of activity might help to prevent brain shrinkage or perhaps even lead to an increase in brain size. The 80 (non-demented) volunteers were aged between 60 and 69. Each of them had an MRI to determine brain size before the study began. They were then randomly allocated to one of three activity groups: TaiChi, Social or Nolntervention. Except for the Nolntervention group, the groups met with their leaders three times a week over a period of 40 weeks. The Nolntervention group were called four times by the study coordinator during the study period. At the end of the study, the participants had another MRI and the percentage change in size of each participant's brain was calculated. Adapted from: Mortimer, J. A., Ding, D., Borenstein, A. R., DeCarli C., Guo, Q., Wu, Y., Zhao, Q. and Chu, S. (2012), Changes in Brain Volume and Cognition in a Randomized Trial of Exercise and Social Interaction in a Community-Based Sample of Non-Demented Chinese Elders. The two variables used are defined as: Activity BrainChange Percentage change in size of participant's brain 00 The activity the participant was randomly assigned to - TaiChi (meet two Tai Chi masters to practise Tai Chi) - Social Questions 8 and 9 refer to the following additional information. -2 (meet at a community centre to discuss interesting topics) - NoIntervention (no activity assigned) A plot of BrainChange for the participants who were assigned to the Nolntervention group is shown in Figure 1. The mean is indicated by the triangle. (where a positive value means the brain increased in size) Nolntervention ooooo Nolntervention 0 BralnChange Figure 1: BrainChange for the Nolntervention group 00 8 N 24 0 0 0 One-Sample Statistics -.935 O Let uNoInt be the underlying mean BrainChange when there is no activity assigned. A one-sample t-test with hypotheses Ho: "NoInt = 0 vs H₁ : NoInt #0 was conducted to investigate whether there was an underlying mean BrainChange when there was no intervention. The output for this test is shown in Table 1. df 23 00 00 Mean Std. Deviation Std. Error Mean -2401 1.25843 25688 1 One-Sample Test Sig. (2-tailed) .360 Test Value = 0 00 2 Mean Difference - 24012 95% Confidence Interval of the Lower -.7715 Difference Upper 2913
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS