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A paper described the results of a medical study in which one treatment was shown to be better for men and better for women than a competing treatment. However, if the data for men and women are combined, it appears as though the competing treatment is better. To see how this can happen, consider the following data tables constructed from information in the paper. Subjects in the study were given either Treatment A or Treatment B, and survival was noted. Let S be the event that a patient selected at random survives, A be the event that a patient selected at random received Treatment A, and B be the event that a patient selected at random received Treatment B. (Round your answers to three decimal places.) (a) The following table summarizes data for men and women combined. Treatment A Treatment B Total (0) Find P(S). (ii) Find P(SIA). (ii) Find P(SIB). Treatment A Treatment B Total (iv) Which treatment appears to be better? O Treatment A O Treatment B (i) Find P(S). Survived Died Total 218 300 57 300 (b) Now consider the summary data for the men who participated in the study. Survived Died Total 120 80 200 (ii) Find P(SIA). 243 (iii) Find P(SIB). 461 82 20 139 140 20 100 (iv) Which treatment appears to be better? O Treatment A O Treatment B 40

A paper described the results of a medical study in which one treatment was shown to be better for men and better for women than a competing treatment. However, if the data for men and women are combined, it appears as though the competing treatment is better. To see how this can happen, consider the following data tables constructed from information in the paper. Subjects in the study were given either Treatment A or Treatment B, and survival was noted. Let S be the event that a patient selected at random survives, A be the event that a patient selected at random received Treatment A, and B be the event that a patient selected at random received Treatment B. (Round your answers to three decimal places.) (a) The following table summarizes data for men and women combined. Treatment A Treatment B Total (0) Find P(S). (ii) Find P(SIA). (ii) Find P(SIB). Treatment A Treatment B Total (iv) Which treatment appears to be better? O Treatment A O Treatment B (i) Find P(S). Survived Died Total 218 300 57 300 (b) Now consider the summary data for the men who participated in the study. Survived Died Total 120 80 200 (ii) Find P(SIA). 243 (iii) Find P(SIB). 461 82 20 139 140 20 100 (iv) Which treatment appears to be better? O Treatment A O Treatment B 40

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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(c) Now consider the summary data for the women who participated in the study. Treatment A Treatment B Total (i) Find P(S). (ii) Find P(SIA). (iii) Find P(SIB). Survived 98 223 321 Died Total 2 37 39 (iv) Which treatment appears to be better? O Treatment A O Treatment B 100 260 (d) You should have noticed from parts (b) and (c) that for both men and women, Treatment A appears to be better. But in part (a), when the data for men and women are combined, it looks like Treatment B is better. This is an example of what is called Simpson's paradox. Write a brief explanation of why this apparent inconsistency occurs for this data set. (Hint: Do men and women respond similarly to the two treatments?) O The results are distorted in favor of Treatment A, as women respond to both treatments better than men, but Treatment A was given to far more women than men. O The results are distorted in favor of Treatment B, as women respond to these treatments better than men, but Treatment A was given to far more women than men. O The results are distorted in favor of Treatment A, as women respond to these treatments better than men, but Treatment B was given to far more women than men. O The results are distorted in favor of Treatment B, as women respond to both treatments better than men, but Treatment B was given to far more women than men.
Transcribed Image Text:(c) Now consider the summary data for the women who participated in the study. Treatment A Treatment B Total (i) Find P(S). (ii) Find P(SIA). (iii) Find P(SIB). Survived 98 223 321 Died Total 2 37 39 (iv) Which treatment appears to be better? O Treatment A O Treatment B 100 260 (d) You should have noticed from parts (b) and (c) that for both men and women, Treatment A appears to be better. But in part (a), when the data for men and women are combined, it looks like Treatment B is better. This is an example of what is called Simpson's paradox. Write a brief explanation of why this apparent inconsistency occurs for this data set. (Hint: Do men and women respond similarly to the two treatments?) O The results are distorted in favor of Treatment A, as women respond to both treatments better than men, but Treatment A was given to far more women than men. O The results are distorted in favor of Treatment B, as women respond to these treatments better than men, but Treatment A was given to far more women than men. O The results are distorted in favor of Treatment A, as women respond to these treatments better than men, but Treatment B was given to far more women than men. O The results are distorted in favor of Treatment B, as women respond to both treatments better than men, but Treatment B was given to far more women than men.
A paper described the results of a medical study in which one treatment was shown to be better for men and better for women than a competing treatment. However, if the data for men and women are combined, it appears as though the competing treatment is better. To see how this can happen, consider the following data tables constructed from information in the paper. Subjects in the study were given either Treatment A or Treatment B, and survival was noted. Let S be the event that a patient selected at random survives, A be the event that a patient selected at random received Treatment A, and B be the event that a patient selected at random received Treatment B. (Round your answers to three decimal places.) (a) The following table summarizes data for men and women combined. Treatment A Treatment B Total (i) Find P(S). (ii) Find P(SIA). (iii) Find P(SIB). (i) Treatment A Treatment B Total Find P(S). Survived (ii) Find P(SIA). 218 (iv) Which treatment appears to be better? O Treatment A O Treatment B (iii) Find P(SIB). 243 461 (b) Now consider the summary data for the men who participated in the study. Died 120 82 20 57 140 139 Survived Died Total 80 20 Total 100 300 (iv) Which treatment appears to be better? O Treatment A O Treatment B 300 200 40
Transcribed Image Text:A paper described the results of a medical study in which one treatment was shown to be better for men and better for women than a competing treatment. However, if the data for men and women are combined, it appears as though the competing treatment is better. To see how this can happen, consider the following data tables constructed from information in the paper. Subjects in the study were given either Treatment A or Treatment B, and survival was noted. Let S be the event that a patient selected at random survives, A be the event that a patient selected at random received Treatment A, and B be the event that a patient selected at random received Treatment B. (Round your answers to three decimal places.) (a) The following table summarizes data for men and women combined. Treatment A Treatment B Total (i) Find P(S). (ii) Find P(SIA). (iii) Find P(SIB). (i) Treatment A Treatment B Total Find P(S). Survived (ii) Find P(SIA). 218 (iv) Which treatment appears to be better? O Treatment A O Treatment B (iii) Find P(SIB). 243 461 (b) Now consider the summary data for the men who participated in the study. Died 120 82 20 57 140 139 Survived Died Total 80 20 Total 100 300 (iv) Which treatment appears to be better? O Treatment A O Treatment B 300 200 40
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