Understanding “table margins”












2












$begingroup$


I'm working on a statistics quiz and asked the following:






What tables (with the same margins) would constitute stronger evidence of a gender bias effect in the calculation of the p-value using Fisher's exact test?



table with sex vs promoted




Using R I've calculated Fishers exact test with following results: 



fisher.test(table, alternative="greater")



#    Fisher's Exact Test for Count Data

# 

# data:  table

# p-value = 0.2596

# alternative hypothesis: true odds ratio is greater than 1

# 95 percent confidence interval:

#  0.4173146       Inf

# sample estimates:

# odds ratio 

#   2.838407


I'm unsure how to answer the question. What does "same margins" mean in this context? The closest I've found is this comment in relation to "margin totals" from Wikipedia's article on Fisher's exact test:




In this sense, the test is exact only for the conditional distribution and not the original table where the margin totals may change from experiment to experiment.







r hypothesis-testing fishers-exact







share|cite|improve this question











$endgroup$












  • $begingroup$
    Please add the [self-study] tag & read its wiki.
    $endgroup$
    – gung♦
    2 hours ago
















2












$begingroup$


I'm working on a statistics quiz and asked the following:






What tables (with the same margins) would constitute stronger evidence of a gender bias effect in the calculation of the p-value using Fisher's exact test?



table with sex vs promoted




Using R I've calculated Fishers exact test with following results: 



fisher.test(table, alternative="greater")



#    Fisher's Exact Test for Count Data

# 

# data:  table

# p-value = 0.2596

# alternative hypothesis: true odds ratio is greater than 1

# 95 percent confidence interval:

#  0.4173146       Inf

# sample estimates:

# odds ratio 

#   2.838407


I'm unsure how to answer the question. What does "same margins" mean in this context? The closest I've found is this comment in relation to "margin totals" from Wikipedia's article on Fisher's exact test:




In this sense, the test is exact only for the conditional distribution and not the original table where the margin totals may change from experiment to experiment.







r hypothesis-testing fishers-exact







share|cite|improve this question











$endgroup$












  • $begingroup$
    Please add the [self-study] tag & read its wiki.
    $endgroup$
    – gung♦
    2 hours ago














2












2








2





$begingroup$


I'm working on a statistics quiz and asked the following:






What tables (with the same margins) would constitute stronger evidence of a gender bias effect in the calculation of the p-value using Fisher's exact test?



table with sex vs promoted




Using R I've calculated Fishers exact test with following results: 



fisher.test(table, alternative="greater")



#    Fisher's Exact Test for Count Data

# 

# data:  table

# p-value = 0.2596

# alternative hypothesis: true odds ratio is greater than 1

# 95 percent confidence interval:

#  0.4173146       Inf

# sample estimates:

# odds ratio 

#   2.838407


I'm unsure how to answer the question. What does "same margins" mean in this context? The closest I've found is this comment in relation to "margin totals" from Wikipedia's article on Fisher's exact test:




In this sense, the test is exact only for the conditional distribution and not the original table where the margin totals may change from experiment to experiment.







r hypothesis-testing fishers-exact







share|cite|improve this question











$endgroup$




I'm working on a statistics quiz and asked the following:






What tables (with the same margins) would constitute stronger evidence of a gender bias effect in the calculation of the p-value using Fisher's exact test?



table with sex vs promoted




Using R I've calculated Fishers exact test with following results: 



fisher.test(table, alternative="greater")



#    Fisher's Exact Test for Count Data

# 

# data:  table

# p-value = 0.2596

# alternative hypothesis: true odds ratio is greater than 1

# 95 percent confidence interval:

#  0.4173146       Inf

# sample estimates:

# odds ratio 

#   2.838407


I'm unsure how to answer the question. What does "same margins" mean in this context? The closest I've found is this comment in relation to "margin totals" from Wikipedia's article on Fisher's exact test:




In this sense, the test is exact only for the conditional distribution and not the original table where the margin totals may change from experiment to experiment.







r hypothesis-testing fishers-exact




r hypothesis-testing fishers-exact






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share|cite|improve this question













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edited 2 hours ago









gung♦

109k34264532




109k34264532










asked 3 hours ago









blue-skyblue-sky

198214




198214












  • $begingroup$
    Please add the [self-study] tag & read its wiki.
    $endgroup$
    – gung♦
    2 hours ago


















  • $begingroup$
    Please add the [self-study] tag & read its wiki.
    $endgroup$
    – gung♦
    2 hours ago
















$begingroup$
Please add the [self-study] tag & read its wiki.
$endgroup$
– gung♦
2 hours ago




$begingroup$
Please add the [self-study] tag & read its wiki.
$endgroup$
– gung♦
2 hours ago










1 Answer
1






active

oldest

votes


















4












$begingroup$

The "margins" means the numbers along the right side and bottom of the table that indicate the sum of the elements in that row or column. You're being asked: "what kind of tables would indicate stronger evidence of gender bias given the restriction that there must be: 8 people promoted, 12 people not promoted, 12 males, and 8 females?"



For example, if the table looked like:



         Promoted      Not

Male     8             4

Female   0             8


We can see clear evidence of gender bias in who gets promoted or not. So you're being asked to characterize all such tables that look "worse" in terms of gender bias.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    +1, but please be cautious about providing complete answers to homework type questions, our policy is to engage & give hints (see the [self-study] tag's wiki).
    $endgroup$
    – gung♦
    2 hours ago











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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









4












$begingroup$

The "margins" means the numbers along the right side and bottom of the table that indicate the sum of the elements in that row or column. You're being asked: "what kind of tables would indicate stronger evidence of gender bias given the restriction that there must be: 8 people promoted, 12 people not promoted, 12 males, and 8 females?"



For example, if the table looked like:



         Promoted      Not

Male     8             4

Female   0             8


We can see clear evidence of gender bias in who gets promoted or not. So you're being asked to characterize all such tables that look "worse" in terms of gender bias.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    +1, but please be cautious about providing complete answers to homework type questions, our policy is to engage & give hints (see the [self-study] tag's wiki).
    $endgroup$
    – gung♦
    2 hours ago
















4












$begingroup$

The "margins" means the numbers along the right side and bottom of the table that indicate the sum of the elements in that row or column. You're being asked: "what kind of tables would indicate stronger evidence of gender bias given the restriction that there must be: 8 people promoted, 12 people not promoted, 12 males, and 8 females?"



For example, if the table looked like:



         Promoted      Not

Male     8             4

Female   0             8


We can see clear evidence of gender bias in who gets promoted or not. So you're being asked to characterize all such tables that look "worse" in terms of gender bias.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    +1, but please be cautious about providing complete answers to homework type questions, our policy is to engage & give hints (see the [self-study] tag's wiki).
    $endgroup$
    – gung♦
    2 hours ago














4












4








4





$begingroup$

The "margins" means the numbers along the right side and bottom of the table that indicate the sum of the elements in that row or column. You're being asked: "what kind of tables would indicate stronger evidence of gender bias given the restriction that there must be: 8 people promoted, 12 people not promoted, 12 males, and 8 females?"



For example, if the table looked like:



         Promoted      Not

Male     8             4

Female   0             8


We can see clear evidence of gender bias in who gets promoted or not. So you're being asked to characterize all such tables that look "worse" in terms of gender bias.






share|cite|improve this answer









$endgroup$



The "margins" means the numbers along the right side and bottom of the table that indicate the sum of the elements in that row or column. You're being asked: "what kind of tables would indicate stronger evidence of gender bias given the restriction that there must be: 8 people promoted, 12 people not promoted, 12 males, and 8 females?"



For example, if the table looked like:



         Promoted      Not

Male     8             4

Female   0             8


We can see clear evidence of gender bias in who gets promoted or not. So you're being asked to characterize all such tables that look "worse" in terms of gender bias.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 2 hours ago









klumbardklumbard

786512




786512












  • $begingroup$
    +1, but please be cautious about providing complete answers to homework type questions, our policy is to engage & give hints (see the [self-study] tag's wiki).
    $endgroup$
    – gung♦
    2 hours ago


















  • $begingroup$
    +1, but please be cautious about providing complete answers to homework type questions, our policy is to engage & give hints (see the [self-study] tag's wiki).
    $endgroup$
    – gung♦
    2 hours ago
















$begingroup$
+1, but please be cautious about providing complete answers to homework type questions, our policy is to engage & give hints (see the [self-study] tag's wiki).
$endgroup$
– gung♦
2 hours ago




$begingroup$
+1, but please be cautious about providing complete answers to homework type questions, our policy is to engage & give hints (see the [self-study] tag's wiki).
$endgroup$
– gung♦
2 hours ago


















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