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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?

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

edited 2 days ago

gung♦

109k34264532

asked 2 days ago

blue-skyblue-sky

198214

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

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

  
  
  
  

add a comment | 

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?

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

edited 2 days ago

gung♦

109k34264532

asked 2 days ago

blue-skyblue-sky

198214

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

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

  
  
  
  

add a comment | 

$begingroup$

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?

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

edited 2 days ago

gung♦

109k34264532

asked 2 days ago

blue-skyblue-sky

198214

$endgroup$

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

share|cite|improve this question

edited 2 days ago

gung♦

109k34264532

asked 2 days ago

blue-skyblue-sky

198214

share|cite|improve this question

edited 2 days ago

gung♦

109k34264532

asked 2 days ago

blue-skyblue-sky

198214

edited 2 days ago

gung♦

109k34264532

edited 2 days ago

gung♦

109k34264532

asked 2 days ago

blue-skyblue-sky

198214

asked 2 days ago

blue-skyblue-sky

198214

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

answered 2 days ago

klumbardklumbard

786512

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  +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 days ago
  

  
  
  
  

add a comment | 

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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

answered 2 days ago

klumbardklumbard

786512

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  +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 days ago
  

  
  
  
  

add a comment | 

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

answered 2 days ago

klumbardklumbard

786512

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  +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 days ago
  

  
  
  
  

add a comment | 

$begingroup$

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

answered 2 days ago

klumbardklumbard

786512

$endgroup$

 Promoted Not
Male 8 4
Female 0 8

share|cite|improve this answer

answered 2 days ago

klumbardklumbard

786512

answered 2 days ago

klumbardklumbard

786512

answered 2 days ago

klumbardklumbard

786512