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Understanding “table margins”

Performing a two tailed test given a contingency tableDirection of relationship in 2x2 contingency tablesWhy do odds ratios from formula and R's fisher.test differ? Which one should one choose?Validity of a statistical procedure to calculate an odds ratio for a Fisher's exact test?Exact test for m x n contingency table conditional (i.e. fixed by design) on one marginHow to calculate significance for pairwise Fst (fixation index)?How can p=1 in Fisher's exact test?What is the difference using a Fisher's Exact Test vs. a Logistic Regression for $2 times 2$ tables?Fishers exact test meaning of “greater” and “less”Interpreting infinite odds ratio and confidence interval from Fisher's test

.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;

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 Mar 28 at 14:30

gung♦

113k3434 gold badges283283 silver badges554554 bronze badges

asked Mar 28 at 13:42

blue-skyblue-sky

20533 silver badges1515 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Please add the [self-study] tag & read its wiki.
  $endgroup$
  – gung♦
  Mar 28 at 14:31
  

  
  
  
  

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 Mar 28 at 14:30

gung♦

113k3434 gold badges283283 silver badges554554 bronze badges

asked Mar 28 at 13:42

blue-skyblue-sky

20533 silver badges1515 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Please add the [self-study] tag & read its wiki.
  $endgroup$
  – gung♦
  Mar 28 at 14:31
  

  
  
  
  

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 Mar 28 at 14:30

gung♦

113k3434 gold badges283283 silver badges554554 bronze badges

asked Mar 28 at 13:42

blue-skyblue-sky

20533 silver badges1515 bronze badges

$endgroup$

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 Mar 28 at 14:30

gung♦

113k3434 gold badges283283 silver badges554554 bronze badges

asked Mar 28 at 13:42

blue-skyblue-sky

20533 silver badges1515 bronze badges

share|cite|improve this question

edited Mar 28 at 14:30

gung♦

113k3434 gold badges283283 silver badges554554 bronze badges

asked Mar 28 at 13:42

blue-skyblue-sky

20533 silver badges1515 bronze badges

edited Mar 28 at 14:30

gung♦

113k3434 gold badges283283 silver badges554554 bronze badges

edited Mar 28 at 14:30

gung♦

113k3434 gold badges283283 silver badges554554 bronze badges

asked Mar 28 at 13:42

blue-skyblue-sky

20533 silver badges1515 bronze badges

asked Mar 28 at 13:42

blue-skyblue-sky

20533 silver badges1515 bronze badges

1 Answer
1

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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 Mar 28 at 13:54

klumbardklumbard

92066 silver badges1212 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  +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♦
  Mar 28 at 14:32
  

  
  
  
  

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 Mar 28 at 13:54

klumbardklumbard

92066 silver badges1212 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  +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♦
  Mar 28 at 14:32
  

  
  
  
  

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 Mar 28 at 13:54

klumbardklumbard

92066 silver badges1212 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  +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♦
  Mar 28 at 14:32
  

  
  
  
  

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 Mar 28 at 13:54

klumbardklumbard

92066 silver badges1212 bronze badges

$endgroup$

 Promoted Not
Male 8 4
Female 0 8

share|cite|improve this answer

answered Mar 28 at 13:54

klumbardklumbard

92066 silver badges1212 bronze badges

answered Mar 28 at 13:54

klumbardklumbard

92066 silver badges1212 bronze badges

answered Mar 28 at 13:54

klumbardklumbard

92066 silver badges1212 bronze badges