Understanding "table margins"

Question

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.

Answer 1

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.