Editing Simpson's paradox (section)

===UC Berkeley gender bias===
One of the best-known examples of Simpson's paradox comes from a study of gender bias among graduate school admissions to [[University of California, Berkeley]]. The admission figures for the fall of 1973 showed that men applying were more likely than women to be admitted, and the difference was so large that it was unlikely to be due to chance.<ref name="freedman">[[David A. Freedman|David Freedman]], Robert Pisani, and Roger Purves (2007), ''Statistics'' (4th edition), [[W. W. Norton & Company|W. W. Norton]]. {{isbn|0-393-92972-8}}.</ref><ref name="Bickel">{{cite journal
 | author = [[Peter J. Bickel|P.J. Bickel]], E.A. Hammel and J.W. O'Connell
 | year = 1975
 | title = Sex Bias in Graduate Admissions: Data From Berkeley
 | journal = [[Science (journal)|Science]]
 | volume = 187
 | pages = 398–404
 | doi = 10.1126/science.187.4175.398
 | pmid = 17835295
 | issue = 4175
 | bibcode = 1975Sci...187..398B
 | s2cid = 15278703
 | url=http://homepage.stat.uiowa.edu/~mbognar/1030/Bickel-Berkeley.pdf |archive-url=https://web.archive.org/web/20160604220121/http://homepage.stat.uiowa.edu/~mbognar/1030/Bickel-Berkeley.pdf |archive-date=2016-06-04 |url-status=live
}}</ref>

{| class="wikitable" style="margin-left:auto; margin-right:auto; border:none; text-align:right;"
|-
! rowspan="2" |
! colspan="2" | All
! colspan="2" | Men
! colspan="2" | Women
|-
! Applicants
! Admitted
! Applicants
! Admitted
! Applicants
! Admitted
|-
! Total
| 12,763
| 41%
| 8,442
| style="background: #9EFF9E;" | 44%
| 4,321
| 35%
|}

However, when taking into account the information about departments being applied to, the different rejection percentages reveal the different difficulty of getting into the department, and at the same time it showed that women tended to apply to more competitive departments with lower rates of admission, even among qualified applicants (such as in the English department), whereas men tended to apply to less competitive departments with higher rates of admission (such as in the engineering department). The pooled and corrected data showed a "small but statistically significant bias in favor of women".<ref name="Bickel" />

The data from the six largest departments are listed below:

{| class="wikitable" style="margin-left:auto; margin-right:auto; border:none; text-align:right;"
|-
! rowspan="2" | Department
! colspan="2" | All
! colspan="2" | Men
! colspan="2" | Women
|-
! Applicants
! Admitted
! Applicants
! Admitted
! Applicants
! Admitted
|-
! A
| 933
| 64%
| style="background: #FE9;" | '''825'''
| 62%
| 108
| style="background: #9EFF9E;" | 82%
|-
! B
| 585
| 63%
| style="background: #FE9;" | '''560'''
| 63%
| 25
| style="background: #9EFF9E;" | 68%
|-
! C
| 918
| 35%
| 325
| style="background: #9EFF9E;" | 37%
| style="background: #FE9;" | '''593'''
| 34%
|-
! D
| 792
| 34%
| style="background: #FE9;" | 417
| 33%
| 375
| style="background: #9EFF9E;" | 35%
|-
! E
| 584
| 25%
| 191
| style="background: #9EFF9E;" | 28%
| style="background: #FE9;" | '''393'''
| 24%
|-
! F
| 714
| 6%
| style="background: #FE9;" | 373
| 6%
| 341
| style="background: #9EFF9E;" | 7%
|-
! Total
! 4526
! 39%
! 2691
! 45%
! 1835
! 30%
|-
| colspan="7" style="text-align:left;" |
Legend:<br>
{{legend|#9EFF9E|greater percentage of successful applicants than the other gender}}
{{legend|#FE9|greater number of applicants than the other gender}}
'''bold''' - the two 'most applied for' departments for each gender
|}

The entire data showed total of 4 out of 85 departments to be significantly biased against women, while 6 to be significantly biased against men (not all present in the 'six largest departments' table above). Notably, the numbers of biased departments were not the basis for the conclusion, but rather it was the gender admissions pooled across all departments, while weighing by each department's rejection rate across all of its applicants.<ref name="Bickel" />