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Figure 1From “What is Simpson's paradox?”

Women admitted at Berkeley in fall 1973, against two expected counts

Against the campus-wide expectation, 277 fewer women were admitted than expected. Against each department's own admission rate, 60 more were.

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Figure 1Women admitted at Berkeley in fall 1973, against two expected counts

Grouped bar chart from Bickel, Hammel and O’Connell 1975, Tables 1 and 3: women admitted to graduate study at Berkeley in fall 1973 against two expected counts. Pooled across departments, 1,771.3 expected and 1,494 admitted, a shortfall of 277.3. Department by department over 96 departments, 1,432.9 expected and 1,493.0 admitted, a surplus of 60.1.ExpectedObserved05001,0001,5002,0001,771.31,494.0Pooled across departments (Table 1)1,432.91,493.0Department by department (Table 3)Women admitted, fall 1973

Source: Bickel et al. (1975), p. 399, Table 1 (12,763 applications to 101 departments; expected counts from the campus totals under assumptions 1 and 2) and p. 402, Table 3 (96 departments; expected counts from each department's admission rate for all applicants, under assumption 1 only). Administrative admissions records of one university.

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  • A BHO75-C1 Berkeley graduate admissions for fall 1973: 12,763 applications to 101 departments, 8,442 from men and 4,321 from women; about 44% of the men and 35% of the women admitted; expected frequencies from the marginal totals under assumptions 1 and 2 give 277 fewer women and 277 more men admitted than expected, chi-square 110.8; Table 1 prints men 3,738 admitted and 4,704 denied, women 1,494 admitted and 2,827 denied, expected admissions 3,460.7 for men and 1,771.3 for women (pp. 398, 399, Table 1): "were 8442 male applicants and 4321"; "of the males and about 35 percent of"; "chi-square value for this table is 110.8,"Bickel, Hammel & O'Connell (1975) · Bickel, Hammel & O'Connell. (1975)
  • A BHO75-C6 Expected women admitted computed department by department (each department's admission rate for all applicants times its women applicants, summed): 1,432.9 expected, 1,493.0 observed, difference 60.1, chi-square 8.55, P = .003 two-tailed; 96 departments, five with a single applicant left out; the test was proposed in another context by Cochran and by Mantel and Haenszel (pp. 401, 402, Table 3): "Expected female admittees"; "Observed female admittees"; "Ninety-six departments"Bickel, Hammel & O'Connell (1975) · Bickel, Hammel & O'Connell. (1975)

Grades: A, verified against the printed page of the primary source · B, primary source, text layer only · C, authoritative secondary · D, reported.

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APA 7

Isoglu, S. (2026). Women admitted at Berkeley in fall 1973, against two expected counts [Figure]. isoglu.com. https://isoglu.com/insights/exhibits/isoglu-2026-what-is-simpsons-paradox-fig01/

BibTeX
@misc{isoglu-2026-what-is-simpsons-paradox-fig01,
  author = {Isoglu, Sinan},
  title = {{Women admitted at Berkeley in fall 1973, against two expected counts}},
  year = {2026},
  howpublished = {Figure 1, isoglu.com},
  url = {https://isoglu.com/insights/exhibits/isoglu-2026-what-is-simpsons-paradox-fig01/},
  note = {From the essay {What is Simpson's paradox?}}
}
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<figure>
  <a href="https://isoglu.com/insights/exhibits/isoglu-2026-what-is-simpsons-paradox-fig01/">
    <img src="https://isoglu.com/social/isoglu-2026-what-is-simpsons-paradox-fig01.png" alt="Figure 1: Women admitted at Berkeley in fall 1973, against two expected counts" width="3200" height="2400">
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  <figcaption>Figure 1: Women admitted at Berkeley in fall 1973, against two expected counts. Source: Bickel et al. (1975), p. 399, Table 1 (12,763 applications to 101 departments; expected counts from the campus totals under assumptions 1 and 2) and p. 402, Table 3 (96 departments; expected counts from each department&#39;s admission rate for all applicants, under assumption 1 only). Administrative admissions records of one university. <a href="https://isoglu.com/insights/exhibits/isoglu-2026-what-is-simpsons-paradox-fig01/">View exhibit</a>.</figcaption>
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