Fourteen points apart, and a tenth of a point the other way
Berkeley, autumn 1973, the six largest graduate departments.
2,691 men applied and 1,198 were admitted — 44.5%. 1,835 women applied
and 557 were admitted — 30.4%. That is fourteen points, from 4,526
decisions, and there is nothing wrong with the arithmetic. But four of the six
departments admitted women at a higher rate than men, and where they were
not — C and E — the men's edge was 2.9 points and 3.8. No department is fourteen points apart. The
fourteen points appear only when you add the departments up.
The whole table, all twenty-four numbers
Every figure on this page comes from these twenty-four whole numbers and nothing else. The departments are lettered rather than named in the source, and they happen to fall in order of how hard they were to get into: A took 64.4% of everyone who applied, F took 6.4%.
| dept | men | in | rate | women | in | rate | apart |
|---|
·
Six departments, and the two numbers underneath them
Each row is one department: a blue dot for the men's rate, an
amber one for the women's, and a line joining them. The dot is drawn as
big as the number of people it stands for. The two vertical marks at the bottom
are the pooled figures — the only place on the whole picture where the gap is
fourteen points, and it is not on any row.
Where they applied
The two bars are the two groups' applications, each cut into the six departments and shaded by how hard that department was to get into — pale for A, which took two in three, dark for F, which took one in sixteen. 72.3% of the women applied to C, E and F, the three that turned most people away. 33.0% of the men did. That is the whole of it: the groups did not face one admissions process, they faced six, and they queued at different ones.
Move one group into the other's departments
Here is the experiment the table cannot run. Keep each group's own admission rates — the rates they actually got, department by department — and slide their application pattern onto the other group's. Nothing about how anybody was treated changes; only where they queued.
·
Splitting the fourteen points in two
The gap comes apart exactly, into the part that is where they applied and the part that is how they were treated, and the two add back to fourteen points with nothing left over. This is a seventy-year-old piece of demography — the decomposition Kitagawa wrote down in 1955 — and it is one line of algebra, not a model: no assumption goes into it that is not already in the twenty-four numbers.
·
What this page checks about itself
Every rate on this page is a ratio of two whole numbers held in
BigInt and divided once, at the end, when it is printed. The crossing
point is solved for as a fraction rather than found by sliding the slider until
the two numbers look equal, so 66.62% and 99.24% are exact.