SIMPSON'S PARADOX

Simpson's paradox is well known in statistics. It occurs when a small population having a high proportion of significant members is agglomerated with a large population that has a low proportion of significant members.

It is illustrated below by a constructed example that prima facie shows sexual discrimination in a college selection test.

College X offered 1000 places in two courses in the faculty of Economics.  In year 2000AD there were 1000 female applicants, and 1000 male applicants.  181 females were accepted, and 819 males were accepted.

So although 50% of applicants were male and 50% were female, only 18.1% of females were accepted, but 81.9% of male applicants were accepted.

Was there a clear case of sexual discrimination in the selection process?

Not so!

The faculty of Economics at college X offered two courses.  One was Accountancy and 900 places were offered.  The other was Ecology and because the course was new, only 100 places were offered.

There were 950 male applicants for the Accountancy qualification, and 100 females.  In Ecology there were 50 male applicants and 900 female applicants.
 

Acceptances Places
Male
Applicants
Male
Acceptances
% Males
Accepted
Female
Applicants
Female
Acceptances
% Females
Accepted
Accountancy
900
950
814
86%
100
86
86%
Ecology
100
50
5
10%
900
95
11%
Total Faculty
1000
1000
819
81.9%
1000
181
18.1%

Despite the fact (row 3) that 81.9% of male applicants to Accountancy and Ecology were accepted,
and that only 18.1% of female applicants to Accountancy and Ecology were accepted,

there was no discrimination.

There was no discrimination in Accountancy, (row 1) because 814 of 950 males and 86 of 100 females obtained places.  So 86% of male applicants students and 86% of females applicant students gained places in Accountancy.

There was no discrimination in Ecology, (row 2) because 5 of 50 males and 95 of 900 females obtained places, so 10% of male applicants and 11% of females applicants for places in Ecology gained places.

When, prima facie a case of discrimination proves on analysis of the parts not to be discrimination, or
when, prima facie a case of no discrimination proves on analysis of the parts to show discrimination:

THAT IS PROBABLY SIMPSON'S PARADOX AT WORK.

BACK
 

Originally published 11 May 2000.