Information Technology Reference
In-Depth Information
others. Following these three questions, we distinguish two types of truth about
SP: the first-level truth and the second-level truth. The significance of the three
questions about the paradox is what we call the “first-level truth”, while the
significance of the first two questions in unlocking its paradoxical nature and
the conditions for its emergence is what we call the “second-level truth.” The
failure to appreciate the difference between these two levels of truth, we will
contend, is the source of its misdiagnosis. Tables 1 and 2 illustrate the two types
of SP. The data in both tables represent acceptance and rejection rates of male
and female applicants for graduate school in two departments of an imaginary
university in some year.
Tabl e 1.
Simpson's Paradox (Type I)
Acceptance
Rates
Dept 1
Dept 2
Two
Groups
Overall
Acceptance Rates
Accept Reject Accept Reject
Dept 1 Dept 2
Females
180
20
100
200
90%
33%
56%
Males
480
120
10
90
80%
10%
70%
Tabl e 2.
Simpson's Paradox (Type II)
Acceptance
Rates
Dept 1
Dept 2
Two
Groups
Overall
Acceptance Rates
Accept Reject Accept Reject
Dept 1 Dept 2
Females
90
1410
110
390
6%
22%
10%
Males
20
980
380
2620
2%
13%
10%
Table 1 represents an example of the paradox in which the association in the
sub-populations (Dept 1 and Dept 2) with higher acceptance rate for females is
reversed
in the combined population, with overall higher rates for males. Table 2
is an example that shows the paradoxical effect when the association between
“gender” and “acceptance rates” in the sub-populations
ceases
to exist in the
combined population. Though the acceptance rates for females are higher in each
department, in the combined population, those rates cease to be different.
This paper is divided into eight sections. In section two, we will propose our re-
sponsetothefirsttwoquestions.Thenwewillbrieflyintroducetwoinfluentialcausal
accounts of SP proposed independently by Judea Pearl [9] and Peter Spirtes, Clark
Glymour andRichardScheines (hereafter called'SGS') [15].In sectionfour,wewill
produce a counter-example to the causal accounts.The nextsection willbe devoted
to the “what-to-do”question. In section six, we evaluate causalaccounts (with spe-
cial attention to Pearl's) of the paradox and compare them with ours. In section
seven, we will discuss how our account affects the general notion of paradoxes and
their classification while providing a general definition of a paradox. We conclude
with some remarks in section eight.
