Russel-Research-Method-in-Anthropology

608 Chapter 20
TABLE 20.5
Monolingual and Bilingual Speakers, by Gender, in a Mexican Village, 1962
old error 55
Men Women Row totals
Bilingual 61 24 85
(82%) (36%)
Monolingual 13 42 55
(18%) (64%)
Column totals 74 66 140
new error 13 24 37
55 37
55
.33
Mexican village in 1962. I’ve included the marginals and the n’s in the cells
to make it easier to do the calculation here.
Reading across table 20.5, we see that 82% of the men were bilingual, compared
to 36% of the women. Clearly, gender is related to whether someone
is a bilingual Indian/Spanish speaker or monolingual in the Indian language
only.
Suppose that for the 140 persons in table 20.5 you were asked to guess
whether they were bilingual or monolingual, but you didn’t know their gender.
Since the mode for the dependent variable in this table is ‘‘bilingual’’ (85
bilinguals compared to 55 monolinguals), you should guess that everybody is
bilingual. If you did that, you’d make 55 mistakes out of the 140 choices, for
an error rate of 55/140, or 39%. We’ll call this the old error.
Suppose, though, that you have all the data in table 20.5—you know the
mode for gender as well as for bilingual status. Your best guess now would be
that every man is bilingual and every woman is monolingual. You’d still make
some mistakes, but fewer than if you just guessed that everyone is bilingual.
How many fewer? When you guess that every man is bilingual, you make
exactly 13 mistakes, and when you guess that every woman is monolingual,
you make 24 mistakes, for a total of 37 out of 140 or 37/140 26%. This is
the new error. The difference between the old error (39%) and the new error
(26%), divided by the old error is the proportionate reduction of error, or
PRE. Thus,
PRE 5537
55
.33