Russel-Research-Method-in-Anthropology

610 Chapter 20
For each cell in a bivariate table, simply subtract the expected frequency
from the observed and square the difference. Then divide by the expected frequency
and sum the calculations for all the cells. Clearly, if all the observed
frequencies equal all the expected frequencies, then 2 will be zero; that is,
there will be no relation between the variables.
While 2 can be zero, it can never have a negative value. The more the O’s
differ from the E’s (i.e., something nonrandom is going on), the bigger 2 gets.
Calculating the Expected Frequencies for 2 in Bivariate Tables
Chi-square is calculated on raw frequencies, not on percentages in tables.
The expected frequencies are calculated for each cell with the formula:
F e (R t)(C t )
n
Formula 20.7
where F e is the expected frequency for a particular cell in a table; (R t ) is the
frequency total for the row in which that cell is located; (C t ) is the frequency
total for the column in which that cell is located; and n is the total sample size
(the lower-right-hand marginal).
The test for 2 can be applied to any size bivariate table. Table 20.6 shows
a hypothetical census of observed adherents, in four Native American tribes,
of three competing religions, and the expected number of adherents to each
religion. Reading across the top of the table, in tribe 1, there are 150 Catholics,
104 Protestants, and 86 members of the Native American Church. For
Tribe 1, we expect:
(340)(590)
2,011
99.75
Catholics (the cell in the upper-left-hand corner of table 20.6). We expect
119.03 Protestants and 121.22 members of the Native American Church for
Tribe 1, and so on.
Chi-square for this table is a walloping 162.08. To determine the number of
degrees of freedom for a bivariate 2 table, we calculate:
df (r1)(c1) Formula 20.8
which means: multiply the number of rows, minus one, by the number of columns,
minus one. For table 20.6, there are:
(41 rows)(31 columns) 6 degrees of freedom
Without even looking it up in appendix D (the 2 distribution), it’s clear that
the competing religions are not evenly distributed across the groups. If you