Materi Analisis Data Kategori

Exact Test
Fisher’s Statistics

Exact Tests
Test
Control
Total
►A

Favorable
Unfavorable
10
2

12

Total
2
4
6

12
6
18

test treatment and a control are
compared to determine whether the rates of
favorable response are the same.
► The sample sizes requirements for the chisquare tests are not met by these data

► if

you can consider the margins (12, 6, 12, 6)
to be fixed, then you can assume that the
data are distributed hypergeometrically and
write
► Pr(nij) = n1+!n2+!n+1!n+2!/n!n11!n12!n21!n22!
► p-value is the probability of the observed
data or more extreme data occurring under
the null hypothesis
► With Fisher’s exact test, determine the pvalue for this table by summing the

probabilities of the tables that are as likely or
less likely, given the fixed margins.

The following table includes all possible table configurations and their
associated probabilities.
Table Cell
► (1,1)
(1,2)
(2,1)
(2,2)
Probabilities
---------------------------------------------------------------------------► 12
0
0
6
0.0001
► 11
1
1
5

0.0039
---------------------------------------------------------------------------► 10
2
2
4
0.0533
---------------------------------------------------------------------------► 9
3
3
3
0.2370
► 8
4
4
2
0.4000
► 7
5
5
1

0.2560
► 6
6
6
0
0.0498
To find the one-sided p-value, you sum the probabilities as small or smaller
than those computed for the table observed, in the direction specified by
the one-sided alternative. In this case, it would be those tables in which
the Test treatment had the more favorable response, or
p = 0.0533 + 0.0039 + 0.0001 = 0.0573

► To

find the two-sided p-value, you sum
all of the probabilities that are as small
or smaller than that observed, or
► p = 0.0533 + 0.0039 + 0.0001 +
0.0498 = 0.1071