Transcript Exact Tests

Exact Test
Fisher’s Statistics
Exact Tests
Favorable
Test
Control
Total
►A
10
2
12
Unfavorable
2
4
6
Total
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 chi-square
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 p-value 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
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
► To