Binary, Ordinal, and Categorical Data Analysis - Agricultural Statistical Data Analysis Using Stata - page 224

One-sided tests:
Ho: median of control - vitamina = 0 vs.
Ha: median of control - vitamina > 0
Pr(#positive >= 4) =
Binomial(n = 14, x >= 4, p = 0.5) = 0.9713
Ho: median of control - vitamina = 0 vs.
Ha: median of control - vitamina < 0
Pr(#negative >= 10) =
Binomial(n = 14, x >= 10, p = 0.5) = 0.0898
Two-sided test:
Ho: median of control - vitamina = 0 vs.
Ha: median of control - vitamina != 0
Pr(#positive >= 10 or #negative >= 10) =
min(1, 2*Binomial(n = 14, x >= 10, p = 0.5)) = 0.1796
In this case, the second one-sided test is appropriate because we are
interested in whether vitamin A increases weight gain. In this case,
with a probability of 0.0898, the gain in weight was not significant at
the 5% level. Interestingly, the paired t-test does indicate a significant
difference showing the greater power in the t-test. Finally, it is pos-
sible to use the signtest with a specific value, such as signtest
control=250 .
Another nonparametric test that can be used is Wilcoxon's Signed
Rank Test. This test also may be referred to as Wilcoxon's Paired
Sample Test or Wilcoxon's Matched Sample Test. This test is consid-
ered somewhat better than the Sign Test because it takes into account
the magnitude of the differences. The only requirement for the data in
this case is that it be symmetrical. In rare cases, the data may have to
be transformed if highly skewed. This test is used with data similar to
what is used with a paired sample t-test. The Wilcoxon's Signed Rank
Test will not be as powerful as the paired t-test when the data reason-
ably match the assumptions for the t-test, but it is often used with
ordinal scale data. This test can be used with paired data or against a
single data point. For an example of the latter application, open the
dataset Linseed Variety Yields.dta, which is a dataset of yields from a
new linseed variety grown at various locations in southeast England
(Clewer and Scarisbrick, 2001, p. 296). The standard linseed variety
for this area produces 2 t/ha. Enter the following command and see
the results:
signrank yield = 2