Binary, Ordinal, and Categorical Data Analysis - Agricultural Statistical Data Analysis Using Stata - page 223

One-sided tests:
Ho: median of tomato - apricot = 0 vs.
Ha: median of tomato - apricot > 0
Pr(#positive >= 7) =
Binomial(n = 22, x >= 7, p = 0.5) = 0.9738
Ho: median of tomato - apricot = 0 vs.
Ha: median of tomato - apricot < 0
Pr(#negative >= 15) =
Binomial(n = 22, x >= 15, p = 0.5) = 0.0669
Two-sided test:
Ho: median of tomato - apricot = 0 vs.
Ha: median of tomato - apricot != 0
Pr(#positive >= 15 or #negative >= 15) =
min(1, 2*Binomial(n = 22, x >= 15, p = 0.5)) = 0.1338
The results are presented with probabilities for equal medians, with
one median greater than the other and, finally, with one median less
than the other. Which of these results to use is dependent on the data
and what specifically the experiment is about. In this particular case,
the two-sided test is the appropriate analysis because we are not inter-
ested in one particular snack being less than or greater than the other.
In this case, with a probability of 0.1338, the medians do not differ
from one another or, to put it another way, the difference between the
medians do not differ from 0.
There are cases where the one-sided test is going to be more appropri-
ate. For example, load the dataset Heifer Vitamin A.dta. This is a dataset
of heifers paired for size to examine the effect of vitamin A on weight
gain (Steel and Torrie, 1980. p. 98). Enter the following command:
signtest control = vitamina
with the following results:
Sign test
sign | observed expected
-------------+------------------------
positive | 4 7
negative | 10 7
zero | 0 0
-------------+------------------------
all | 14 14