Using the formula for the binomial distribution,
the probability of obtaining 7 or more "successes" with N = 8
and π
= 0.50 can be calculated to be 0.0352 as follows:
Therefore, P(7) + P(8) = 0.03125 + 0.00391 = 0.0352. The
one-tailed probability value is therefore
0.03516; The two-tailed probability value is (2)(0.03516) = 0.0732.
Technically
speaking, the sign test is a test of whether the
median is a particular value. In this example, the test is whether
the median difference between conditions is zero. The sign test is generally
less powerful than a t test of the difference
between dependent means. For the example data, the t test would be:
t(7) = -3.21. The two-tailed probability value for this t is 0.015.