The two-sample paired sign test is used to test the null hypothesis that the
probability of a random value from the
population
of paired differences being above the specified value
is equal to the probability of a random value
being below the specified value.
Each paired difference comes from a continuous
distribution with the same median.
Strictly speaking, the population distributions need not be
the same for all the paired differences.
However, if we want a
consistent test,
we assume that the paired differences
all come from the same continuous distribution.
(The sign test
is a nonparametric
test. We need not specify or know what the
distribution is,
only that all the paired difference follow the same one.)
Because the test statistic for the paired sign test
is based only on the sign (+, -, or 0)
of the paired differences, the test can
be performed when the only information available
the sign of each paired difference.
Note that it is not assumed that the two samples are
independent of each other.
In fact, they should be related to each other such that
they create pairs of data points, such as the measurements
on two matched people in a case/control study, or
before- and after-treatment measurements on the same person.
The two-sample paired sign test is equivalent to performing
a one-sample sign test on the
paired differences.
If you are not familiar with these terms and concepts, you are advised to
consult with a statistician. Failure to understand and properly apply the
two-sample paired sign test may result in drawing erroneous conclusions from your data.
Additionally, you may want to consult the following references:
Brownlee, K. A. 1965. Statistical Theory and Methodology
in Science and Engineering. New York: John Wiley & Sons.
Conover, W. J. 1980. Practical Nonparametric Statistics. 2nd ed.
New York: John Wiley & Sons.
Daniel, Wayne W. 1978. Applied Nonparametric Statistics.
Boston: Houghton Mifflin.
Daniel, Wayne W. 1995. Biostatistics. 6th ed.
New York: John Wiley & Sons.
Hollander, M. and Wolfe, D. A. 1973. Nonparametric Statistical Methods.
New York: John Wiley & Sons.
Lehmann, E. L. 1975. Nonparametrics: Statistical Methods Based on
Ranks. San Francisco: Holden-Day.
Miller, Rupert G. Jr. 1996. Beyond ANOVA, Basics of Applied
Statistics. 2nd. ed.
London: Chapman & Hall.
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