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Purpose
This procedure compares
two dependent samples. It runs Wilcoxon Matched Pairs Test and Sign Test.
Preparations
Run Statistics→Nonparametric
Statistics →Comparing two
dependent samples.... command.
Results
Wilcoxon Matched Pairs Test.
The Wilcoxon
matched pairs test is a nonparametric alternative to the t-test for dependent
(correlated) samples.
The procedure assumes that the variables under consideration were measured on a
scale that allows the rank ordering of observations based on each variable
(i.e., ordinal scale) and that allows rank ordering of the differences between
variables (this type of scale is sometimes referred to as an ordered metric
scale, see Coombs, 1950). Thus, the required assumptions for this test are more
stringent than those for the Sign test. However, if they are met, that is, if
the magnitudes of differences (e.g., different ratings by the same individual)
contain meaningful information, then this test is more powerful than the Sign
test. In fact, if the assumptions for the parametric t-test for dependent
samples are met, then this test is almost as powerful as the t-test.
Sign test.
The Sign test is
a nonparametric alternative to the t-test for dependent samples. The test is
applicable to situations when the researcher has two measures (e.g., under two
conditions) for each subject and wants to establish that the two measurements
(or conditions) are different.
The only assumption required by this test is that the
underlying distribution of the variable of interest is continuous; no
assumptions about the nature or shape of the underlying distribution are
required. The test simply computes the number of times (across subjects) that
the value of the first variable (A) is larger than that of the second variable
(B). Under the null hypothesis (stating that the two variables are not different
from each other) we expect this to be the case about 50% of the time. Based on
the binomial distribution we can compute a z value for the observed number of
cases where A > B, and compute the associated tail probability for that z value.
For small n's (less than 20) you may prefer to use the tabulated values found in
Siegel and Castellan (1988) to evaluate statistical significance.
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