Although normality is not assumed for the paired signed rank test,
departures from normality can suggest the presence of
outliers
in the data, or of skewness in the paired differences.
Conversely, if the population from which
the paired differences were drawn is in fact normally distributed,
the paired two-sample
t test may be a more powerful alternative to the
paired signed rank test.
The normality test will give an indication of whether the
population
from which the paired differences were drawn
appears to be normally distributed, but will not indicate the cause(s)
of the nonnormality. The smaller the sample size, the less
likely the normality test will be able to detect
nonnormality.
The histogram
for paired differences has a reference
normal distribution
curve for a normal distribution with the same mean and variance
as the sample. This provides a reference for detecting gross
nonnormality (such as severe skewness) when the sample sizes are large.
Suspected
outliers
appear in a
boxplot
as individual points o or x outside
the box. If these appear on both sides of the box, they also suggest the
possibility of a
heavy-tailed
distribution. If they appear on only one side,
they suggest the possibility of a
skewed
distribution. Skewness is also
suggested if the mean (+) does not lie on or near the central line of the
boxplot, or if the central line of the boxplot does not evenly divide the box.
Examples of these plots
will help illustrate the various situations.
For values sampled from a
normal distribution,
the
normal probability plot,
(normal Q-Q plot)
has the points all lying on or near the straight line drawn
through the middle half of the points. Scattered points
lying away from the line are suspected
outliers.
Examples of these plots
will help illustrate the various situations.
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it or give you a refund.
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