Although normality is not assumed for the rank sum test,
departures from normality can suggest the presence of
outliers
in the data, or of dissimilar distributional
shape.
Conversely, if the populations from which
the samples were drawn are in fact normally distributed,
the unpaired two-sample
t test may be a more powerful alternative to the
rank sum test.
The normality test will give an indication of whether the
populations
from which the samples were drawn
appear 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.
If the sample sizes are large enough for the normality test
to correctly detect normality or nonnormality, differing results
for the normality test when applied to the two samples (i.e., normality is
rejected for only one of the samples) may indicate that
the samples do not come from populations that differ
only in location.
In that situation, the possibility of
dissimilar distributional shapes
should be considered.
The histogram
for each sample 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 when the sample sizes are large. It may also
help in judging whether the two histograms could come from
the distributions (normal or not) with the same shape and dispersion.
If the histograms for the two samples are dissimilar, then
the possibility of
dissimilar distributional shapes
should be considered.
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 suggest the
possibility of a
heavy-tailed
distribution. If they appear on only one side,
they also 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.
If the boxplots for the two samples are dissimilar, then
the possibility of
dissimilar distributional shapes
should be considered.
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.
If the normal probability plots for the two samples are dissimilar, then
the possibility of
dissimilar distributional shapes
should be considered.
If you are unsatisfied with your purchase, you may return it within 30
days for an
exchange, credit or refund.
This guarantee does not cover electronic download products, special requests requiring photocopying
or
engineering aids; however, if you cannot
edit our document(s) in your MS Word, Excel or Visio program we will fix
it or give you a refund.
Can't find what you're
looking for...?
Please call, Fax or Email Us at:
Office: (719) 649-4242
Fax: (719) 573-4205 Home Page
Click here to bookmark At-PQC™ then visit our
Toolbox to find a quality control plan that will
help you achieve an effective and efficient business
infrastructure that focuses on customer satisfaction,
continuous improvement and desirable cost savings. Visit
with us today for comprehensive assistance in developing
or choosing the right quality control plan for your
business.
Click here to visit our extensive selection of
quality control plans, policies, procedures and forms or
click here
for help with where-to-start.
We can interact with you anywhere in the USA from
8:00am to 5:00pm Monday through Friday except holidays.
At-PQC™
JnF Specialties, LLC
664 Greenscape Lane
Colorado Springs, Colorado 80916-5534
Office:
(719) 649-4242
Fax: (719) 573-4205
Email Us at:
Send an email to request next-day support or call our helpline at 719-649-4242
during your office hours
Mon - Fri except holidays.
Featured
Article:
Where to
start...
