PROPHET StatGuide: Compare SamplesTesting equality of means or locations
Compare Samples lets you perform a test comparing the means
or medians (locations)
of 1 or more samples. You provide the basic
components of the design (number of samples,
pairing/blocking,
and the normality
of the distribution
of the sampling
population(s)).
Given this information and the data, Prophet selects the
test by the following scheme, based on your selection for the
question "Are all samples sampled from a normal distribution?"
in the Compare Samples dialog.

If you designate that each sample is sampled from a
normal distribution,
then Prophet performs the appropriate normaltheorybased test
(onesample t test,
paired twosample t test,
unpaired twosample t test,
oneway ANOVA,
or
oneway blocked ANOVA)
based on the number of samples and whether or not the data are
paired/blocked.

If you designate that at least one sample is not sampled
from a
normal distribution,
then Prophet performs the appropriate
nonparametric test
(onesample signed rank test,
paired signed rank test,
rank sum test,
KruskalWallis test,
or
Friedman's test) based on the number of samples
and whether or not the data are
paired/blocked.

If you designate that the
normality
of the population distributions
is undetermined, then Prophet first performs a
normality test
for each of the samples. If one or more of the samples fails
the normality test, then Prophet performs the appropriate
nonparametric test
(onesample signed rank test,
paired signed rank test,
rank sum test,
KruskalWallis test,
or
Friedman's test) based on the number of samples
and whether or not the data are
paired/blocked.
Otherwise, Prophet performs the appropriate normaltheorybased test
(onesample t test,
paired twosample t test,
unpaired twosample t test,
oneway ANOVA,
or
oneway blocked ANOVA)
based on the number of samples and whether or not the data are
paired/blocked.
Compare Samples is a way of choosing among possible tests
that may be suitable for your data.
The complete list of tests that might be performed is given
below. For each pair of tests listed, the first test is
the one that will be performed if you specify that each
sample is sampled from a normal population distribution, or
if you are undecided and the normality test does not
reject the null hypothesis
of normality. The second test is the one that will be performed
if you specify that the
data are not all sampled from normal population distributions, or
if you are undecided and the normality test rejects the null hypothesis
of normality.
For more information about a particular test, follow the appropriate link.
To properly analyze and interpret
results of a Compare Samples analysis, you should be familiar with the
following terms and concepts:
If you are not familiar with these terms and concepts, you are advised to
consult with a statistician. Failure to understand and properly apply a
Compare Samples analysis 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: HoldenDay.
 Miller, Rupert G. Jr. 1986. Beyond ANOVA, Basics of Applied
Statistics. New York: John Wiley & Sons.
 Neter, J., Wasserman, W., and Kutner, M.H. 1990. Applied
Linear Statistical Models. 3rd ed. Homewood, IL: Irwin.
 Sokal, Robert R. and Rohlf, F. James. 1995. Biometry. 3rd. ed.
New York: W. H. Freeman and Co.
 Winer, B.J., Brown, D.R., and Michels, K.M. 1991. Statistical Principles
in Experimental Design. 3rd ed. New York: McGraw Hill.
 Zar, Jerrold H. 1996. Biostatistical Analysis. 3rd ed.
Englewood Cliffs, NJ: PrenticeHall.
Onesample tests:
Twosample unpaired tests:
Twosample paired tests:
Multisample (oneway) unblocked tests:
Oneway ANOVA
(unblocked) (test whether several treatment effects
(means) are equal)
KruskalWallis test
(test whether several population distribution functions are
identical against the alternative that they differ by location)
Multisample (oneway) blocked tests:
Do a keyword search of PROPHET
StatGuide.
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Last modified: March 17, 1997
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