Home
Tutorial Menu
More About WINKS
What's New?
Order WINKS


These WINKS statistics tutorials explain the use and interpretation of standard statistical analysis techniques for Medical, Pharmaceutical, Clinical Trials, Marketing or Scientific Research. The examples include howto instructions for WINKS SDA Version 6.0 Software. Download evaluation copy of WINKS. 
Parametric and Nonparametric Statistics
When
analyzing data for a research project you’re often confronted with a
decision about what kind of statistical analysis to perform. There are
literally hundreds of tests from which to choose and you have to careful to
select the one that is the most appropriate for your data. If you select an
inappropriate test then you may make an incorrect interpretation about your
data and your manuscript will likely be rejected during a journal review
process. Although it is impossible to give a definitive method for selecting
appropriate tests in a brief article such as this, one aspect of statistical
tests that is often confusing will be discussed – the difference between
parametric and nonparametric statistical tests.
When you gather scientific data, one of the first statistics you’ll
typically calculate is the mean. This statistic is used to indicate average
value of a population or sample. If the mean is combined with another common
statistic called the standard deviation, then the pair of number tells the
research both the central tendency of the group of number and their spread.
A large standard deviation reflects a large spread in the data – the numbers
are diverse and far apart. A small standard deviation reflects a tightness
of the data – the numbers are close together. However, before you can really
depend on these statistics to give you accurate information about the data,
you’re required to make the assumption that the data are normally
distributed – that is, if you were to plot the data in a histogram, it would
create a graph that looks like the wellknown bellshaped curve. When data
behave in this way you can make some simple assumptions about the data. For
example, the mean plus or minus one standard deviation contains about 65% of
the data, and the mean plus or minus two standard deviations contains about
95% of the data. This information is often used to create a range of values
in which you might expect future sampled data to appear.
When statistics are calculated under the assumption that the data follow
some common distribution such as the normal distribution we call these
parametric statistics. It follows that statistical tests based on these
parametric statistics are called parametric statistical tests. Thus, when
the data are normal, we can then use a host of wellknown parametric
statistical tests to analyze our data  such as ttests, analysis of
variance, linear regression, and others.
However, what happens when your data are not normally distributed?
Suppose you create a histogram of your data and it doesn’t look like the
bellshaped curve. Suppose it has two humps or it has most of its data at
one end of the distribution with some of the data trailing off into a long
tail. Now what can you do? There are several ways to approach nonnormal
data, but we’ll only discuss one in this article – using a nonparametric
test in lieu of a standard parametric test. Nonparametric tests are also
called distributionfree tests since they do not make the assumption that
the data follows some distribution.
For example, suppose you have two independent groups (corresponding to
two drugs) on which some measurement has been made – for example, the length
of time until relief of pain. You want to determine if one drug has a better
overall (shorter) time to relief than the other drug. However, when you
examine the data it’s obvious that the distribution of the data is not
normal (You can test for normality of data using a statistical test.) If the
data had been normally distributed, you would have performed a standard
independent group ttest on this data. But since the assumption of normality
cannot be made, what can you do? Fortunately for almost every parametric
test in the statistical toolbox, there is a corresponding nonparametric
test. In this case a corresponding nonparametric test is the MannWhitney
test. Using the MannWhitney test you can calculate a significance level to
help you determine the answer to your research question – are the values of
the observations from one group significantly lower than the observations
from the other group? (Notice that we’re not comparing means.)
Other standard parametric tests also have corresponding nonparametric
counterparts. The Wilcoxon Signed Rank test can be used for the paired
ttest. The KruskalWallis test can be used for a oneway independent group
analysis of variance, and so on.
Why not just always use nonparametric tests? Since nonparametric tests
do not make an assumption about a distribution of the data, they have less
information to use to determine significance. Thus, they are less powerful
than the parametric tests. That is, they have a more difficult time finding
statistical significance.
Therefore, if a parametric test is appropriate it should be used because
it gives you a better chance of finding significances when they exist. If
the parametric test is not appropriate, then a nonparametric test is a
reasonable substitute.
When using WINKS, you may refer to the diagrams in Appendix B (in
the printed manual) to help you determine which parametric or nonparametric
test is appropriate for your data.
