Explanations Wilcoxon

It is used to compare two sets of scores that come from the same participants.
This can occur

when we wish to investigate any change in scores from one time point to another, or when
individuals are subjected to more than one condition.
For example, you could use a Wilcoxon signed-rank test to understand whether there was a
difference in smokers' daily cigarette consumption before and after a 6 week hypnotherapy
programme (i.e., your dependent variable would be "daily cigarette consumption", and your two
related groups would be the cigarette consumption values "before" and "after" the hypnotherapy
programme).
Characteristics explanation:
Assumption #1: Your dependent variable should be measured at the ordinal or continuous
level. Examples of ordinal variables include Likert items (e.g., a 7-point item from "strongly
agree" through to "strongly disagree"), amongst other ways of ranking categories (e.g., a 5-point
item explaining how much a customer liked a product, ranging from "Not very much" to "Yes, a
lot"). Examples of continuous variables (i.e., interval or ratio variables) include revision time
(measured in hours), intelligence (measured using IQ score), exam performance (measured
from 0 to 100), weight (measured in kg), and so forth.
Assumption #2: Your independent variable should consist of two categorical, "related

groups" or "matched pairs". "Related groups" indicates that the same subjects are present in both
groups. The reason that it is possible to have the same subjects in each group is because each subject
has been measured on two occasions on the same dependent variable. For example, you might have
measured 10 individuals' performance in a spelling test (the dependent variable) before and after they
underwent a new form of computerized teaching method to improve spelling. You would like to know if
the computer training improved their spelling performance. The first related group consists of the
subjects at the beginning (prior to) the computerized spelling training and the second related group
consists of the same subjects, but now at the end of the computerized training. The Wilcoxon signed-
rank test can also be used to compare different subjects within a "matched-pairs" study design, but this
does not happen very often. Nonetheless, to learn more about the different study designs you use with
a Wilcoxon signed-rank test, see our enhanced Wilcoxon signed-rank test guide.
Assumption #3: The distribution of the differences between the two related groups (i.e.,

the distribution of differences between the scores of both groups of the independent variable; for
example, the reaction time in a room with "blue lighting" and a room with "red lighting") needs to
be symmetrical in shape.
This is where the Wilcoxon Rank Sum Test comes in. It only makes the first two
assumptions of independence and equal variance. It does not assume our data have have a
known distribution. Known distributions are described with math formulas. These formulas
have parameters that dictate the shape and/or location of the distribution. For example,
variance and mean are the two parameters of the Normal distribution that dictate its shape
and location, respectively. Since the Wilcoxon Rank Sum Test does not assume known
distributions, it does not deal with parameters, and therefore we call it a non-parametric test.
Whereas the null hypothesis of the two-sample t test is equal means, the null hypothesis of
the Wilcoxon test is usually taken as equal medians. Another way to think of the null is that
the two populations have the same distribution with the same median. If we reject the null,
that means we have evidence that one distribution is shifted to the left or right of the other.
Since we’re assuming our distributions are equal, rejecting the null means we have
evidence that the medians of the two populations differ. The R statistical programming
environment, which we use to implement the Wilcoxon rank sum test below, refers to this a
“location shift”.
In order to run a Mann-Whitney U test, the following four assumptions must be met.
o Assumption #1: You have one dependent variable that is measured at

the continuous or ordinal level. Examples of continuous
variables include revision time (measured in hours), intelligence
(measured using IQ score), exam performance (measured from 0 to
100), weight (measured in kg), and so forth. Examples of ordinal
variables include Likert items (e.g., a 7-point scale from "strongly
agree" through to "strongly disagree"), amongst other ways of ranking
categories (e.g., a 5-point scale explaining how much a customer liked a
product, ranging from "Not very much" to "Yes, a lot").
o Assumption #2: You have one independent variable that consists
of two categorical, independent groups (i.e., a dichotomous
variable). Example independent variables that meet this criterion
include gender (two groups: "males" or "females"), employment status
(two groups: "employed" or "unemployed"), transport type (two groups:
"bus" or "car"), smoker (two groups: "yes" or "no"), trial (two groups:
"intervention" or "control"), and so forth.
o Assumption #3: You should have independence of observations,
which means that there is no relationship between the observations in
each group of the independent variable or between the groups
themselves. For example, there must be different participants in each
group with no participant being in more than one group. This is more of
a study design issue than something you can test for, but it is an
important assumption of the Mann-Whitney U test. If your study fails this
assumption, you will need to use another statistical test instead of the
Mann-Whitney U test (e.g., a Wilcoxon signed-rank test).
o Assumption #4: You must determine whether the distribution of
scores for both groups of your independent variable (e.g., the
distribution of scores for "males" and the distribution of scores for
"females" for the independent variable, "gender") have the same
shape or a different shape. This will determine how you interpret the
results of the Mann-Whitney U test. Since this is a critical assumption of
the Mann-Whitney U test, and will affect how to work your way through
this guide, we discuss this further in the next section.

Explanations Wilcoxon

Uploaded by

Copyright:

Available Formats

Explanations Wilcoxon

Uploaded by

Document Information

Original Description:

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Explanations Wilcoxon

Uploaded by

Copyright:

Available Formats

It is used to compare two sets of scores that come from the same participants.

This can occur

Assumption #2: Your independent variable should consist of two categorical, "related

Assumption #3: The distribution of the differences between the two related groups (i.e.,

o Assumption #1: You have one dependent variable that is measured at

You might also like