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Guideling: Mann-Whitney
Sample Question: Two Elementary School teachers take two different approaches towards teaching Science content in their
3rd grade classrooms. Mrs. Smith teaches with an Inquiry method and Mr. Jones uses straight lecture. Both give the scheduled
SoL pre-test as scheduled by the district with the hope that one method might appear to be a better pedagogical tool.
Unfortunately, because of several school delays due to inclement weather, both teachers missed classes and were scrambling to
cover the content. The two classrooms ended up covering not only a different amount of content, but also different content
overall.
Data Why a Mann – Whitney?
1) A Mann-Whitney is a non-parametric version of a 2-sample t-test. While there weren’t
violations of the normal curve in this dataset (there wasn’t anything wrong with the test –
the score is a valid one), there were differences in the content being measured by the test.
In the end – this means that the test could be more/less fair depending on how closely the
content tested matched the content given. This alone could account for any variation
among the data – so a non-parametric test would be more valid.
2) There is a nominal DV that has two categories. The DV can be Ordinal, Interval, or
Ratio.
Step by step:
Smith Rank Jones Rank
1) Create and sum ranking columns for the (U1) (U2)
data. 19 18.5 12 13
NOTE: the ranking is done over the entire 15 16 18 17
sample.
2 1.5 11 11
2) As with any ranking system: if there are 11 11 9 8.5
ties (and there are many in this dataset),
9 8.5 2 1.5
determine which rank values the tied
variable would have received, take the 14 14.5 14 14.5
mean of those rankings and assign that 8 6.5 7 5
value to ALL of the tied scores.
5 4
3) For the Mann-Whitney, you will need the 11 11
sample size for each category. So it is 7 8 6.5
for Smith, and 12 for Jones.
19 18.5
Hint: If you want to make it easier – rearrange the 4 3
data in the columns from lowest to highest before Sum 76.5 113.5
ranking.
n1(n1 1) U1 7 12 7(7 1) 76.5
U1 n1n 2 R1
4) Calculate U 2 2 Smith (U1) = 35.50
values for each
n 2(n 2 1) 12(12 1) 113.50
Group: U2 n1n 2 R2 U2 7 12
2 2 Jones (U2) = 48.50
5) For the Mann-Whitney test, you 6) Degrees of freedom for the MW
look at the two calculated scores are the 2 sample sizes (7 and 12).
U(7,12) = 35.50, p>.05
and you will use the LOWER of
the two as the final value. 7) The Critical Value from the table
is = 18 for this sample size. With
the MW – significance is found if There are no significant differences between
the obtained value is LOWER the test scores of the two classes.
than the CV.
Psyc219: Lobo (1/12)
SPSS Guide: Mann Whitney U
Variable View:
From Menus - Select: When the window pops up:
<ANALYZE> 1) You will start with a special screen that has
3 tabs across the top: Objectives, Fields,
<Non-parametric tests> and Settings.
<Independent Samples> 2) With the Objectives tab active: Select
“Customize Analysis.”
3) When this is done – click on the “Fields”
tab.
4) With the “Fields” tab active: Place your DV into the box
marked “Test Fields”
5) With the “Fields” tab active: Place your IV into the box
marked “Groups”
6) When this is done – click on the “Settings” tab up top.
7) With the “Settings” tab active: Select Mann-Whitney U
option.
8) When completed – Hit “Run”
9) You will be presented with the following summary. Note
that while it provides the level of significance of the analysis,
and the decision to accept or reject the null hypothesis – it
does NOT give you a calculated value.
If you need that value (for publication or presentation) –
you will have to do analysis by hand.
Psyc219: Lobo (1/12)
