Mann Whitney U test

1. By khurram

2. Ho- samples are taken from identical distributions.
H1- samples are not taken from identical
distributions.
These are the standard hypothesis’s for the Mann-
Whitney U test.

3. After writing the hypothesis’s the data must be ranked this
can be easily done.
Ranking data
•Start by giving the smallest data number 1 rank.
•Keep giving ranks (smallest to largest) until you have two
data pieces with the same number. Here must choose the
mid point of the ranks which the data is between and give
this rank to both data pieces e.g. If three eights where in
the data and this was your smallest data piece u would not
give each eight a rank 1, but instead give the number
between all three eights, which would be 2 (between 1-3)
from then on you must carry on from rank 3, so your next
data piece will be rank 4.
•Carry on until all data pieces are given a rank
•Add up the ranks in each column

4. n(n-1)
Using the formula U= T - 2
T = the sum of the ranks in one column
N= the number of data pieces in that column
An example of formula being used is
8x7
U= 91.5 - 2 = 28

5. This is the easiest part of the hypothesis test.
Use the formula booklet (page 33) to determine the critical
value where n= sample 1 (total data pieces) and m=
sample 2 (total data pieces)
An example of this is n=8 m=11 and then using the
formula booklet to determine the critical value as 24.

6. If the critical value is larger than the test statistic (U) then
we reject Ho
But if the test statistic is larger than the critical value then
we accept the Ho
After this we must write a couple of short sentences to
sum up the test and conclude
A model answer is
Accept/reject Ho there is sufficient/insufficient evidence
at the 5/10/20% significance level to suggest there the
samples are (not) taken from identical distributions