# Mann-Whitney U Test by fjwuxn

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```									Mann-Whitney U Test
Mann-Whitney U Test

Are you sure you want
to go over this?
Mann-Whitney U Test

Difficult!!!!
Mann-Whitney                                          Here You Go!

“In statistics, the Mann–Whitney U test (also called the
Mann–Whitney–Wilcoxon (MWW), Wilcoxon rank-sum test,
or Wilcoxon–Mann–Whitney test) is a non-parametric test
for assessing whether two independent samples of
observations come from the same distribution. It is one of
the best-known non-parametric significance tests. It was
proposed initially by Frank Wilcoxon in 1945, for equal
sample sizes, and extended to arbitrary sample sizes and
in other ways by H. B. Mann and Whitney (1947). MWW is
virtually identical to performing an ordinary parametric two-
sample t test on the data after ranking over the combined
samples.”
http://en.wikipedia.org/wiki/Mann–Whitney_
U
Mann-Whitney----BREAK IT DOWN

Mann–Whitney U test --- A.K.A
-- Mann–Whitney–Wilcoxon (MWW),
-- Wilcoxon rank-sum test
-- Wilcoxon–Mann–Whitney test

http://en.wikipedia.org/wiki/Mann–Whitney_
U
Mann-Whitney...”a non-parametric
test...”
   Non-Parametric
− Tests of differences between groups (independent
samples);
− Tests of differences between variables (dependent samples);
− Tests of relationships between variables.
   nonparametric methods were developed to be used in cases
when the researcher knows nothing about the parameters of the
variable of interest in the population (hence the name
nonparametric)‫‏‬

http://www.statsoft.com/textbook/stnonpar.htm
l
Mann-Whitney
Mann-Whitney

Where:
U=Mann-Whitney U test
N1=sample size one
N2= Sample size two
R = Rank of the sample size

http://en.wikipedia.org/wiki/Mann–Whitney_
U
Example?
It's So easy....
IQ TEST          Test Score
44
Stress
2
Rank
1
SCORES:          50
68
2
2
2
3
Step 1:
70                  2     4
- Order Data
72                  2     5
- Make Sure Ranks
74                  1     6
Assigned (low-hight)‫‏‬
75                  2     7
76                  2     8
78                  1     9
79                  1    10
81                  2    11
82                  1    12
83                  2    13
87                  1    14
88                  2    15
90                  1    16
91                  1    17
92                  2    19
92                  1    19
92                  1    19
93                  1    21
94                  2    22
http://www.harding.edu/sbreezeel/460%20Files/Statbook/CHAPTER12.pd
f
2:
IQ TEST                                    Step e into two
d         n
- Divi s based o e
l
group ng Variab
SCORES:                                      group
i

X1               R1         X2           R2
74               6          44           1
78               9          50           2
79               10         68           3
Fewer Values    82               12         70           4
assigned to    87               14         72           5
group 1      90               16         75           7
91                17        76           8
92               19         81           11
92               19         83           13
93               21         88           15
n=10                         92          19     Sum of Values
94           22
n=12

ƩR1 = 143         ƩR2 = 110

http://www.harding.edu/sbreezeel/460%20Files/Statbook/CHAPTER12.pd
f
This is now called
IQ TEST                                      a “Solution Matrix”

SCORES:
X1               R1         X2     R2
74               6          44     1
n is the
78               9          50     2
number of
79               10         68     3
cases
82               12         70     4
87               14         72     5
90               16         75     7
91
92
17
19
76
81
8
11
n2 =
92               19         83     13    12
93               21         88     15    n1 = 10
92     19
94     22

ƩR1 = 143         ƩR2 = 110
Mann-Whitney
Apply these two
Formulas

http://www.harding.edu/sbreezeel/460%20Files/Statbook/CHAPTER12.pd
f
Mann-Whitney

http://www.harding.edu/sbreezeel/460%20Files/Statbook/CHAPTER12.pd
f
Mann-Whitney
Mann-Whitney

Now....
Look up values in two charts of critical values....

If U < than the lowest two R's
and U' < than the highest two R's

then

The observed differences were not large enough to be
statistically significant

http://www.harding.edu/sbreezeel/460%20Files/Statbook/CHAPTER12.pd
f
Mann-Whitney                                            if it is unlikely to
have occurred by
chance

www2.enel.ucalgary.ca/People/eberlein/publications/s3028.pd
f
First Challenge met---MANN-
WHITLEY SOLVED!!!!!
2nd Challenge: Find alternative
ways of communicating during
requirements negotiation
Tools for Requirements
Negotitations
   WINWIN:
− Developed at USC in 1990's by Boehm
− Aids in the capture, negotiation, and coordination of
requirements for a large system.
− Assumes a group of people, called stakeholders, have signed
on with the express purpose of discussing and reﬁning the
requirements of their proposed system.

Boehm, B., Egyed, A., Port, D., Shah, A., Kwan, J., Madachy, R.,
"A Stakeholder Win-Win Approach to Software Engineering
Education", Annals of Software Engineering, 1999.
Tools for Requirements
Negotitations
   The WinWin Process:

https://www.goldpractices.com/practices/rto/images/3.jp
g
Boehm, B. and Egyed, A. (1998). WinWin Requirements
Negotiation Processes: A Multi-Project Analysis.
Proceedings of the International Conference on Software
Processes (ICSP’98).
Communication in Distributed
Software RE
   Easy WinWin is a requirements deﬁnition
approach that is based on a Group Support
System (GSS) to enable the involvement and
interaction of key stakeholders.

Boehm B., & P. Grünbacher, “Supporting Collaborative
Requirements Negotiation: The EasyWinWin Approach”,
Proc. International Conference on Virtual
Worlds and Simulation VWSIM 2000
Communication in Distributed
Software RE
   Easy WinWin:
−    Step 1. Refine and Expand Negotiation Topics
−    Step 2. Brainstorm Stakeholder Win Conditions
−    Step 3. Converge on Win Conditions.
−    Step 4. Define a Glossary of Key Terms
−    Step 5. Prioritize Win Conditions
−    Step 6. Surface Issues and Constraints
−    Step 7. The WinWin Tree: Win Conditions, Issues,
Options, Agreements.
−    Step 8. Organize Negotiation Results.
Gruenbacher, P. and Briggs, B.: "Surfacing Tacit
Knowledge in Requirements Negotiation: Experiences using
EasyWinWin," Proceedings of the Hawaii International
Conference on Systems Sciences, 2001.
Communication in Distributed
Software RE

−   WikiWinWin: Easy WinWin implementation using
the Wiki framework

Da Yang, Di Wu, Supannika Koolmanojwong, A. Winsor
Brown, Barry W. Boehm, "WikiWinWin: A Wiki Based
System for Collaborative Requirements Negotiation," Hawaii
International Conference on System Sciences, pp. 24,
Proceedings of the 41st Annual Hawaii International
Conference on System Sciences (HICSS 2008), 2008.
“Communication Tools for Distributed Software
Development Teams”

By M. R. Thissen, J. M. Page, M. C. Bharati, and
T. L. Austin (From RTI International)
Tools

Instant Messing and Chat
Groupware / Shared services

Web Conferencing

Email

Telephone
Instant Messaging and Chat

   Example
−   Different messengers (yahoo, gtalk, skype, etc.)
−   IRC
−   Instant interaction
−   Less intrusive than phone (may be…)
−   Low cost, low set up effort….
−   ???
−   Connection availability
−   Bandwidth?
−   ??
Groupware / Shared cervices

   Example
−   Lotus Notes [1]
−   Microsoft Exchange [2]
−   Calendar
−   Contract list
−   Arrange meeting
−   ???
−   Connection availability
−   ??
Web Conferencing

   Example
−   AT&T [3]
−   WebEx [4]
−   Live audio-video
−   ??
−   Connection availability
−   Bandwidth
−   Cost and setup effort
−   Geographical distance and time issue??
Email

   Example
−   Numerous free applications
−   No timing or scheduling issue
−   Sending message or files
−   Not suitable for issues that require discussion
−   Might not be good in case of emergencies
Telephone

   Example
−   Plain Old Telephone Service (POTS)
−   Voice Over Internet Protocol (VOIP) [5]
−   Direct calls, Conference calls
−   ??
−   Security issue
−   Audio only, no visual support
References


    “IBM Lotus Notes,” http://en.wikipedia.org/wiki/IBM_Lotus_Notes (current Oct. 21,
2009)
   “Microsoft Exchange Client,” http://en.wikipedia.org/wiki/Microsoft_Exchange_Client
(current Oct. 21, 2009)