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Mann-Whitney U Test

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					Mann-Whitney U Test
Mann-Whitney U Test


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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
   Advantage
    −   Instant interaction
    −   Less intrusive than phone (may be…)
    −   Low cost, low set up effort….
    −   ???
   Disadvantage
    −   Connection availability
    −   Bandwidth?
    −   ??
Groupware / Shared cervices

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

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

   Example
    −   Numerous free applications
   Advantage
    −   No timing or scheduling issue
    −   Sending message or files
   Disadvantage
    −   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]
   Advantage
    −   Direct calls, Conference calls
    −   ??
   Disadvantage
    −   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)
   “AT&T Connect,” http://www.business.att.com/enterprise/Service/unified-
     communications-enterprise/conferencing-services-enterprise/web-conferencing-
     enterprise/campaign=telepresence/?GUID=680D43A7-7F15-422E-BEAB-
     010C0671C441&WT.srch=1 (current Oct. 21, 2009)
   “WebEx,” http://www.webex.com/ (current Oct. 21, 2009)
   “Voice Over Internet Protocol,”
     http://en.wikipedia.org/wiki/Voice_over_Internet_Protocol (current Oct. 21, 2009)
   M. R. Thissen, J. M. Page, M. C. Bharati, and T. L. Austin, “Communication Tools for
     Distributed Software Development Teams,” ACM, Jul. 7 2004.

				
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