Difference between revisions of "Manuals/calci/MANNWHITNEYUTEST"

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==Feature==
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<div style="font-size:25px">'''MANNWHITNEYUTEST (XRange,YRange,ConfidenceLevel,NewTableFlag)'''</div><br/>
 +
*<math>XRange</math> is the array of x values.
 +
*<math>YRange</math> is the array of y values.
 +
*<math>ConfidenceLevel</math> is the value between 0 and 1.
 +
*<math>NewTableFlag</math> is either TRUE or FALSE.
 +
 
 +
 
 +
==Description==
 +
*This function gives the test statistic value of the Mann Whitey U test.
 +
*It is one type of Non parametric test.It is also called Mann–Whitney–Wilcoxon,Wilcoxon rank-sum test or Wilcoxon–Mann–Whitney test.
 +
*Using this test we can analyze rank-ordered data.
 +
*This test is  alternative to the independent-sample, Student t test, and yields results identical to those obtained from the Wilcoxon Two Independent Samples Test.
 +
*This test is used to compare differences between two independent groups when the dependent variable is either ordinal or continuous, but not normally distributed.
 +
*Mann whitey u test is having the following properties:
 +
*1.Data points should be independent from each other.
 +
*2.Data do not have to be normal and variances do not have to be equal.
 +
*3.All individuals must be selected at random from the population.
 +
*4.All individuals must have equal chance of being selected.
 +
*5.Sample sizes should be as equal as possible but for some differences are allowed.
 +
*Suppose the two groups of the populations have  distributions with the same shape it can be viewed as a comparison of two medians.With out the assumption the Mann-Whitney test does not compare medians.
 +
*To find statistic value of this test the steps are required:
 +
**1.For the two observations of values, find the rank all together.
 +
**2.Add up all the ranks in a first observation.
 +
**3.Add up all the ranks in a second group.
 +
**4.Select the larger rank.
 +
**5.Calculate the number of participants,number of people in each group.
 +
**6.Calculate the test statistic:<math>U=\frac{n_1*n_2+nx(nx+1)}{2-Tx}</math>
 +
*where <math>n_1</math> and <math>n_2</math> are number of participants and number of people.
 +
*<math>Tx</math> is the larger rank total.<math>nx</math> is the similar value of <math>n1</math>.
 +
**7.State Result: In this step we have to take a decision of null hypothesis either accept or reject depending on the z value using critical value table.
 +
**8.State Conclusion: To be significant, our obtained U has to be equal to or LESS than this critical value.
 +
 
 +
==Example==
 +
{| class="wikitable"
 +
|+
 +
| X || Y
 +
|-
 +
| 87 || 71
 +
|-
 +
| 72 || 42
 +
|-
 +
| 94 || 69
 +
|-
 +
| 49 || 97
 +
|-
 +
| 56 || 78
 +
|-
 +
| 88 || 84
 +
|-
 +
| 74 || 57
 +
|-
 +
| 61 || 64
 +
|-
 +
| 80 || 78
 +
|-
 +
| 52 || 73
 +
|-
 +
| 75 || 85
 +
|-
 +
| 0 || 91
 +
|}
 +
 
 +
#=MANNWHITNEYUTEST(A1:A12,B1:B12,0.05,true)
 +
 
 +
'''Mann Whitney U Test'''
 +
{| class="wikitable"
 +
|+Ranks
 +
|-
 +
! x !! y
 +
|-
 +
|20|| 10
 +
|-
 +
|11||2
 +
|-
 +
| 23||9
 +
|-
 +
| 3|| 24
 +
|-
 +
| 5||15.5
 +
|-
 +
| 21 || 18
 +
|-
 +
|13 || 6
 +
|-
 +
| 7 || 8
 +
|-
 +
|17|| 15.5
 +
|-
 +
| 4|| 12
 +
|-
 +
| 14|| 19
 +
|-
 +
| 1|| 22
 +
|}
 +
 
 +
{| class="wikitable"
 +
|-
 +
| Ranks|| 139 || 161
 +
|-
 +
|Median||73|| 75.5 
 +
|-
 +
| n || 12  || 12   
 +
|}
 +
 
 +
{| class="wikitable"
 +
|+Results
 +
|-
 +
|U1|| 83
 +
|-
 +
|U2||61
 +
|-
 +
| U||61
 +
|-
 +
| E(U1) || 150
 +
|-
 +
|E(U2) || 150
 +
|-
 +
|E(U) || 72
 +
|-
 +
|StDdev || 17.320508075688775
 +
|-
 +
|<math>\alpha</math> || 0.05
 +
|-
 +
|  z  || -0.6350852961085883
 +
|-
 +
| p ||0.5253738185447192
 +
|}
 +
 
 +
==Related Videos==
 +
 
 +
{{#ev:youtube|hw3z49QoB1s|280|center|MannWhitney U Test}}
 +
 
 +
==See Also==
 +
*[[Manuals/calci/LEVENESTEST| LEVENESTEST]]
 +
*[[Manuals/calci/MOODSMEDIANTEST| MOODSMEDIANTEST]]
 +
*[[Manuals/calci/RIEMANNZETA| RIEMANNZETA]]
 +
 
 +
==References==
 +
 
 +
*[http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test Mann-Whitney U test documentation on Wikipedia]
 +
*[http://www.qimacros.com/hypothesis-testing/mann-whitney-test-excel/ Mann-Whitney test for independent samples in Excel]
 +
 
 +
 
 +
 
 +
 
 +
*[[Z_API_Functions | List of Main Z Functions]]
 +
 
 +
*[[ Z3 |  Z3 home ]]

Latest revision as of 16:35, 14 June 2018

MANNWHITNEYUTEST (XRange,YRange,ConfidenceLevel,NewTableFlag)


  • is the array of x values.
  • is the array of y values.
  • is the value between 0 and 1.
  • is either TRUE or FALSE.


Description

  • This function gives the test statistic value of the Mann Whitey U test.
  • It is one type of Non parametric test.It is also called Mann–Whitney–Wilcoxon,Wilcoxon rank-sum test or Wilcoxon–Mann–Whitney test.
  • Using this test we can analyze rank-ordered data.
  • This test is alternative to the independent-sample, Student t test, and yields results identical to those obtained from the Wilcoxon Two Independent Samples Test.
  • This test is used to compare differences between two independent groups when the dependent variable is either ordinal or continuous, but not normally distributed.
  • Mann whitey u test is having the following properties:
  • 1.Data points should be independent from each other.
  • 2.Data do not have to be normal and variances do not have to be equal.
  • 3.All individuals must be selected at random from the population.
  • 4.All individuals must have equal chance of being selected.
  • 5.Sample sizes should be as equal as possible but for some differences are allowed.
  • Suppose the two groups of the populations have distributions with the same shape it can be viewed as a comparison of two medians.With out the assumption the Mann-Whitney test does not compare medians.
  • To find statistic value of this test the steps are required:
    • 1.For the two observations of values, find the rank all together.
    • 2.Add up all the ranks in a first observation.
    • 3.Add up all the ranks in a second group.
    • 4.Select the larger rank.
    • 5.Calculate the number of participants,number of people in each group.
    • 6.Calculate the test statistic:
  • where and are number of participants and number of people.
  • is the larger rank total. is the similar value of .
    • 7.State Result: In this step we have to take a decision of null hypothesis either accept or reject depending on the z value using critical value table.
    • 8.State Conclusion: To be significant, our obtained U has to be equal to or LESS than this critical value.

Example

X Y
87 71
72 42
94 69
49 97
56 78
88 84
74 57
61 64
80 78
52 73
75 85
0 91
  1. =MANNWHITNEYUTEST(A1:A12,B1:B12,0.05,true)

Mann Whitney U Test

Ranks
x y
20 10
11 2
23 9
3 24
5 15.5
21 18
13 6
7 8
17 15.5
4 12
14 19
1 22
Ranks 139 161
Median 73 75.5
n 12 12
Results
U1 83
U2 61
U 61
E(U1) 150
E(U2) 150
E(U) 72
StDdev 17.320508075688775
0.05
z -0.6350852961085883
p 0.5253738185447192

Related Videos

MannWhitney U Test

See Also

References



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