Difference between revisions of "Manuals/calci/MANNWHITNEYUTEST"
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− | <div style="font-size:25px">'''MANNWHITNEYUTEST( | + | <div style="font-size:25px">'''MANNWHITNEYUTEST (XRange,YRange,ConfidenceLevel,NewTableFlag)'''</div><br/> |
− | *<math> | + | *<math>XRange</math> is the array of x values. |
− | *<math> | + | *<math>YRange</math> is the array of y values. |
− | *<math> | + | *<math>ConfidenceLevel</math> is the value between 0 and 1. |
− | *<math> | + | *<math>NewTableFlag</math> is either TRUE or FALSE. |
+ | |||
==Description== | ==Description== | ||
Line 19: | Line 20: | ||
*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. | *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: | *To find statistic value of this test the steps are required: | ||
− | *1.For the two observations of values, find the rank all together. | + | **1.For the two observations of values, find the rank all together. |
− | *2.Add up all the ranks in a first observation. | + | **2.Add up all the ranks in a first observation. |
− | *3.Add up all the ranks in a second group. | + | **3.Add up all the ranks in a second group. |
− | *4.Select the larger rank. | + | **4.Select the larger rank. |
− | *5.Calculate the number of participants,number of people in each group. | + | **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> | + | **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. | *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>. | *<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. | + | **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 | + | **8.State Conclusion: To be significant, our obtained U has to be equal to or LESS than this critical value. |
− | critical value. | ||
==Example== | ==Example== | ||
{| class="wikitable" | {| 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 17:35, 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 |
- =MANNWHITNEYUTEST(A1:A12,B1:B12,0.05,true)
Mann Whitney U Test
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 |
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
See Also
References