MANNWHITNEYUTEST(xRange,yRange,Confidencelevel,Logicalvalue,Testtype)
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle xRange}
is the array of x values.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle yRange}
is the array of y values.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Confidencelevel}
is the value between 0 and 1.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Logicalvalue}
is either TRUE or FALSE.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Testtype}
is the type of the test.
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:Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle U={\frac {n_{1}*n_{2}+nx(nx+1)}{2-Tx}}}
- where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n_1}
and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n_2}
are number of participants and number of people.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Tx}
is the larger rank total.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle nx}
is the similar value of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n1}
.
- 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:B13,0.05,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
|
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha}
|
0.05
|
| z |
-0.6350852961085883
|
| p |
0.5253738185447192
|
Mann Whitney U Test
Ranks
| X
|
Y
|
| 19
|
9
|
| 10
|
1
|
| 22
|
8
|
| 2
|
23
|
| 4
|
14.5
|
| 20
|
17
|
| 12
|
5
|
| 6
|
7
|
| 16
|
14.5
|
| 3
|
11
|
| 13
|
18
|
| 0
|
21
|
| Ranks
|
127
|
149
|
| Median
|
74
|
75.5
|
| n
|
11
|
12
|
RESULTS
|
|
| U1
|
71
|
| U2
|
61
|
| U
|
61
|
| E(U1)
|
132
|
| E(U2)
|
144
|
| E(U)
|
66
|
| StdDev
|
16.24807680927192
|
| a
|
0.05
|
| z
|
-0.3077287274483318
|
| p
|
0.7582891742833224
|
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