the mann-whitney u test what you need to know
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The Mann-Whitney U Test What you need to know. When Should I Use the Mann-Whitney U Test?. Non-parametric distribution Independent Measures Ratio or interval data, but must be reduced to ordinal data because it is non-parametric Different variances for two groups - PowerPoint PPT PresentationTRANSCRIPT
The Mann-Whitney U The Mann-Whitney U TestTest
What you need to knowWhat you need to know
When Should I Use the When Should I Use the Mann-Whitney U Test?Mann-Whitney U Test?
• Non-parametric distributionNon-parametric distribution• Independent MeasuresIndependent Measures• Ratio or interval data, but must be reduced Ratio or interval data, but must be reduced
to ordinal data because it is non-to ordinal data because it is non-parametricparametric
• Different variances for two groupsDifferent variances for two groups• It assumes Random assignments to groupsIt assumes Random assignments to groups• Test statistic: UTest statistic: U
Mann-Whitney U TestMann-Whitney U Test What is it for? A non-parametric test to compare What is it for? A non-parametric test to compare
the central tendencies of two groupsthe central tendencies of two groups It assumes Random assignments to groupsIt assumes Random assignments to groups Test statistic: UTest statistic: U
SampleNull hypothesisThe two groupsHave the same
median
Null distributionU with n1, n2
compare
How unusual is this test statistic?
P < 0.05 P > 0.05
Reject Ho Fail to reject Ho
Mann-Whitney U test
Test statisticU1 or U2
Null HypothesisNull Hypothesis Involves the creation of two competing Involves the creation of two competing
explanations for the data recorded.explanations for the data recorded.• Idea 1:These are pattern-less random data. Idea 1:These are pattern-less random data.
Any observed patterns are due to chance. This Any observed patterns are due to chance. This is the null hypothesis is the null hypothesis H0H0
• Idea 2: There is a defined pattern in the data. Idea 2: There is a defined pattern in the data. This is the alternative hypothesis This is the alternative hypothesis H1H1
Without the statement of the competing Without the statement of the competing hypotheses, no meaning test can be run.hypotheses, no meaning test can be run.
Step OneStep One Arrange all the observations into a Arrange all the observations into a
single ranked series. That is, rank all single ranked series. That is, rank all the observations without regard to the observations without regard to which sample they are in. which sample they are in.
In other words, combine all of the In other words, combine all of the data from both groups into a single data from both groups into a single column, in order, but keep track of column, in order, but keep track of what group they came from.what group they came from.
Mann-Whitney U TestMann-Whitney U Test If you have ties:If you have ties:
• Rank them anyway, pretending they Rank them anyway, pretending they were slightly differentwere slightly different
• Find the average of the ranks for the Find the average of the ranks for the identical values, and give them all that identical values, and give them all that rankrank
• Carry on as if all the whole-number Carry on as if all the whole-number ranks have been used upranks have been used up
ExampleExampleData
142542141814
ExampleExampleSortedData
2 G12 G24 G25 G114 G114 G214 G118 G2
Data
142542141814
ExampleExampleSortedData
2 G12 G24 G25 G114 G114 G214 G118 G2
Data
142542141814
TIES
ExampleExampleSortedData
2 G12 G24 G25 G114 G114 G214 G118 G2
Data
142542141814
TIES
Rank them anyway, pretending they were slightly different
ExampleExampleRank A
2 G12 G24 G25 G114 G114 G214 G118 G2
12345678
SortedDataData
142542141814
ExampleExampleRank A
2 G12 G24 G25 G114 G114 G214 G118 G2
12345678
SortedDataData
142542141814
Find the average of the ranks for the identical values, and give them all that rank
ExampleExampleRank A
2 G12 G24 G25 G114 G114 G214 G118 G2
12345678
SortedDataData
142542141814
Average = 1.5
Average = 6
ExampleExampleRank A
2 G12 G24 G25 G114 G114 G214 G118 G2
12345678
SortedDataData
142542141814
1.51.5346668
Rank
ExampleExampleRank A
2 G12 G24 G25 G114 G114 G214 G118 G2
12345678
SortedDataData
142542141814
1.51.5346668
Rank
First, sort them back into the two groups,Then these can now be used for the Mann-Whitney U test
Step TwoStep Two Add up the ranks for the Add up the ranks for the
observations which came from observations which came from sample 1(the smaller group, fewer sample 1(the smaller group, fewer participants). participants).
Then add up the sum of ranks in Then add up the sum of ranks in sample 2 (Larger group)sample 2 (Larger group)
Step ThreeStep Three UU is then given by: is then given by:
where where nn1 is the sample size for 1 is the sample size for sample 1(smaller group), and sample 1(smaller group), and RR1 is 1 is the sum of the ranks in sample 1the sum of the ranks in sample 1
Step FourStep Four
Step FiveStep Five The smaller value of The smaller value of UU1 and 1 and UU2 is the 2 is the
one used when consulting one used when consulting significance tables. significance tables.
CompareCompare If the smaller value of U1 or U2 is If the smaller value of U1 or U2 is
smaller than the critical value in the smaller than the critical value in the chart, then the probability that the chart, then the probability that the differences in the groups is obtained differences in the groups is obtained by chance is less than 0.05, and you by chance is less than 0.05, and you may reject the null hypothesis.may reject the null hypothesis.