Mann Whitneyipa
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Hallmon, David. (Summer 2008) C&I 557 Final Project. Mann-Whitney U-Test Technique—IPA. Southern Illinois University-Carbondale.
Information Processing Analysis of the Mann-Whitney U-Test Technique Start Enter w/ previously unseen sample of data having only two groups with no duplicate values & a Critical Values of U and U’ Table for a One-tailed Test at α = 0.05. (max group size = 20)
Recall Rule: Ordinal measurements: attributes of the data can be rank-ordered e.g. lowest to highest. Also, continuous interval & ratio data can be converted to ordinal data.
End
Mann-Whitney U-Test is not an appropriate technique for this data sample.
Can each group’s data values follow an ordinal scale of measurement?
No
Yes Determine how many values are found in each group.
Label the group with the most values A and the smaller group B End
Sample too large to determine statistical significance with the given Critical Values of U Table.
Yes
Either group have more than 20 values?
No
Combine the A + B to determine the Total Number of Values TNV
Create a table with three rows labeled: Rank, Value & Group; and have enough columns for the TNV
Recall Fact: Rows are horizontal and columns are vertical.
Sort all values from the least in value (far left) to highest in value (far right) in your table & record in appropriate row: rank, value, and group.
Assign a rank of 1 to the smallest of the values (far left) and a 2 for the next smallest, and continue consecutive ranks until the highest rank (far right).
Recall Example: Hypothetical data set 1 a
2 a
3 b
4 a
5 b
6 a
7 b
8 a
9 b
10 b
The first B is preceded by 3A’s, the second B by 2A’s, and the third B by 1A’s. Count the number of times each B precedes a A
Calculate U
Recall Technique: U= the sum of the number of times each A proceeds a B. In hypothetical data set U = 3+2+1+0+0 = 6
Count the number of times each A precedes a B Recall Example: Hypothetical data set 1 a
Calculate U’
2 a
3 b
4 a
5 b
6 a
7 b
8 a
9 b
10 b
The first A is preceded by 5B’s, the second A by 5B’s, the third A by 4B’s, the fourth A by 3B’s, and the fifth by 2B’s.
Z Recall Technique: U= the sum of the number of times each B proceeds an A. In hypothetical data set U’ = 5+5+4+3+2 = 19
1
Hallmon, David. (Summer 2008) C&I 557 Final Project. Mann-Whitney U-Test Technique—IPA. Southern Illinois University-Carbondale.
Information Processing Analysis of the Mann-Whitney U-Test Technique Cont.
Z
Yes
Are your calculated U & U’ equal?
Mann-Whitney U-Test is an appropriate technique for this data sample, but the data is not statistically significant.
End
No Refer to Critical Values of U and U’ for a One-tailed Test at a = 0.05 Table. Locate the top left corner. Replace n1 with A, and n2 with B.
Recall Fach: The Critical Values of U and U’ are determined by the formula: U= A*B – U’
Locate the size of your A group in the top row of the Critical Values of U and U’ for a One-tailed Test at a = 0.05 Table and circle it.
Locate the size of your B group in the left most column of the Critical Values of U and U’ for a One-tailed Test at a = 0.05 Table and circle it.
Locate where your critical values of U & U’ are located by intersecting your circled column and rows in the Critical Values of U and U’ for a One-tailed Test at a = 0.05 Table.
End
Recall Fact: The top number represents your U critical limit. The bottom number represents your U’ critical limit.
No
Is your U value ≤ the U critical limit?
Yes
The results from the Mann-Whitney U-Test reveal that your data is NOT statistically significant at the α = .05 level.
No
Is your U’ value ≥ the U’ critical limit?
Yes Recall Example: Hypothetical data set U = 6 which was not ≤ the critical limit.
The results from the Mann-Whitney U-Test reveal that your data IS statistically significant at the α = .05 level. Other factors must be involved!
End
Recall Example: Hypothetical data set U’ = 19 which was not ≥ the critical limit.
The results from the Mann-Whitney U-Test reveal that your data IS statistically significant at the α = .05 level. Other factors must be involved!
End
2
Information Processing Analysis of the Mann-Whitney U-Test Technique Start Enter w/ previously unseen sample of data having only two groups with no duplicate values & a Critical Values of U and U’ Table for a One-tailed Test at α = 0.05. (max group size = 20)
Recall Rule: Ordinal measurements: attributes of the data can be rank-ordered e.g. lowest to highest. Also, continuous interval & ratio data can be converted to ordinal data.
End
Mann-Whitney U-Test is not an appropriate technique for this data sample.
Can each group’s data values follow an ordinal scale of measurement?
No
Yes Determine how many values are found in each group.
Label the group with the most values A and the smaller group B End
Sample too large to determine statistical significance with the given Critical Values of U Table.
Yes
Either group have more than 20 values?
No
Combine the A + B to determine the Total Number of Values TNV
Create a table with three rows labeled: Rank, Value & Group; and have enough columns for the TNV
Recall Fact: Rows are horizontal and columns are vertical.
Sort all values from the least in value (far left) to highest in value (far right) in your table & record in appropriate row: rank, value, and group.
Assign a rank of 1 to the smallest of the values (far left) and a 2 for the next smallest, and continue consecutive ranks until the highest rank (far right).
Recall Example: Hypothetical data set 1 a
2 a
3 b
4 a
5 b
6 a
7 b
8 a
9 b
10 b
The first B is preceded by 3A’s, the second B by 2A’s, and the third B by 1A’s. Count the number of times each B precedes a A
Calculate U
Recall Technique: U= the sum of the number of times each A proceeds a B. In hypothetical data set U = 3+2+1+0+0 = 6
Count the number of times each A precedes a B Recall Example: Hypothetical data set 1 a
Calculate U’
2 a
3 b
4 a
5 b
6 a
7 b
8 a
9 b
10 b
The first A is preceded by 5B’s, the second A by 5B’s, the third A by 4B’s, the fourth A by 3B’s, and the fifth by 2B’s.
Z Recall Technique: U= the sum of the number of times each B proceeds an A. In hypothetical data set U’ = 5+5+4+3+2 = 19
1
Hallmon, David. (Summer 2008) C&I 557 Final Project. Mann-Whitney U-Test Technique—IPA. Southern Illinois University-Carbondale.
Information Processing Analysis of the Mann-Whitney U-Test Technique Cont.
Z
Yes
Are your calculated U & U’ equal?
Mann-Whitney U-Test is an appropriate technique for this data sample, but the data is not statistically significant.
End
No Refer to Critical Values of U and U’ for a One-tailed Test at a = 0.05 Table. Locate the top left corner. Replace n1 with A, and n2 with B.
Recall Fach: The Critical Values of U and U’ are determined by the formula: U= A*B – U’
Locate the size of your A group in the top row of the Critical Values of U and U’ for a One-tailed Test at a = 0.05 Table and circle it.
Locate the size of your B group in the left most column of the Critical Values of U and U’ for a One-tailed Test at a = 0.05 Table and circle it.
Locate where your critical values of U & U’ are located by intersecting your circled column and rows in the Critical Values of U and U’ for a One-tailed Test at a = 0.05 Table.
End
Recall Fact: The top number represents your U critical limit. The bottom number represents your U’ critical limit.
No
Is your U value ≤ the U critical limit?
Yes
The results from the Mann-Whitney U-Test reveal that your data is NOT statistically significant at the α = .05 level.
No
Is your U’ value ≥ the U’ critical limit?
Yes Recall Example: Hypothetical data set U = 6 which was not ≤ the critical limit.
The results from the Mann-Whitney U-Test reveal that your data IS statistically significant at the α = .05 level. Other factors must be involved!
End
Recall Example: Hypothetical data set U’ = 19 which was not ≥ the critical limit.
The results from the Mann-Whitney U-Test reveal that your data IS statistically significant at the α = .05 level. Other factors must be involved!
End
2
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