Decision-Based Learning -What is a Mann Whitney U?

1. Mann Whitney U
Conceptual Explanation

2. Parametric inferential tests assume certain things about
the variables being tested which are sometimes not
true,

3. Parametric inferential tests assume certain things about
the variables being tested which are sometimes not
true, such as, the distribution should be somewhat
normal but,

4. Parametric inferential tests assume certain things about
the variables being tested which are sometimes not
true, such as, the distribution should be somewhat
normal but,
… is actually skewed.

5. When the assumption of a normal distribution is not
met, there is another class of statistical test which can
still answer important questions.

6. When the assumption of a normal distribution is not
met, there is another class of statistical test which can
still answer important questions.
These tests are called non-parametric tests.

7. One non-parametric test is the Mann-Whitney U test
which is an analogical to the independent samples t-test.

8. One non-parametric test is the Mann-Whitney U test
which is an analogical to the independent samples t-test.
Remember that the independent t-test compares the
means of a dependent variable (pizza slice
consumption) across two levels (football and basketball
players) of an independent variable (Type of Athlete).

9. One non-parametric test is the Mann-Whitney U test
which is an analogical to the independent samples t-test.
Remember that the independent t-test compares the
means of a dependent variable (pizza slice
consumption) across two levels (football and basketball
players) of an independent variable (Type of Athlete).
Football Players Pizza Slices Eaten
Bubba 7
Cutter 8
Raider 9
Thunder 9
Thor 10
Zetron 11
Basketball Players Pizza Slices Eaten
Duncan 3
Durant 4
George 5
Lebron 5
Wade 6
Westbrook 7

10. These two distributions happen to be normally
distributed,

11. These two distributions happen to be normally
distributed,
Average of 5
slices
Average of 9
slices

12. These two distributions happen to be normally
distributed,
Average of 5
slices
Average of 9
slices
. . . so we would use an independent-sample t-test.

13. But what if one or both of the distributions were not
normal

14. But what if one or both of the distributions were not
normal
Football Players Pizza Slices Eaten
Bubba 7
Cutter 8
Raider 9
Thunder 9
Thor 10
Zetron 11
Basketball Players Pizza Slices Eaten
Duncan 3
Durant 4
George 5
Lebron 5
Wade 15
Westbrook 16
Average of 8
slices
Average of 9
slices

15. Notice how Westbrook and Wade are extreme outliers.
Notice also how the number of pizzas they eat (15 & 16
respectively) pulls the average up from 5 to 8 slices.

16. Notice how Westbrook and Wade are extreme outliers.
Notice also how the number of pizzas they eat (15 & 16
respectively) pulls the average up from 5 to 8 slices.
Computing an independent samples t-test would show
that the difference between football and basketball
players is not significant.

17. We need a statistical method that is NOT SENSITIVE TO
OUTLIERS.

18. Below we compare the Means of these two groups with
their Medians:

19. Below we compare the Means of these two groups with
their Medians:
Football Players Pizza Slices Eaten
Bubba 7
Cutter 8
Raider 9
Thunder 9
Thor 10
Zetron 11
Mean 9
Median 9
Basketball Players Pizza Slices Eaten
Duncan 3
Durant 4
George 5
Lebron 5
Wade 15
Westbrook 16
Mean 8
Median 5

20. Below we compare the Means of these two groups with
their Medians:
Football Players Pizza Slices Eaten
Bubba 7
Cutter 8
Raider 9
Thunder 9
Thor 10
Zetron 11
Mean 9
Median 9
Basketball Players Pizza Slices Eaten
Duncan 3
Durant 4
George 5
Lebron 5
Wade 15
Westbrook 16
Mean 8
Median 5
Notice how the Median is not sensitive or another way
of saying – it is resistant to Outliers.

21. Below we compare the Means of these two groups with
their Medians:
Football Players Pizza Slices Eaten
Bubba 7
Cutter 8
Raider 9
Thunder 9
Thor 10
Zetron 11
Mean 9
Median 9
Basketball Players Pizza Slices Eaten
Duncan 3
Durant 4
George 5
Lebron 5
Wade 15
Westbrook 16
Mean 8
Median 5
Notice how the Median is not sensitive or another way
of saying – it is resistant to Outliers.

22. The Mann-Whitney U is a NON-PARAMETRIC test that is
NOT sensitive to outliers because it is computed using
the MEDIAN and NOT THE MEAN.

23. The Mann-Whitney U is a NON-PARAMETRIC test that is
NOT sensitive to outliers because it is computed using
the MEDIAN and NOT THE MEAN.
Because it uses the MEDIAN, the Mann-Whitney U test
operates on subjects, rank-order position in the overall
distribution rather than on their deviance from the
mean or the differences between the means of the two
groups.