Mann Whitney U

Conceptual Explanation

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

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,

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.

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

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.

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

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).

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

These two distributions happen to be normally distributed,

These two distributions happen to be normally distributed,

Average of 5 slices

Average of 9 slices

These two distributions happen to be normally distributed,

. . . so we would use an independent-sample t-test.

Average of 5 slices

Average of 9 slices

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

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

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.

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.

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

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

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

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

Notice how the Median is not sensitive or another way of saying – it is resistant to Outliers.

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

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

Notice how the Median is not sensitive or another way of saying – it is resistant to Outliers.

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

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.

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.