CK-12 Probability and Statistics - Advanced

http://www.ck12.org Chapter 12. Non-Parametric Statistics

U 1 =n 1 n 2 +

n 1 (n 1 + 1 )

2

−R 1

U 2 =n 1 n 2 +

n 2 (n 2 + 1 )

2

−R 2

where:

n 1 =number of observations in sample 1

n 2 =number of observations in sample 2

R 1 =sum of the ranks assigned to sample 1

R 2 =sum of the ranks assigned to sample 2

We use the smaller of the two calculated test statistics (i.e. – the lesser ofU 1 orU 2 ) to evaluate our hypotheses in
smaller samples or to calculate thezscore when working with larger samples.

When working with larger samples, we need to calculate two additional pieces of information: the mean of the
sampling distribution(μU)and the standard deviation of the sampling distribution(σU). These calculations are
relatively straightforward when we know the numbers of observations in each of the samples. To calculate these
figures we use the following formulas:

μU=

n 1 n 2

2

and

σU=

√

[(n 1 )](n 2 )(n 1 +n 2 + 1 )

12

Finally, we use the general formula for the test statistic to test our null hypothesis:

z=

U−μU

σU

Example:

Say that we are interested in determining the attitudes on the current status of the economy from women that work
outside the home and from women that do not work outside the home. We take a sample of 20 women that work
outside the home (sample 1) and a sample of 20 women that do not work outside the home (sample 2) and administer
a questionnaire that measures their attitude about the economy. These data are found in the tables below:

TABLE12.5:

Women Working Outside the Home Women Working Outside the Home

Score Rank

9 1

12 3

13 4

19 8

21 9