Statistical Methods for Psychology

and

Since the distribution is normal and we know its mean and standard deviation (the standard

error), we can calculate

and obtain from the tables of the normal distribution an approximation of the true probability

of a value of at least as low as the one obtained. (It is immaterial whether we use or

in this situation, since they will produce equal values of z, differing only in sign.)

To illustrate the computations for the case in which the larger ranks fall in the smaller

groups and to illustrate the use of the normal approximation (although we do not really need

to use an approximation for such small sample sizes), consider the data in Table 18.4. These

WS¿

WS WS

z=

Statistic 2 Mean

Standard deviation

=

WS 2

n 11 n 11 n 2112

2

B

n 1 n 21 n 11 n 2112

12

Standard error=

B

n 1 n 21 n 11 n 2112

12

676 Chapter 18 Resampling and Nonparametric Approaches to Data

Table 18.4 Hypothetical data on birthweight of infants born to

mothers with different levels of prenatal care

Beginning of Care

Third Trimester First Trimester

Birthweight Rank Birthweight Rank

1680 2 2940 10

3830 17 3380 16

3110 14 4900 18

2760 5 2810 9

1700 3 2800 8

2790 7 3210 15

3050 12 3080 13

2660 4 2950 11

1400 1

2775 6

=

100276

2 126.6667

=2.13

=

1002

818110112

2

B

8110218110112

12

z=

WS 2

n 11 n 11 n 2112

2

B

n 1 n 21 n 11 n 2112

12

WS¿= 2 W 2 WS= 1522100 = 52

WS= a 1 Ranks in Group 2 2 = 100