Statistical Analysis for Education and Psychology Researchers

3 Select the test statistic SR which is the sum of the ranks for the smallest group (n). The
twenty-two observations, ranked from smallest to largest are shown (lower school
teachers are underlined):
Observation 21 26 28 30 30 30 31 32 34 38 39
Rank 12355 5 7891011
Observation 40 40 42 44 48 51 52 54 65 66 68
Rank 12.5 12.5 14 15 16 17 18 19 20 21 22

The test statistic S (Sum of the rank scores) for the smallest group (n=10) is 116.

This approximates to the following sampling distribution:

where SE is the standard error

The observed SR is 116, and the expected Sum where ns is the

number in the smaller group and N is the total sample size (n 1 +n 2 ). Expected or

mean SR is 115 (10×11.5).

The standard error of SR is

where t is the number of ties in the jth group and h is the number of groupings of

different tied scores. In this example is evaluated as:

tied scoren of ties Total

30 3 =2

40 2× =0.5

Summed over all tied scores=2.5

The standard error of SR is therefore:

4 The test statistic Z, adjusted for continuity (observed score −0.5) and corrected for ties
in the data is:

Inferences involving rank data 223