I. EMPLOYMENT PSYCHOLOGY 
which are used when the number of cases is small, when the 
divisions are alternative rather than continuous, or when the 
measures are in terms of ranks. 
The method of rank difference takes into account only the 
positions of the measures in the series, and should be used 
when the measures are expressed as ranks. There are two 
formulas: Spearman’s method of rank differences: 
(17) ptm 
N(N2—1) 
where D represents any difference in the rank of a person in 
the two series of measurements, and IV represents the num- 
ber of paired measurements; and his “footrule for correla- 
tion”: 
6Zg 
(18) R=1 TR 
where g represents only differences in ranks where there is a 
gain in the second series over the first. Both p and R may 
be converted into 7 by use of tables provided in most text- 
books on statistics, based on formulas derived by Pearson 
(see Tables 5 and 6). The conversion of p into r has doubt- 
ful value since the difference will usually be much less than 
the probable error of the correlation coefficient. For ex- 
ample, a p value of .48 has an r value of .50, but the prob- 
able error of a correlation coefficient of .50 with 30 cases is 
.09. Since the error of the coefficient is so much greater than 
the correction to obtain 7, it would have been just as well 
to leave it as p. The Scott Company (164) published con- 
venient tables to shorten the labor of calculating p. These 
tables are reproduced in the Appendix as Tables 3 and 4. 
Instructions for their use are given below. 
INSTRUCTIONS FOR CALCULATING RANK DIFFERENCE COEFFICI- 
ENTS (ForMuULA 17) WITH THE USE OF TABLES 3, 4, 
AND 5. (SEE REFERENCE 164). 
1. Arrange each of the two series of measurements to be corre- 
lated in rank order. Every pair of measurements is thus repre- 
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