VALIDATION OF MEASURING INSTRUMENTS 187 
ad —bc 
(25) Om 
where a, b, c¢, and d are the numbers of cases in each of the 
four quadrants of the fourfold table (233, p. 38). 
If a test is scored in terms of accuracy, in effect two series 
of measurements are made. One is the number of right 
answers, R, and the other the number of wrong answers, WW. 
Thurstone (199) has derived formulas for weighting right 
and wrong answers in such a way as to give the highest pos- 
sible correlation with the criterion, I. The number of wrong 
answers is multiplied by a constant, C, which is usually neg- 
ative, and then added to the number of right answers. Thus 
the score for a test is R + CW. The following formula 
gives the best value for the multiplying constant, C: 
(26) C= or(71R * "Rw —"1w) 
ow(’tw * rw —71r) 
If this constant is used in scoring the test, the best correla- 
tion possible between test scores and criterion will be ob- 
tained. The formula for this correlation is 
(27) Biro =f 02 £1 Ss: ph. Im Taw 
— rw 
The probable error of a correlation coefficient is an index 
of its unreliability and should be computed as an aid to the 
interpretation of the significance of the relationship which 
has been discovered. Thus a coefficient of .50 is a better 
estimate of the true relationship if its P.E. is .0o2 than if its 
PE. is .13. 
The formula for the probable error of 7 computed by any 
of the variations of the Pearson product-moment formula, or 
by the rank difference method, is 
1—r? 
(28) PE, =0.6745 = 
This formula assumes a normal correlation surface, and 
should therefore be avoided when the number of cases is 
small (233, pp. 321, 352). It also assumes that the coeffi 
3