2 EMPIRICAL STUDIES OF MEASUREMENT 



which would be correct, supposing the cases within that unit of the 

 scale to be equally frequent in all equal subdivisions of that unit 

 of scale. 



The series used were the four presented in Table I. A is an 

 almost perfect representative of the so-called 'normal' surface of 

 frequency, limited at about -f 3.2* and 3.2*. B is also a sym- 

 metrical distribution following, but not so closely, the so-called 'nor- 

 mal' type. C is a skewed distribution of the kind so frequently 

 found in mental and social measurements. D is a flattened and 

 rather sharply cut-off type of distribution, such as occurs often in 

 facts subject to conventional regulation. The number of cases was 

 for A 1,000, for B 1,307, for C 1,250 and for D 600. The mechan- 

 ical arrangement of each series was simply so many small cards or 

 slips of paper each with a number written on it. In each series 

 these cards were approximately of the same size, shape and weight. 

 From such a series, properly shuffled in a large bowl, drawings were 

 made. 



The total number of cases in any series is of course of no signifi- 

 cance. Whether a series contains 1,000, 1,100, 1,426, 13,982 or 

 160,000 cases makes no appreciable difference to any of the matters 

 to be investigated here, and in the case of a distribution of the type 

 of D, drawings of 100 from 6,000 cases would not differ appre- 

 ciably from drawings from 600. The reason for the particular 

 sizes of the total series was economy of time. 



It is most convenient to arrange series for such experiments 

 with measures + and from the central tendency, as in B and D ; 

 the time of recording the results of draws is lessened and also the 

 likelihood of errors. Thus in A 31, 37, 35, etc., would 

 be better than 61, 63, 65, etc. I give the series, however, in just 

 the way they were made and used. 



Every drawing of 10 or 50 or 55 or whatever number of cases 

 was made from the full series. However, a draw of 10 having been 

 made and recorded, a draw of 50 was obtained by adding 40 to the 

 10 and one of 100 by adding 50 to the 50. The 100 is thus from 

 the full series, but is obtained with a saving of time. 



As a rule drawings of 10 or 11, 50 or 55, 100 or 110 and 275 

 were made, but, with the larger drawings, if not exactly 50 or 100 

 were drawn, the drawing was still utilized. Of course exact sim- 

 ilarity in the size of the drawings is of no consequence whatever to 

 any of the conclusions drawn. 



