VALIDATION OF MEASURING INSTRUMENTS 179
sented by a pair of ranks—the relative positions assigned those
measurements in the two series.
2. Obtain the difference between the two ranks assigned each
case.
3. Square each of these differences. The squares are read from
Table 3. Note that the decimals may be omitted from the squares
without appreciable error.
4. Add these squares of the differences. This sum (TD?) is
to be found in the body of Table 4.
5. Refer in Table 4 to the proper column for the number of
cases used (NV). Thus, if 21 cases were ranked, use the second
column on page 253. Run down this column until you find the
entry nearest the obtained ZD2.
6. Read the entry in this same line at either side of the page
(first or last column). This entry is p. The desired coefficient of
correlation (7) may be obtained from Table s.
Rank Rank Differ- Example: 21 cases are arranged in rank
Sones’ || Sores Sod order for two variables; the sum of the
I 11 squares of the differences in the correspond-
» 26 ing ranks is found to be 531 (five-tenths
‘ A is disregarded).
: fr Refer to the second column on page 253,
k run down to the entry which most nearly
equals 531, that is, 524, and read beside it
the value of p, .66. The corresponding
2 value of 7 (.68) is found in Table 5.
I 3 Note: (a) If the obtained =D? is nearly
L I i midway between two entries, use the p fall-
t. 1 ing between the p's corresponding to the
‘ 5: two entries. (If the =D? in the example
2s were 540, p would be .65.)
I 21Y,
l (b) For ZD? greater than those corre-
I ‘ sponding to p=0 (i. e. in case of negative
[ I 9 correlation) subtract the obtained =D?
1 10 5a from the entry in that column correspond-
[ 21 ing to p= —1.00. Find the p correspond-
2 1:5 5 ing to this number obtained by subtraction.
z . Si With a negative sign prefixed, this is the
desired ».
ELC = 3531.5
The fourfold table method (tetrachoric correlation) as-
sumes that both variables are continuous but takes account
only of position above or below the measure of central ten-
dency in each series. The fourfold table corresponds to the
scatter diagram divided into four compartments by the
