6-2.1 Comparison vectors.

In the following we will refer to the year field as field one; the month field as field two, and the day field as field three. One of the first problems we have not addressed as yet is a suitable way to refer to the subscripts Rk and Ck. Each k is a different combination of agreement, disagreement, and missing. It is customary to refer to such combinations as vectors. A vector in this sense is simply a single dimensioned array of values. In this case the values are ternary, i.e., there are three possible [Agreement, Disagreement, Missing]. We need to adjust the presence values when the data is not missing. For three fields there are eight combinations (vectors) when data is either present or absent: 1 = [   ], i.e., no fields present, 2 = [ 1 ], i.e., only year present, 3 = [ 2 ], i.e., only month present, 4 = [ 3 ], i.e., only day present, 5 = [ 1, 2 ], i.e., year and month present, 6 = [ 1, 3 ], i.e., year and day present, 7 = [ 2, 3 ], i.e., month and day present, 8 = [ 1, 2, 3 ], i.e., year, month and day all present. As pointed out in 5-2.4, there is a presence dependence, so the adjusted presence on only four of these is non-zero: 1 = [   ], i.e., no fields present, 2 = [ 1 ], i.e., only year present, 5 = [ 1, 2 ], i.e., year and month present, and 8 = [ 1, 2, 3 ], i.e., all three date fields present. We also explained in 5-2.4, that when we compare two records their various comparisons are then grouped into four cases; these cases we then refer to as ap0, ap1, ap2, ap3. Table 1 includes these values as some of the raw data needed before beginning probability calculations.

Case Comparisons Adjusted Presence Eq. (4.1) Value
0 1:1   1:2   1:5   1:8 ap0 = 1 – p12 1.0000 – 0.0119 = 0.9881
1 2:2   2:5   2:8 ap1 = p12 - p22 0.0119 – 0.0087 = 0.0032
2 5:5   5:8 ap2 = p22p32 0.0087 – 0.0082 = 0.0005
3 8:8 ap3 = p32 0.0082
Reliability Coincidence
Agreement Disagreement Agreement Disagreement
r1 = 0.9506 1 – r1 = 0.0494 c1 = 0.0040 1 – c1 = 0.9960
r2 = 0.9063 1 – r2 = 0.0437 c2 = 0.0178 1 – c2 = 0.9822
r3= 0.8525 1 – r3 = 0.1475 c3 = 0.0326 1 – c3 = 0.9674

Table 1 — Preliminary Calculations