SECTION 8.10 MISSING SCORES AND UNEOUAL SIZE SUBGROUP 3 281

The two solutions for unegual n's illvstrated in this section each
reguire that the number of observations with n each block be egual.

THE PROBLEM OF ONE MISSING SCORE

The preceding solutions are appropri ite when an entire bloc. is
missing. The following procedure is applicab e when only one score a
block is missing. It is analogous to the metho« in Section 5.6 for estima :g
missing values in a randomized block design. A missing score is estimatec »y

u(xS,) Na 4(>AB l — ŽA;

ABŠ S o ba DJ
wherc — < number of blocks in level A,.
1 — number of levels of B.
x , — sum of remaining scores in block containing missing score.
XA ,— sum of remaining scores in treatment combination AB;; c 1-
taining missing score.
3 , < sum of remaining scores in treatment A; containing mis« ig

score.

For .ample, assume that score ABS,,, in Table 8.2-| is missing. ' is
scor s estimated by

422) £ 4(11) — 86

ABS,22 — — 4 — DA CI) < SI,
whe XS, <27—5-—22.
IB,, < 16 —- 5—
ZA, <9l-5::..

Th« stimated score is r« 'sonably close to the original score in that Il,
wh. is 5.

After inserting the stimate of the missing score into the data ma' (x,
the. nalysis of variance i carried out in the normal way. The degrec of
fre. »m for MSpxgubj w. oups Should be reduced by one; for exan: le,
df — pin — 1Xg — 1)— 1. An unbiased estimate of MS;,,yi wgroups 15
ob. ned by this procedu e, but all other mean sguares are slightly ov r- Ni
est nated. According to Xnderson (1946), the biases are small. He gi :s
m. hods for obtaining ui biased estimates, but it is doubtful if the add :d
lal »r is justified. If another missing score occurs in the same A; treatme 1t,
th. iterative procedure described in Chapter S may be used. If the second
m' sing score occurs in a different level of treatment A, the procedure of
es mating the score described above is repeated. A more complete d s-
cu sion of procedures for estimating missing scores may be found in And. r-
so (1946) and Khargonkar (1948).