282

SPLIT-PLOT DESIGN

O — Ča DOL —j—,] no —-————

8.11

Standard error formulas due to Anderson (1946) for making com-
parisons among means by the t test, when only one score has been estimated,
are shown below.

Comparisons among A, means can be made using the following t denomina-

tor:
2[MS,,e; w.groups t žin — lXa — IXMSp x subj w.groups)]
V ng

Comparisons among B; means employ the following t denominator:

2MS, x subj w.groupsl.! t žin ni 1X4 — 1Xa/P)] .
V np

Comparisons among AB;; means at level a, use the following denominator:

2MS, x subj w.groupsl.! t žin — 1Xa — 1Xa/P)]
V ——— TT n .

Comparisons among AB;; means at level b; use the following denominator:

2MS,.aj wigruge/ HA t 2MS; x subj waroapal (4 — b) -. žin — iXa — 1(49')]
V ng :

The foregoing formulas are used in comparing means based on one esti-
mated missing score. Procedures for determining the critical value for the
t test for pooled error terms appear in Section 8.7. If a comparison among
means does not involve a missing score, formulas given in Section 8.7
are appropriate.

If several missing scores occur in designs having three or more
treatments, the reader should consult Hazel (1946), Henderson (1953), and
Krishna Iyer (1940).

RELATIVE EFFICIENCY
OF SPLIT-PLOT DESIGN

An experimenter wishing to use a multitreatment factorial design
with subjects assigned to blocks may consider two of the designs described
thus far —a randomized block factorial design and a split-plot design.
However, he should examine several factors in choosing between these
two designs. If it is not possible to administer all treatment level com-
binations within each block, there is no choice. A split-plot design is
reguired. On the other hand, if there is a choice concerning the assignment
of treatment combinations in each block, the relative efficiency of the A,