ih
4

(BY), is the error term for y;, (aBy)ix is the error term for (cy);, and if the number of observations
per cell is greater than 1, then (aB);,, (BY) and (aBYy)ix can be tested against the within-cells error.

The following MANOVA specifications may be used to perform an analysis of variance of a 3
X 2 split-plot design:

MANOVA Y BY BLOCK(1,3), A(1,3), B(1,2)/
DESIGN<BLOČK, A VS 1, A BY BLOCK-1, B, A BY B/

In the above DESIGN specification, effect A is tested against the error 1 term which is the
interaction of A and BLOCK. Effects B and AB are tested against the residual, since there is no
within-cells error in this example.

This type of design can be extended by subdividing each subplot into sub-subplots, etc. The
model for a split-split-plot design would be

Yi — prta Bert (aB)ib yet (ory)ijt reje Be (a8) (VO) je (YB)i je Ein

where 8, is the effect for the sub-subplot factor, m, < subplot residual — (yB); £ (yB)i;, ea is the
residual, and (aB)x, Tri, and ej are the appropriate error terms for plot, subpiot, and sub-subplot
factors, respectively.

An example of a split-split-plot design is taken from Hicks (1973, p. 223). The SPSS
commands are given in Figure l.27a.

Figure 1.27a
a —--——— mmm

RUN NAME SPLIT-SPLIT-PLOT DESIGN.

COMMENT DATA ARE TAKEN FROM HICKS(1973) PAGE 223.

COMMENT LAB : THREE DIFFERENT LABORATORIES—PLOT FACTOR.

COMMENT TEM : THREE LEVELS OF TEMPERATURE—SUB-PLOT FACTOR.

COMMENT MIX : THREE TYPES OF MIX—SUB-SUB-PLOT FACTOR.

COMMENT FOUR REPLICATES (BLOCK).

VARIABLE LIST BLOCK LAB TEM MIX RESP

N OF CASES UNKNOWN

INPUT FORMAT  FIXED(4F1.0,1X,F4.l)
INPUT MEDIUM CARD
MANOVA RESP BY. BLOCK(1,4),LAB,TEM,MIX(1,3)/
DESIGN<:BLOCK, LAB VS l,LAB BY BLOCK:1L,

TEM VS 2,LAB BY TEM VS 2,TEM BY BLOCKt

LAB BY TEM BY BLOCK-2,

MIX,LAB BY: MIX,TEM BY MIX,LAB BY TEM BY MIX/
READ INPUT DATA
llli 18
1ll2 14.
1li3 21.
ll2l 9.
ll22 7
1123 1l.
llšl 5.
1132 5.
1155 6.
121l 20.
1212 18.
1213 22.

GROUNANRALNOO

4321
4322
4323 1
4331
4332
4333
END INPUT DATA
FINISH

NO h- OBD
OBKOKOM

Ee PE 2 IVO ENE POT

As can be seen from the DESIGN specification, the interaction of LAB and BLOCK is the
error term for the plot factor LAB, the interaction of TEM and BLOCK and the interaction of
LAB, TEM, and BLOCK are pooled together as the error term for the subplot factors. The
sub-subplot factors are to be tested against the residual. The analysis of variance from the output
for this run is shown in Figure 1.27b.

sa

MANOVA

27