Since a; should be tested against variation within a;, i.e., Bys, the following MANOVA
specfications can be used:

MANOVA Y BY COUNTY(1,5),TOWN(1,3)/
DESIGN<COUNTY VS l, TOWN WITHIN COUNTY-1l VS WITHIN/

Note that the first keyword WITHIN (or just W) indicates nesting. The DESIGN specification
reguests that COUNTY be tested against the error 1 term, which is the effect of TOWN (nested
within COUNTY), and that the within-cells error term (second WITHIN) be used for testing the
TOWN eftect.

When crossing and nesting are both used in the design, attention must be paid to the choice of
appropriate error terms for testing the various effects. Consider a three-factor example, with
factors A, B, and C. if

1 C is nested within B, and B is nested within A, the model is
Yi 5 pot a; Bio Vari h €ijk

The DESIGN specification should be
DESIGN<A VS l, B W Asl VS 2, C W B W A-2 VS WITHIN/

2 C is nested within B, and B is crossed with A, the model is

Yi č at ot Bi t (aB)ij vx b (ey)io tt €ik

The rule for writing down the model is that no interaction in which the subseript j appears
twice is in the model. For example, interactions (BYy);x; and (aBYy)ijxrj; do not exist.

Since C is nested within B, B, is tested against y,;. The appropriate error term for a; and
(aB);; is the residual of the A-B two-way table, (ay)ir;, which is the interaction effect of a; and
ij 1f the number of observations per celi is greater than one, then (ay);,;, and y«; can be
tested against the within-cells error term. The DESIGN specification for this model is

DESIGN-A VS 2, B VS l, C W B-l VS WITHIN,
A BY B VS 2, A BY C W B<2 VS WITHIN/

3 CC is crossed with B, and B is nested within A. The model and the DESIGN specification are
the same as those in (2) except for the names of the effects.

An experiment (Hicks, 1973, p. 195) was conducted to compare a new gun-loading method with
the existing one (factor METHOD). Three teams were chosen randomly from each of three
groups. Each team used the two methods of gun loading in random order. The data and SPSS
commands for the analysis are as given in Figure 1.25a, and the ANOVA table is presented in
Figure 1.25b.

Figure 1.25a
RUN NAME NESTED DESIGN.
COMNENT DATA ARE TAKEN FROM HICKS(1973) P. 194.
COMMENT METHOD : 2 LEVELS CROSSEU WITH GROUP.
COMMENT GROUP : 3 LEVELS.
COMMENT TEAM : 3 LEVELS NESTED WITHIN GROUP.
COMMENT NUMBER OF OBSERVATJONS PER CELL < 2.
VARIABLE LIST GROUP, TEAM, METHOD, RESP
N OF CASES UNKNOWN

INPUT FORMAT  FREEFIELD

INPUT MEDIUM CARD

MANOVA RESP BY METHOD(1,2),GRO0UP, SRAMU, 3)/
DESIGN<METHOD VS 1,GROUP VS 2
METHOD BY GROUP VS 1,TEAM W GROUP<- 2,
METHOD BY TEAM W GROUP-1/

READ INPUT DATA
l 11 20.2

l 1 i 24.1
l1l2li4.2
l1l2l6e.2

1 21 26.2

I 2 1 26.9

3 3 Il 2l.8

3 3 l 23.5
33.2 12.7

3 3215.1

END INPUT DATA
FINISH

MANOVA — 23