10  sPSS UPDATE 7-9

PRINT<DESIGN( SOLUTION) /

| For example, in a 2 x 3 (factors A, B) design with one empty cell. The solution matrix P of this
design would be

Pi; Pe Pa: Pu Ps
Pi Paz Psa Paz Pse
P < Pis Pas Ps Ps Pss
Pu Pu Pu Pu Ps
Pis Pas Pss P4s5s Pss
Pis P2s Pse Pse Pse

Sooočo

The first column of P indicates that the hypothesis corresponding to the sum of sguares of
CONSTANT is z

Pribui t Pralna Disktis Piskar Pistee  Prskas — 0

where yu; is the population mean of cell (i,j).
Similarly, column 2 of P represents the coefficients of the linear combinations of cell means

being tested for the sum of sguares of A, columns 3 and 4 are for the sum of sguares of B, and the
last two columns are for the sum of sguares of AB.

An Example. The following example is taken from Bancroft (1968, p. 20). Ouantitative
chemical experiments were run to determine the reacting weights of silver (SILVER) and iodine
(IODINE) in silver iodine. Five different batches of silver and two different batches of iodine were
used in the experiment. These were treated, and then a determination of the reacting weights was
made. The coded data are given in Table 1.15. Note that there are two empty cells in the

experiment.
| Table 1.15
Silver
1 2 3 4 5
1
lodine

The MANOVA commands illustrated in Figure 1.15a produce the analysis shown in Figures

1.15b-1.15d.
Figure 1.15a
RUN NAME A 5"2 DESIGN WITH EMPTY CELLS.
COMMENT DATA ARE TAKEN FROM BANCROFT(1968) PAGE 20.

VARIABLE LIST SILVER IODINE RESP

INPUT FORMAT  FREEFIELD

INPUT MEDIUM CARD

MANOVA RESP BY SILVER(1,5) IODINE(1,2)/
PRINT<DESIGN( DECOMP,BIAS) /
DESIGNSSILVER, IODINE, SILVER BY IODINE/
DESIGN<IODINE,SILVER, SILVER BY IODINE/

EAD INPUT DATA

JU

AABAAHUVNNNNEEE EP
—Uu-E- 5-E—- DUE -DODNI- >
[AS]
idi
.

END INPUT DATA
FINISH

AE REEEERAEN