20 SPSS UPDATE 7-9

PBIB designs represent a large class of designs, many of which can be found in Cochran and
Cox (1957). An example with t < 15,b<15,k< 4, and r — 4 is given On P. 456 of that text. The
MANOVA commands and the output ANOVA table are given in Figure 1.22a and Figure 1.22b.

Figure 1.224
RUN NAME 15 X 15 PARTIALLY BAL. INC. BLOCK DESIGN.
COMMENT DATA ARE TAKEN FROM COCHRAN a COX(1957) P.456.

VARIABLE LIST BLOCKS, TREATMNT, DEP
INPUT MEDIUM CARD

N OF CASES UNKNOWN
INPUT FORMAT FIXED(2F2.0,8X,F3.0)
MANOVA DEP BY BLOCČKS(1,15), TREATMNT(1,15)/

DESIGN < BLOCKS, TREATMNT /
READ INPUT DAT

ll 2.6

19 2.5

113 2.0

115 2.4

21l 2.7

15 4 2.5
15 8 3.2
1510 2.4
3.1

1511
END INPUT DATA

FINISH

Figure 1.22b

TESTS OF SIGNIFICANCE FOR DEP USING SEOUENTIAL SUMS OF SOVARES

SOURCE OF VARIATION SUM OF SOUARES DpF MEAN SOUARE F SIG. OF F

RESIDUAL 2.68589 31 . 08664

CONSTANT 448.26654 l 448 .26654 5173.80518 0.0

BLOCKS 4 .92333 14 .35167 4 .O5S887 001
1.56411 la 11172 1.28948 . 268

TREATMNT

1.23 Latin and Other Sguares

A Latin sguare isa design in which each treatment appears exactly once in each row and column.
The main interest is stili on the estimation of treatment differences, but two restrictions are put on
the randomization of the treatment assignment. The model of this design is

ije s ot mit Bit vet €ik

where a,, B; and »x are the row, column and treatment effects respectively. An example of a 4 x 4
Latin sguare is shown in Table 1.23a.

e

Table 1.232

Column

The following MANOVA specifications may be used to analyze a 4 X 4 Latin sguare.

MANOVA Y BY RON(1,4),COL(1.4).TRT(1,4)/
DESIGN<ROM, COL, TRT/