IM ETIKE TERE, Kolko jaga

Figure 1.21a

RUN NAME TYPE l BALANCED INCOMPLETE BLOCK DESIGN.

COMMENT DATA ARE TAKEN FROM COCHRAN č COX(1957).

VARIABLE LIST  REPLICS, TREATMNT, BLOCKS, DEP

INPUT MEDIUM CARD

INPUT FORMAT  FIXED(3Fl.0,F2.0)

N OF CASES UNKNOWN

MANOVA DEP BY REPLICS(1,5), TREATMNT(1,6), BLOCKS(1,3)/
DESIGN - REPLICS, TREATMNT, BLOCKS W REPLICS/
DESIGN < REPLICS, BLOCKS W REPLICS, TREATMNT/

READ INPUT DATA

lll 7

12117

13226

14225

54326
55332
56127
END INPUT DATA
FINISH

The ANOVA tables from the output for Figure 1.21a are given in Figure l.21b.

Figure 1.21b

TESTS OF SIGNIFICANCE FOR DEP USING SEOUENTIAL, SUMS OF SOUARES

SOURCE OF VARIATION SUM OF SOUARES DF O MEAN SOUARE F SIG. OF F
RESIDUAL TT1.33333 10 7.13333

CONSTANT 19712.03333 1 19712.03333 2548 . 96983 0.0
REPLICS 298. 46667 4 74.61667 9.64871 -002
TREATNNT 1059.76667 5 21l.95333 27.40776 000
BLOCKS W REPLICS 213.40000 10 21.34000 2.75948 -062

TESTS OF SIGNIFICANCE FOR DEP USING SEGUENTIAL SUMS OF SOUARES

SOURCE OF VARIATION SUM OF SOUARES DF MEAN SOUARE F SIG. OF F
RESIDUAL T1.33335 10 7.713333

CONSTANT 19712.03333 1 19712.03333 2548 . 96983 0.0
REPLICS 298.46667 4 T4.61667 9.64871 002
BLOCKS W REPLICS 753 .00000 10 75.30000 9.73707 001
TREATMNT 520. 16667 5 104.03333 13.45259 -000

1.22 Partially Balanced Incomplete Block Designs (PBIB)

Because balanced incomplete block designs often reguire a large number of blocks, it may not be
possible to find a design that fits the size of the experiment. A general class of BIB designs that do
not have the uniform variances for treatment contrasts but still permit the estimation of treatment
differences are the partially balanced incomplete block designs.

Consider the design in Tabie 1.22, with t < 20, k < 4, r < 2and b < 10. Recall that for a BIB
design any pair of treatments must appear together A times. In this design, some treatments occur
together in the same blocks and some do not. This is the main difference between BIB and PBIB
designs.

Table 1.22