An Example.

The following example is taken from Searle (1971, pp. 287,375). An experiment was
conducted to compare the effects of three different types of fertilizer and four varieties of grain on
the weight of grain (WEIGHT). The milligrams of seed planted (MSEED) for each plot were also
recorded and used as the covariate. The SPSS commands and data for model 3 are presented in
Figure 1.18a, and the analysis of variance tables in Figure 1.18b.

Figure 1.18a
RUN NAME EMPTY CELLS EXAMPLE FROM SEARLE(1971).
COMMENT DATA ARE TAKEN FROM P. 287 AND P. 375.
VARIABLE LIST  TREATMNT, VARIETY, WEIGHT, MSEED
N OF CASES 18
INPUT FORMAT FREEFIELD
INPUT MEDIUM CARD

MANOVA

7 MN OAONAANNNNE— > > ee
ZAABAKOGNNONUEEBAKA--E-
o—
(A
S4NOKODOVOBOANOGJOAN

I

WEIGHT MSEED BY TREATMNT(l1,3), VARIETY(1,4)/

ANALYSIS-WEIGHT /

DESIGN < MSEED WITHIN VARIETY BY TREATMNT ,
VARIETY, TREATMNT, VARIETY BY TREATMNT/

DESIGN <- TREATMNT, VARIETY, VARIETY BY TREATMNT,

MSEED WITHIN VARIETY BY TREATMNT/

READ INPUT DATA
8

Figure 1.18b

TESTS OF SIGNIFICANCE FOR WEIGHT USING SEOUENTIAL SUMS OF SOUARES

SOURCE OF VARIATION SUM OF SOUARES DF MEAN SOUARE
WITHINtRESIDUAL 4.30000 3 1.43333
CONSTANT 2178.00000 1 2178.00000
MSEED WITHIN VARIETY BY TREATMNT 92.11472 8 11.51434
VARIETY 5.31810 s 3 1.77270
TREATMNT 36.16611 2 18.08306
VARIETY BY TREATMNT -10107 1 l0l07

TESTS OF SIGNIFICANCE FOR WEIGHT USING SEGUENTIAL SUMS OF SOUARES

SOURCE OF VARIATION SUM OF SOUARES DF MEAN SOUARE
NITHINHRESIDUAL 4.30000 3 1.43333
CONSTANT 2178.00000 1 2178.00000
TREATMNT 10.50000 2 5.25000
VARIETY 36.78571 3 12.26190
VARIETY BY TREATMNT 34.71429 2 17.35714

T 7.38571

MSEED WITHIN VARIETY BY TREATMNT 51.70000

1.19 Randomized Block Designs

In this design the experimental unit is divided into groups (blocks). The main object of this is to
keep the experimental errors within each group as smali as possible. The accuracy of the
experiment is increased by making comparisons within the resulting relatively homogeneous
experimental units. The model for this design is

YjsutB Et 7; t ej

where B; is the block effect and r; is the treatment effect.

F

1519.53488
8.03326
1.23677

12.61609
07051

1519,53488
3.66279
8.55482
12. 10963
5.15282

SIG. OF F

SIG. OF F

-000

MANOVA

17