22 SPSS UPDATE /-9

Figure 1.24a

NE VE TNE EP PE RN |

RUN NAME 4"4"3 FACTORIAL IN RANDOMIZED BLOCKS.
COMMENT 4"4"3 FACTORIAL IN RANDOMIZED BLOCKS WITH
COVARIATE. FROM COCHBAN AND CO0X(1957) PAGE 176.
VARIABLE LIST  REPLIC,LENPER, CURRENT, NTREAT,Y,X
INPUT MEDIUM CARD
INPUT FORMAT  FIXED(4Fl.0,F2.0,F3.0)
N OF CASES 96
IF (LENPER EO 5) LENPER < 4
IF (NTREAT EO 3) NTREAT < 2
IF (NTREAT EO 6) NTREAT < 3
MANOVA Y BY REPLIC(l,2), LENPER(1,4), CURRENT(1,4),
NTREAT(1,3) WITH X/
DESIGN < REPLIC,NTREAT. LENPER, CURRENT, NTREAT BY LENPER,
NTREAT BY CURRENT, LENFER BY CURRENT,
NTREAT BY LENPER BY CURRENT/

READ INPUT DATA
111172152
111574131
111669131
112161130
112361129
112665126
113162141
113365112
113670111
114185147
114376125
114661130
121167136 . s
121352110
121662122
122160111

254159102
254358 98
254688135
FINISH

Figure 1.24b

TESTS OF SIGNIFICANCE FOR Y USING SEOUENTIAL SUMS OF SOUARES
SOURCE OF VARIATION SUM OF SOUARES

iu
ke]

MEAN SOUARE F SIG. OF F

RESIDUAL 2211.96526 4i
REGRESSION 987 .52432
CONSTANT 1316. 19933
REPLIC . 27456
NTREAT 441.20522
LENPER 180.52285
CURRENT ' 2111.03300
NTREAT BY LENPER 211.79056
NTREAT BY CURRENT 467 . B4848
LENPER BY CURRENT 404.37365
NTREAT BY LENPER BY CURRENT 1021.61800

48 .08620
987 .52432 20.53654 000
1316.19933 27.537166 0.0
27456 00571 940
220.60261 4.58765 .015
60.1742B 1.25138 .302
T03.6TT767 14.63367 0.0
35 .29843 .T3407 625
T71.9T475 1.62156 163
44.93041 93437 .505
.75656 1.18031 .315

ODUUNH-E-dO

-
0o
«m
(u)

1.25 Nested Designs

A nested design arranges the experimental units hierarchically. For example, consider an
experiment to compare the yield of wheat per acre for different areas in a given state. Five counties
are selected at random, then three townships are randomly selected from each county. From each
township two farms are selected and the yield of wheat per acre is obtained. The resulting
experiment produces 5 x 3 x 2 — 30 experimental units. The factors of this experiment are county
and township, and the township effects are nested under the county factor, since a given township
appears only under one of the five counties. In other words, the county factor is not crossed with
township factor and so the interaction between county and township is not estimable.
The model for this two-factor nested design is

Yes mota; t Byu t €ijk

where a, is the county effect and B;;, is the township effect nested under the county eftect.