308

REPEATED-MEASUREMENT AND OTHER EXPERIMENTAL DESIGNS

Applying the appropriate computation formulas, the following sums of
sguares are obtained:

H

ROWS
[A,,., T?. 394350 (1970X
C > T, N ——I— 40 — 1,565.00
COLUMNS
I4,,. TE. 1,045,156. (1900?
R p2 T. NČ ——O ČE 7,553.10
INTERACTION
R Cc x 2 l R T Bm 1 C 2 T2
NA ca RA! "N
O 394,350  1,045,756 , (1,970)?
— 122,984 - —IU O t—OU
— 16,843.40
TOTAL
R PNE Kodi — (1,970)? —
bA b Xi NO 122,984 —A 25,961.50

rzi ezl

Table 19.2 summarizes the analysis-of-variance data for this example.
Because this is a mixed model with n< 1 and F, < s,ls, — .279, no
meaningful test of row effects is possible. The proper error term for col-
umn effects is s,,2. The F ratio for column effects is found to be 4.04.
The F ratios reguired for significance with 3 and 27 degrees of freedom as-
sociated with the numerator and denominator, respectively, are 2.96 at the
S percent and 4.60 at the | percent levels. Thus the column differences

v A EIMV

Table 19.2
Analysis of variance for data of Table 19.1

Source of Sum of Degrees of Variance
variation sguares freedom estimate
NI EN Rn
Rows 1,565.00 9 173,89 — s,'
Columns 7,553.10 3 2,517.70 < s?
Interaction 16,843.40 27 623.83 — s,?
en Ga en GE AA NZ
Total 25,961.50

a a EEA REEEEEMOEEEEEEEEEEEEEEEEWAEEEEE,

s,
404 — F,< 2, <.279
S,

re

se —
Sreč

Fse

a V a ERA EEEEEE OEEO

NR