316 REPEATED-MEASUREMENT AND OTHER EXPERIMENTAL DESIGNS

The expectations of the variance estimates or mean sguares for a wo-
factor experiment with repeated measurements on one factor, and assum-
ing the row and column treatment variables to be fixed, are as follows:

ROWS, s," 0,4 Co 4 nCo'
SIR, si, ot Co?
COLUMNS, s,' ot opt nRon?
RXC, sre oi Op NO
(C x S)/R, six oi one

The guantities oa,', 04", c,4%, and o," are variance components as de-
seribed in Section 16.6. The guantity o," is a variance component which is
due to the variation of subjects within groups.

Examination of the above expectations indicates that the correct error
term for testing row effects is the S/R variance estimate. The correct error
term for testing column and R X C interaction effects is the (C x S)/R
variance estimate.

19.8 COMPUTATION FORMULAS FOR TWO-FACTOR
EXPERIMENTS WITH REPEATED MEASUREMENTS
ON ONE FACTOR

Computation formulas may readily be obtained to compute the reguired
sums of sguares. As previously the sum of all »RC observations will be
denoted by 7. We denote the row and column totals by T,.. and 7T.,
respectively. "The total for the rth row and cth column summed over sub-
jects is T,,... The total for any subject in any row summed over columns is
T,,. The total for a subjects for any group summed over columns is T,...
Given this notation, the computation formulas are as follows:

BETWEEN SUBJECTS

| T?

RO mn
[19.1] Cc nM Trs — TRE