324 REPEATED-MEASUREMENT AND OTHER EXPERIMENTAL DESIGNS

tigator. Examples are sex, socioeconomic level, scholastic achievement,
TO, litter membership, strain, and so on. A blocking variable may be of
the nominal, ordinal, or interval-ratio type. With ordinal or interval-ratio
variables arbitrary groupings (such as high, medium, and low) are used as
blocks.

In some experiments the blocking variable is of no interest to the in-
vestigator and is used purely for the purpose of error reduction. ln other
experiments the blocking variable may be of considerable intrinsic interest
in itself and may be an integral part of the experiment. ln such experi-
ments error reduction may not be a matter of concern. Such experiments
are in effect ordinary factorial experiments, where one or more of the vari-
ables are classification rather than treatment variables.

Randomized block experiments are on occasion conducted with one
observation per cell. To illustrate, let the treatment variable be four dif-
ferent dosages of a drug intended to alleviate depression and let the
blocking variable be a score on a depression scale administered prior to the
administration of any drug. Let the dependent variable be a measure of
motor performance, such as reaction time. If 20 subjects were available,
these subjects could be divided into 5 blocks of 4 subjects each. The four
subjects with the highest scores on the depression scale would constitute
the first block, the next highest subjects the second block, and so on.
Within each block subjects are assigned to treatments at random. The
result is a 5 X 4 table of numbers with one observation per cell. Such data
are analyzed using the two-way classification analysis with one observation
per cell. The total sum of sguares is partitioned into treatment, block, and
interaction sums of sguares. Care must be exercised in the choice of error
term in applying the F ratio. Freguently, as in the illustrative example
above, the blocking variable may be viewed as a random variable and the
treatment variable as a fixed variable; that is, the model is mixed. The
proper error term for testing treatment effects is the interaction mean
sguare. No test of the effects due to blocks can be made. ln general in
randomized block designs investigators must concern themselves with
whether the blocking variable may be viewed as fixed or random, and gov-
ern themselves accordingly in the choice of the appropriate error term.

19.42 EXPERIMENTS WITH NESTED FACTORS

Consider an experiment which is intended to investigate two different
drugs, 4 and B, in the treatment of depressed patients. The dependent
variable is a measure of improvement under the drug. Assume that the pa-
tients are under treatment by three different therapists. Such an experi-
ment might be conducted as a 2 X 3 factorial experiment with six groups of
n experimental subjects. All six treatment combinations are present in the
experiment. In such a factorial experiment both factors are said to be
crossed. ln the example above each of the two drugs crosses, as it were,