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in analyst capability through the blocking of average times; thus, we are control-
ling for individual differences in capability. As an extreme case, a block can be
comprised of a single analyst. In this case, the analysts will have all four treat-
ments (software products) administered in randomly selected order. The random
application of the treatments helps eliminate the possible interference (learning,
fatigue, loss of interest, etc) of a ﬁxed order of application. Note this randomized
block experiment with a single subject in a block (20 blocks) leads to 80 data
points (20 blocks
4 products), while the ﬁrst block experiment (5 blocks) leads
to 20 data points (5 blocks
×
×
4 products).
Factorial Design : A factorial design is one where we consider more than one
factor in the experiment. For example, suppose we are interested in assessing the
capability of our customer service representatives by considering both training
(standard and special) and their freedom status (prisoners or non-prisoners) for
SC. Factorial designs will allow us to perform this analysis with two or more fac-
tors, simultaneously. Consider the customer representative training problem. It
has 2 treatments in each of 2 factors, resulting in a total of 4 unique treatment
combinations, sometimes referred to as a cell: prisoner/special training, pris-
oner/standard training, non-prisoner/special training, and non-prisoner/standard
training. To conduct this experimental design, we randomly select an equal num-
ber of prisoners and non-prisoners and subject equal numbers to special training
and standard training. So, if we randomly choose 12 prisoners and 12 non-
prisoners from SC (a total of 24 subjects), we then allocate equal numbers of
prisoners and non-prisoners to the 4 treatment combinations—6 observations in
each treatment. This type of design results in replications for each cell, 6 to be
exact. Replication is an important factor for testing the adequacy of models to
explain behavior. It permits testing for lack-of-ﬁt . Although it is an important
topic in statistical analysis, it is beyond the scope of this introductory material.
There are many, many types of experimental designs that are used to study spe-
ciﬁc experimental effects. We have covered only a small number, but these are some
of the most important and commonly used designs. The selection of a design will
depend on the goals of the study that is being designed. Now for some examples of
experimental design.
6.7.1 Randomized Complete Block Design Example
Now, let us perform one of the experiments discussed above in the Randomized
Complete Block Design . Our study will collect data in the form of task completion
times from 20 randomly selected analysts. The analysts will be assigned to one of
ﬁve blocks (A–E) by considering their average task performance times in the past
6 months. The consideration (blocking) of their average task times for the previous
6 months is accomplished by sorting the analysts on the 6 Month Task Average key
in Table 6.12. Groups of 4 analysts (A–E) will be selected and blocked until the list
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