THE 2n-FACTORIAL TRIAL


 A useful arrangement of treatments that produces
exploratory information on several factors and their
interaction is a 2n-factorial trial. This is an
arrangement of n factors taken at two levels each. An
example of a 23-factorial experiment will be used to
illustrate the detailed methodology of analysis. The
nature of the trial was to explore three factors: plant
density, nitrogen, and variety in a 23 factorial. The
levels of the variables in this trial are given for plant
density (P), nitrogen (N), and variety (V) as follows:

 PO = 25,000 plants/ha
 P1 = 50,000 plants/ha

 NO = None applied
 N1 = 100 kg N/ha

 V0 = Local variety
 V1 = Tuxpeio

Table III-3 shows the field design by blocks and the grain
yield in kg/plot. To estimate the factorial effects and
perform the analysis of variance, the following procedure
is applied:

Step 1. Using treatment yield totals from Table III-3, a
two-way table can be constructed in which the treatments
are placed on the horizontal axis and the factorial
effects are listed vertically as shown in Table III-4. In
each of the factorial effects, half the treatment
combinations receive a plus (+) sign and half receive a
minus (-) sign. The row corresponding to M (mean of the
entire experiment) has only plus signs. When the higher
level of a factor (PI, N1, Vl) in the factorial effect is
present in the treatment combination, it receives a plus
(+) sign; it receives a minus (-) sign if not present (Po,
No, Vo). When two or more factors at higher levels are
present in the treatment combination, the sign is found by
using the algebraic rule for signs.