Principles of Plant Genetics and Breeding

148 CHAPTER 9
Concept of statistical error
Error in statistics does not imply a mistake. As previously
stated, statistics is not used to prove anything.
Experimental conditions are seldom, if ever, perfect. If
five samples of a uniform cultivar (e.g., pure line) are
planted under identical conditions, it would be expected
that a measurement of a trait (e.g., height) would be
identical for all samples. In practice, differences, albeit
minor, would be observed. This variation that cannot be
accounted for is called experimental error (or simply
error). No effort can completely eliminate experimental
error. However, efforts can be made to reduce it such
that true differences in a study are not obscured.
Laboratory or controlled environment research often
allows the researcher more effective control over variation
in the experimental environment. Field studies
are subject to significant variation from the soil as well
as the above-ground environment. Other sources of
undesirable variation are competition among plants
and operator (human) error. Plant breeders need to
understand the principles of experimental design. A
large error would not permit small real differences in
the experiment to be detached.
Errors may be random or systematic, the former
being responsible for inflated error estimates. Practical
ways of reducing error include the use of proper plot
size and shape. Within limits, rectangular plots and
larger plots tend to reduce variation per plot. Also, the
use of experimental designs that include local control
of variation (e.g., randomized complete block design)
helps to reduce error.
Principles of experimental design
This subject is treated in detail in Chapter 23. It is
introduced here only to further explain the concept of
error. The unit to which a treatment is applied is called
the experimental unit. In plant breeding common
examples of treatment are genotypes (to be evaluated),
locations (where genotypes will be evaluated), years,
and seasons (over which evaluations are conducted). An
experimental unit may be a plant or groups of plants
(in a pot).
Experimental designs are statistical procedures for
arranging experimental units (experimental design)
such that experimental error is minimized. Three tactics
or techniques are used in experimental designs for this
purpose. These are replication, randomization, and
local control.
Replication
Replication is the number of times a treatment is
repeated in a study. It is important in experimental
design for several reasons, two key ones being:
1 Estimation of statistical error. To establish that
experimental units treated alike vary in their response
requires at least two of the same units that have been
treated alike.
2 To reduce the size of statistical error. A measure
of the consistency in a data set (standard error)
will be presented later in the book. Calculated as
σ/√(number of replications), it is obvious that the
larger the number of replications, the smaller the
error (σ=standard deviation).
Another pertinent question is the number of replications
to use in a study. It should be noted that the more
replications used, the more expensive the experiment
will be to conduct. In plant breeding, breeders commonly
use fewer replications (e.g., two) for preliminary
field trials, which often contain hundreds of lines, and
more replications (e.g., four) for advanced trials that
contain about 10–20 entries.
Randomization
This is the principle of equal opportunity whereby treatment
allocation to experimental units is made without
bias. To make the statistical test of significance valid,
errors should be independent of treatment effect.
Randomization may be completely random or may have
restrictions to accommodate a specific factor in the
experiment.
Local control
This is an additional tactic used by researchers to “contain”
variation within an experiment through grouping
of experimental units on the basis of homogeneity.
Variation within groups is kept to a minimum, while
enhancing variation between groups. Statistical procedures
are then used to extract this group-based variation
from the error estimate. Blocking is recommended if a
distinct variation occurs in the experimental field. For
example, where a field has a slope, there will be a fertility
gradient. Completely random allocation of treatments
may place all the replications of one treatment in one
fertility zone. Use of the blocking techniques will allow
one replication of each treatment to be represented in
each distinct fertility zone by placing a restriction on