Principles of Plant Genetics and Breeding

averages, to the more complex multivariate analysis.
Computers are required for complex analyses, but
sometimes, the breeder may have a small amount of
data and might want to use a handheld calculator for
quick results. Hence, there is the need to know the
computational basis of the commonly used statistical
methods.
Population versus sample
A statistical population is the totality of the units (individuals)
of interest to the researcher. It follows then
that, depending on the researcher’s objectives, a population
may be small or infinitely large. A small population
can be measured in its entirety. Plant breeders often
handle large populations, and obtaining measurement
from the entire population is often impractical. Instead,
researchers obtain measurements from a subset of
the population, called a sample. The scores from the
sample are used to infer or estimate the scores we would
expect to find if it were possible to measure the entire
population.
In order to draw accurate conclusions about the
population, the sample must be representative of
the population. To obtain a representative sample, the
statistical technique of random sampling (in which all
possible scores in the population have an equal chance
of being selected for a sample) is used. There are other
methods of drawing samples from a population for a
variety of purposes. These include quota, convenience,
and stratified sampling methods. A number that
describes a characteristic of a population is called a
sample statistic or simply, a statistic. A number that
describes a population is called a population parameter,
or simply, a parameter.
Issue of causality
Scientific conclusions are drawn from the preponderance
of the evidence obtained from properly conducted
research. Cause and effect is implicit in the logic of
researchers. However, it is difficult to definitely prove
that variable X causes variable Y. There is always the
possibility that some unknown variable is actually
responsible for the effect observed (change in scores).
No statistical procedure will prove that one variable
causes another variable to change (i.e., statistics does
not prove anything!). An experiment provides evidence
to argue for a certain point of view, not prove it.
COMMON STATISTICAL METHODS IN PLANT BREEDING 147
Statistical hypothesis
A hypothesis is an informed conjecture (educated
guess) about a phenomenon. It is arrived at after taking
into account pertinent scientific knowledge and personal
experience. Researchers often have preconceived
ideas about the phenomenon that they seek to investigate.
However, they should be willing to approach an
investigation with an open mind. A hypothesis declares
the prediction of the researcher concerning the relationship
between two or more variables associated with the
study. An experiment is designed to test this relationship.
In plant breeding, a breeder ends up with about a
dozen promising genotypes from which one would
eventually be selected for release to farmers for use in
cultivation. The breeder conducts field tests or trials
(over locations and years) to help in the decision-making
process. He or she suspects or predicts differences
among these genotypes. The predicted difference represents
a true phenomenon. To avoid any biases, the
hypothesis is formulated in the opposite direction to the
predicted or suspected outcome. That is, the researcher
would state that no real differences exist among the
genotypes (i.e., any differences are due to chance).
This is the null hypothesis (H 0 ) or the hypothesis of
no difference. The alternative hypothesis (H 1 ) would
indicate a real difference exists. There is a standard way
of mathematically stating a hypothesis. If four genotypes
were being evaluated, a hypothesis could be formulated
as follows:
Null hypothesis, H 0 : µ 1 =µ 2 =µ 3 =µ 4
(i.e., all genotype means are equal)
Alternate hypothesis, H 1 : µ 1 ≠µ 2 ≠µ 3 ≠µ 4
(i.e., all genotype means are not equal)
The H 0 is accepted (i.e., automatically reject H 1 ), or
rejected (accept H 0 ), at a chosen level of statistical
significance, α (e.g., α =0.01 or 0.05; acknowledging
that 1% or 5% of the time you could be mistaken in
your conclusion). In other words, the research does not
prove anything outright, as previously pointed out.
Rejecting H 0 when it is true (i.e., you are saying a difference
exists when in fact none really does) is called a
Type I error. On the other hand, failure to find a true
difference when it exists (accepting a false H 0 ) is called a
Type II error.
The goal of a plant breeder is to conduct research in
such a way that true differences, when they exist, are
observed. This depends on the adoption of sound
experimental procedures, often called field plot techniques,
and is discussed later in this chapter.