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theory and methods. However, with the help
of the explanations given and the working
examples dealing with QC presented
throughout the chapter, the reader will
acquire the necessary concepts and methods
to solve most of the problems encountered
with QC in mass-rearing and production of
beneficial organisms. Thus, this chapter can
be considered as a starting-point, leading the
interested reader to understand more
advanced methods that can be found in sev-
eral textbooks mentioned at the end of the
chapter.

Basic Terminology

Consider that a given parasitoid species is
mass-produced and that the average fecun-
dity of the females needs to be quantified.
All mass-reared females form, in statistical
terminology, the population. This population
is the unit of interest and the one we want to
describe. Of course, the fecundity of all the
females constituting the population cannot
be measured. Instead, a random samplehas to
be collected. In this case, the word ‘random’
is important. It means that the sample has to
be a correct representation of the whole pop-
ulation. The animals belonging to the sample
have to be collected randomly, and it would
thus be a wrong method to only use the first
emerging females, or the biggest, etc. After
taking a correct random sample, the fecun-
dity of each female of this sample is quanti-
fied. Each value obtained is called an
observation, and the total number of observa-
tions is the sample size. Using all the observa-
tions, the sample can be described. For
example, we can compute the average fecun-
dity of the females (see below for a detailed
description of the method to be used here).
However, our goal is not to describe the sam-
ple, but the population from which the sam-
ple was taken. Fortunately, most of the
parameters used to describe a sample can be
used to compute, for each of them, what is
called an estimation of the corresponding
parameter describing the population. When
the descriptive parameter is an average
value, as for fecundity, then it can be shown
that the best estimation of the average of the

population is exactly the average value com-

puted for the sample.

Usual Statistical Distributions

QC workers are collecting data that may

have different statistical characteristics.

Therefore, the nature of the data collected

has to be clearly identified. QC workers usu-

ally work with two types of variables: regu-

lar quantitative traits (e.g. size, fecundity) or

proportions (e.g. sex ratio, percentage emer-

gence). Quantitative traits follow a normal

(or Gaussian) distribution and proportions

follow a binomial distribution. Other statisti-

cal distributions (i.e. Poisson, exponential,

etc.) may also be encountered, but it is in

most cases possible to transform the corre-

sponding data into a normal distribution.

The normal distribution

As indicated by its name, this is the most

commonly encountered distribution. It is

used to describe the distribution of a contin-

uous quantitative trait that is quantified for

each individual of the sample, such as the

size of an organism. This distribution is also

regularly used for discrete variables (i.e.

variables that can only be expressed as inte-

ger values, such as the number of eggs). The

normal distribution is often expressed as the

well-known ‘bell-shape’ curve, and its sym-

metry around the average value of the trait

studied is its main feature. This distribution

can be completely described with only two

parameters: its average, and its variance. A

method to compute these two descriptive

parameters is given below. Data that are nor-

mally distributed are expressed using clearly

identified units: longevity of adults (in days)

or size of pupae (in mm).

The binomial distribution

Sometimes we have to describe the number

of times that a particular event will occur

among all the individuals of the sample. The

event may or may not occur, and the mea-

306 E. Wajnberg