0851996884.pdf

sured trait is expressed as a percentage of the
occurrence of the event, such as the insect
being a female or male (sex ratio) or the
insect having emerged or not (percentage
emergence). In this case, the trait studied is
estimated from measures done on several
individuals simultaneously, and ranges from
0.0 to 1.0 (or from 0% to 100%). This second
type of variable, which cannot be expressed
in clearly identified units, is supposed to fol-
low a so-called binomial distribution. This
distribution is usually non-symmetric. This
type of variable can also be described com-
pletely with only two parameters: the proba-
bility of occurrence of the event, and the
number of individuals used to quantify it. A
description of the method used to compute
the two parameters is also given below.

Describing a Sample with a Regular

Quantitative Trait

When only one quantitative trait is measured
for each individual of a sample, several
descriptive statistics have to be computed in
order to summarize the main features of the
population from which the sample has been
drawn. In this case, the whole data set corre-
sponds to all the observations of the sample
and two types of parameters have to be com-
puted: (i) position parameters (e.g. arith-
metic mean, median) give the order of
magnitude of the values; and (ii) dispersion
parameters (e.g. range, variance, standard
deviation, standard error) provide informa-
tion regarding the dispersion of the values
around a position parameter (usually around
the arithmetic mean). The sample size is n,
and the observations are x 1 , x 2 , ..., xn.

Position parameters

• Arithmetic mean:
  
  
  • Median: this parameter is defined as the
    middle value when all observations are
    arranged from lowest to biggest. Thus, by
    definition, half of the observations are
    below the median, and half are above the
    median.
  
  
  
  

Dispersion parameters

• Range: maximal value – minimal value


• Variance:


• Standard deviation: SD


• Standard error: SE

When a sample is described by a quantita-

tive trait, at least three values must be pro-

vided: (i) the sample size; (ii) a position

parameter (e.g. the mean); and (iii) a disper-

sion parameter (e.g. the standard error).

Finally, there is no way to describe accu-

rately a sample without a graphical repre-

sentation. Two possibilities are available

here: either a histogram of the full distribu-

tion of all the observations; or a distribution

summary, by plotting, for example, the inter-

val [x–SE; x– SE] in a graph.

Working example: fecundity of Trichogramma

Thirty mated females of Trichogramma brassi-

cae(i.e. an egg parasitoid used for biological

control of the European cornborer in

Europe), less than 24 h old, are isolated each

in a single test-tube for 7 days with more

than 200 Ephestia kuehniella eggs as hosts.

Then females are removed and the number

of black (i.e. parasitized) eggs is counted 3

days later. The recorded data were:

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Statistical Methods for Quality Control 307

= σ^2

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n

75 81 60 90 57 67 69 57 79 81 64 62 54 86 65

85 59 76 25 62 75 70 64 46 84 61 45 63 67 20