0851996884.pdf

Building a Confidence Interval Around

the Mean: a Way to Compare the Sample

with a Predefined Standard

Once a sample is described with the parame-
ters presented above (e.g. mean, standard
error, etc.), one must check whether the cor-
responding mass-reared animals satisfy a
predefined standard (i.e. a QC criterion). For
this, a statistical procedure is available,
based on the estimation of a confidence
interval around the estimated value of inter-
est. The procedure is the same both for the
average value of a regular quantitative trait
(e.g. fecundity) and for a trait expressed as a
percentage (e.g. sex ratio). The confidence
interval of the estimated parameter, at a 5%
probability level, is computed using the fol-
lowing equation:

[parameter – 1.96 ×SE; parameter+ 1.96 ×SE]

where parameteris the computed average or
percentage of the sample, and SEis its stan-
dard error. So, for a regular quantitative trait
(e.g. fecundity), the confidence interval of
the average value, at a 5% probability level,
is:

and, for a percentage (e.g. sex ratio):

Then, if the predefined standard is not within
this confidence interval, the hypothesis that
the estimated parameter and the guideline

are equal is rejected with a risk of 5% – that

is, with a 5% chance that the hypothesis

rejected is actually true. Saying that the confi-

dence interval is estimated at a 5% probabil-

ity level means that, if 100 equivalent

samples had been used to estimate 100 confi-

dence intervals, the true (unknown) average

value or percentage representing the popula-

tion would occur in only 95 of the confidence

intervals computed. One can, of course, make

more reliable decisions at much lower proba-

bility levels, e.g. 1%. In this case, the value

‘1.96’ should be replaced by a larger value

(e.g. a value of ‘2.58’ should be used for a

decision at a probability level of 1%).

A very important point to make here is

that the procedure explained above is valid

only if the sample size is at least 30. This

point is often violated in QC and leads to

wrong conclusions, both positive and nega-

tive, about the quality of natural enemies.

Working example for a regular quantitative

trait: does the fecundity of Trichogramma

meet the quality control criterion?

The fecundity of 30 T. brassicaefemales has

been quantified and an average value of

64.97 eggs per female was obtained, with an

SEof 2.96 eggs per female (see the working

example above). The predefined fecundity

criterion is a minimum of 40 eggs per female.

The confidence interval at a probability level

of 5% is [64.97 – 1.96 × 2.96; 64.97 + 1.96 ×

2.96] resulting in [59.17; 70.77]. The standard

of 40 eggs per female is not within this confi-

dence interval. So we conclude, with a risk of

5%, that the average fecundity of the sample

differs significantly from the standard fecun-

dity. In the population tested, the fecundity

is higher. For the mass rearing, there should

of course be no problem in this case.

Working example for a percentage: does

the sex ratio of Trichogramma meet the

quality control criterion?

The sex ratio (% females) estimated from a

sample of 500 adults of T. brassicaewas 0.460

(with an SEof 0.022). According to the QC

p

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196

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196

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196 .;. 196

SD SD

Statistical Methods for Quality Control 309

Fig. 20.2.A graphical representation of the
estimated sex ratio in T.brassicae.