0851996884.pdf

guidelines, a standard of 0.50 (i.e. 50%
females) is required. The estimated confi-
dence interval at a 5% probability level is
[0.460 – 1.96 × 0.022; 0.460 + 1.96 × 0.022],
which results in [0.417; 0.503] or, in terms of
percentages, [41.7%; 50.3%]. The calculated
confidence interval of the sample includes
the standard value of 0.50. So the conclusion
is that the estimated sex ratio is not signifi-
cantly different from the standard value,
although it is somewhat lower.

Studying the Correlation Between Two

Quantitative Traits

Usually, more than a single quantitative trait
is quantified with data from one sample, and
there are more accurate statistical methods
available than the ones described above to
handle several traits simultaneously. In this
chapter, only methods for simultaneously
handling two quantitative traits will be pre-
sented. When the two quantified traits are
regular quantitative values measured simulta-
neously on each individual of the sample, it is
possible to check if there is a significant rela-
tionship between them. For this, the covari-
ance of the population has to be estimated
first from all the observations of the sample.
This is done using the following equation:

Using the obtained value, the linear corre-
lation between the two quantified traits is
then:

where xand yare the standard deviations
of the variables xand y, respectively.
A bivariate plot is used for a graphical
representation, with one trait on the xaxis,
and the other on the yaxis. Each point corre-
sponds to an observation in the sample.
Sometimes, a bivariate confidence interval

can be added to the graph (i.e. ellipse), but

special statistical computer programs are

needed for this (see example below). As can

be seen in Fig. 20.3, the correlation coefficient

ranges from –1 to +1. A value of –1 indicates

that there is a strictly negative linear rela-

tionship between the two traits. A value of

+1 indicates a strictly positive linear relation-

ship. A value of zero shows the absence of

any relationship. Intermediate values corre-

spond to intermediate situations.

It is important to determine whether the

correlation is significant. This can be done by

calculating twith the following formula:

where nis the sample size. If the computed

value is larger than 1.96, there is a significant

relationship between the two traits studied,

at a probability level of 5%. Again, this test is

valid only if the sample size is at least 30. For

QC problems, such a statistical procedure

can be very useful. Indeed, the existence of a

significant relationship between two quanti-

tative traits can lead to a decision to quantify

only one of them, thus saving both time and

money.

Working example: are longevity and

fecundity correlated in Trichogramma?

Thirty mated T. brassicaefemales are isolated

in test tubes with more than 200 E. kuehniella

eggs as hosts, for 7 days. Then both the num-

ber of parasitized (i.e. black) eggs (i.e. fecun-

dity, expressed in eggs per female) and the

number of days females remained alive (i.e.

longevity, expressed in days) are quantified.

The recorded data for the 30 females were as

in Table 20.1.

From these data, the following descriptive

statistics can be computed: (i) n= 30; (ii) x–=

19.3 days and y– = 99.93 eggs; (iii) x= 4.921

days and y= 17.836 eggs; and (iv) covari-

ance = 51.469. The correlation coefficient is

thus: 51.469/(4.921 ×17.836) = 0.586, and the

corresponding tvalue is:

t

rn

r

=

×−()

−

2

2

2

1

r

xy

covariance

=

σσ×

=

()×

−

−

××

−

=

∑xy

n

nxy

n

ii

i

n

1

11

covariance =

()− ×−()

−

=

∑xx yy

n

ii

i

n

1

1

310 E. Wajnberg

0 586 30 2 1 0 586./..,^22 ×−( ) ( − )= 3 83