0851996884.pdf

which is greater than 1.96. So there is a sig-
nificant positive correlation between
females’ fecundity and longevity, with a
probability level of 5%. Figure 20.4 shows
the graph describing this significant relation-
ship.

Studying the Correlation Between Two

Traits Expressed as Percentages

When the two quantified traits are percent-
ages computed simultaneously with data
from the same sample (e.g. sex ratio and
adult mortality), the significance of a rela-
tionship between them can also be calcu-
lated. For this, a first step consists of
building a so-called contingency table. If the
two traits studied are sex ratio and rate of
adult mortality, then such a table would look
like that in Fig. 20.5.
From this table, the tvalue can be com-
puted as follows:

If the obtained t value is greater that 1.96,

there is a significant relationship between the

two traits at a 5% probability level. For the

example here, this would mean a significant

difference in adult mortality between males

and females.

t

a b c d ad bc

ab cd ac bd

=

()+++×−()

()+ ×+()×+()×+()

2

Statistical Methods for Quality Control 311

r=1.0 r0.8 r 0.0 r 0.8 r 1.0

Fig. 20.3.Examples of relationships between two quantitative traits with different values of the linear
correlation coefficient.

Table 20.1.Data for longevity and fecundity in Trichogramma brassicae.

Female Female Female

number Longevity Fecundity number Longevity Fecundity number Longevity Fecundity

1 16 103 11 20 97 21 20 113

2 24 104 12 19 106 22 21 67

3 23 115 13 26 140 23 23 100

4 18 95 14 14 98 24 23 103

5 17 64 15 15 106 25 21 93

6 15 95 16 22 126 26 15 112

7 9 85 17 20 109 27 13 71

8 33 140 18 20 106 28 13 88

9 24 92 19 23 106 29 24 93

10 13 73 20 17 98 30 18 100

160

140

120

100

80

60

40

0 1020304050

Longevity (days)

Fecundity (eggs per female)

Fig. 20.4.Relationship between the longevity and

the fecundity of T.brassicaefemales. The ellipse

represents a 5%-risk confidence interval of the

bivariate average values.