172
Statistique appliquée aux sciences de la vie
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
(a) correlation= 1
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
(b) correlation= −1
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
(c) correlation= 0
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
(d) correlation= 0.94
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
(e) correlation= 0.66
●
●
●
●
●
●
●
●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
(f) correlation= 0.94
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
(g) correlation= 0.41
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
(h) correlation= −0.03
● ●
●
●
●
●
●
● ●
●
●
●
●
●
●
● ●
●
●
●
●
● ●
●
●●
●
●
●
●
●
●
●
● ●
●
●
● ●
●
●
●
●
●
●
● ●
●
●
●
● ●
● ●
●
●
●
●
●
●
●●
● ● ●
●
●
●
●
●
●
● ● ●
●
● ●
●
● ●
●
●
● ●
●
●
●
●
●
●● ●
●
●
●
● ●
●
●
●
(i) correlation= 0.88
Figure 12.4 – Exemples de corrélations entre variables continues.
linéaire, et c’est précisément cette information que nous donne la corrélation.
Les graphiques (d), (e) et (g) nous montrent trois exemples de relations positives avec plus ou moins d’intensité. Alors que l’on est assez proche d’une
relation exacte linéaire dans le graphique (d) (avec une corrélation de 0.94), on
en est plus loin dans le graphique (g) (avec une corrélation de 0.41). Le graphique (h) nous montre un cas où l’on est proche de l’indépendance entre les
variables (corrélation très proche de 0). On rappelle ainsi que l’indépendance
implique la nullité de la covariance et donc de la corrélation. Par contre, on
a mentionné que la réciproque n’est pas valable. Une covariance/corrélation
nulle n’implique pas l’indépendance entre les variables, comme nous le montre
le graphique (c). On a ici une corrélation nulle (il y a en particulier autant
d’observations dans les quadrants 1 et 3 que dans les quadrants 2 et 4), bien
que la relation entre les variables soit exacte quadratique (les variables ne sont
donc pas du tout indépendantes ; étant donné la valeur de X, on connaît ici
parfaitement la valeur de Y ). Finalement, le graphique (i) nous montre que la
corrélation est très sensible aux valeurs extrêmes ou aberrantes. On voit sur
ce graphique les mêmes données que celles représentées dans le graphique (h),