176
Statistique appliquée aux sciences de la vie
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(a) correlation= 0.71
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(b) correlation= 0.53
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(c) correlation= 0.33
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(d) correlation= 0.89
Figure 12.6 – Effet d’une sélection selon X sur une corrélation.
corrélation séparément pour chaque sexe, on trouve 0.57 chez les filles et 0.53
chez les garçons (c’est-à-dire une corrélation d’à peu près 0.55 au lieu de 0.73).
Si notre question (d’anatomie) est la relation qui peut exister entre la longueur
de la main et la taille chez l’espèce humaine, on ne voudra sans doute pas y
inclure la part confondante due au sexe et on reportera ici une corrélation d’à
peu près 0.55 plutôt que de 0.73.
On pourra également modifier la valeur d’une corrélation entre deux variables en sélectionnant une sous-population particulière d’une population au
départ homogène, selon des critères d’inclusion et d’exclusion parfois artificiels.
Les figures 12.6 et 12.7 nous montrent les conséquences possibles d’une telle
sélection sur la valeur d’une corrélation. Afin de commenter les graphiques de
la figure 12.6, on reprendra l’exemple de la corrélation entre la longueur de la
main et la taille d’une personne. Le graphique (a) nous montre un échantillon
provenant d’une population homogène avec une corrélation de 0.71. Dans le
graphique (b), il s’agit des mêmes données où l’on a éliminé les individus avec
de grandes mains. La corrélation s’en trouve diminuée de 0.71 à 0.53. On a en
effet éliminé la plupart des individus qui se trouvaient dans le quadrant 1 du
graphique (a) et qui contribuaient positivement à la corrélation. La sélection
a été encore plus drastique dans le graphique (c), où l’on n’a retenu que les