12. Analyse de corrélation
177
QI verbal
QI raisonnement
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(a) correlation= 0.37
QI verbal
QI raisonnement
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(b) correlation= −0.23
QI verbal
QI raisonnement
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(c) correlation= −0.16
QI verbal
QI raisonnement
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(d) correlation= −0.53
Figure 12.7 – Effet d’une sélection selon X et Y sur une corrélation.
individus avec de petites mains et où la corrélation n’est plus que de 0.33. On
trouvera souvent ainsi des corrélations plus petites en restreignant le domaine
d’observation. Notons qu’il est aussi possible d’augmenter artificiellement la
valeur d’une corrélation, comme illustré dans le graphique (d), où l’on a retenu
les individus avec de petites mains et avec de grandes mains, mais où l’on a
exclu les mains moyennes. On a ainsi éliminé presque tous les individus qui
se trouvaient dans les quadrants 2 et 4 du graphique (a) et qui contribuaient
négativement à la corrélation, de sorte que celle-ci augmente de 0.71 à 0.89.
Ces exemples nous montrent que l’on peut influencer la valeur d’une corrélation
de manière importante en considérant une sous-population plutôt qu’une autre
(en sélectionnant nos individus d’une façon plutôt que d’une autre)
5 .
Exemple 12.4 La figure 12.7 nous montre d’autres exemples de sélection artificielle d’individus parmi une population au départ homogène. On s’intéresse ici
5 L’assertion « la corrélation entre la longueur de la main et la taille d’une personne est
égale à 0.55 » est donc incomplète. Il faut encore préciser à quelle population cette corrélation
se réfère. On a vu que cette corrélation sera différente selon que l’on considère une population
mélangée de filles et de garçons, ou une population constituée uniquement de filles ou de
garçons. Cette corrélation sera également différente selon que l’on considère par exemple une
population d’étudiants en médecine ou une population de basketteurs, le choix de ces derniers
résultant d’une sélection d’individus en général plutôt grands et avec de grandes mains.