statplus1 the pmrs ottawa chapter would like to acknowledge the support of the following...
TRANSCRIPT
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STATPLUS 1
The PMRS Ottawa Chapter would like to acknowledge the support of the following
organizations.
Without their kind donations we could not continue to offer quality programs such as the one
you are about to see.
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La non-réponse :
Démonter la boîte noire
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STATPLUS 3
Composants principaux de la non-réponse
• Refus de participer
• Non-disponibilité
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STATPLUS 4
Taux de réponse :
Nombre de répondants
Nombre de cas éligibles
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STATPLUS 5
Questions abordées :
• Y a-t-il un lien entre le taux de réponse et le risque de biais?
• La pondération peut-elle atténuer les biais de non-réponse?
• Faut-il se soucier des biais qui sont “à l’intérieur de la marge d’erreur”?
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STATPLUS 6
Impact possible de la non-réponse :
• Engendrer des sur (sous) représentations de divers segments de l’échantillon (âge, sexe, langue d’usage…)
et/ouet/ou
• Engendrer des biais dans les estimations (degré de satisfaction…)
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STATPLUS 7
Distinction entre...
• Variables de profil (structure) :
(âge, sexe, langue d’usage…)
etet
• Variables de contenu :
(degré de satisfaction, cote d’écoute…)
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STATPLUS 8
Décomposition du biais de mesure
Non-réponse
Biais destructure
Biais demesure(structurel)
Non-réponse
Biais demesure
Biaisstructurel + Biais
interne
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STATPLUS 9
Biais si...
Il existe un lien entre :
• la probabilité de répondre au sondage
et
• le phénomène mesuré
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STATPLUS 10
Surreprésentation d’un segment si...
Il existe un lien entre :
• la probabilité de répondre au sondage
et
• le fait d’appartenir ou non au segment
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STATPLUS 11
L’ampleur du biais de surreprésentation d’un segment dépend...
• du taux de réponse
et
• de la corrélation entre la probabilité de réponse et le fait d’appartenir au segment
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STATPLUS 12
Biais de non-réponse en fonction du taux de réponse (tr)et de la corrélation () entre la variable mesurée et le fait de répondre ou non
0%
2%
4%
6%
8%
10%
12%
14%
10 % 20 % 30 % 40 % 50 % 60 % 70 % 80 % 90 % 100 %
Biais (%)
Taux de réponse (tr : %)
Biais ~ (100 - tr) x
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STATPLUS 13
L’ampleur du biais de surreprésentation dépend...
• du taux de réponse (= tr )
et
• de la corrélation entre la probabilité de réponse et l’appartenance au segment (= )
Biais ~ (100 - tr) x
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STATPLUS 14
Interprétation intuitive de
Différence entre :
• la probabilité de répondre si on appartient au segment
et
• la probabilité de répondre si on n’appartient pas au segment
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STATPLUS 15
Surreprésentation biais?
• Oui, si le segment surreprésenté se distingue par rapport à la ‘moyenne’ en ce qui concerne la caractéristique d’intérêt
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16STATPLUS
L’ampleur du biais engendré par la surreprésentation d’un segment dépend...
• de l’ampleur de surreprésentation
et
• de l’écart qui sépare le segment par rapport à la moyenne
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STATPLUS 17
L’ampleur du biais engendré par la surreprésentation d’un segment dépend...
• de l’ampleur de la surreprésentation (x %)
et
• de l’écart qui sépare le segment et son complément sur le phénomène mesuré (D)
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STATPLUS 18
L’ampleur du biais engendré par la surreprésentation d’un segment dépend...
• de l’ampleur de surreprésentation (x %)
et
• de l’écart qui sépare le segment et son complément sur le phénomène mesuré (D)
Biais = x % x D
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STATPLUS 19
Impact de la pondération
Non-réponse
Biais destructure
Pondération Correction dubiais destructure
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STATPLUS 20
Impact de la pondération
Non-réponse
Biais demesure
Biaisstructurel + Biais
interne
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STATPLUS 21
• Faut-il se soucier des biais qui sont “à l’intérieur de la marge d’erreur”?
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STATPLUS 22
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STATPLUS 23
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STATPLUS 24
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STATPLUS 25
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STATPLUS 26
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STATPLUS 27
Évolution de la théorie de l’échantillonnage
• Théorie classique : échantillons probabilistes
• Extension de la théorie : le concept de probabilité de réponse
• Modélisation des échantillons
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STATPLUS 28
Modèle probabiliste
Probabilité de
sélection
Population
Échantillon
Poids = inverse de la probabilité de sélection
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STATPLUS 29
Extension : concept de probabilité de réponse
Probabilité de
sélection
Probabilité de réponse
Population
Échantillon sélectionné
Poids = inverse de la probabilité de sélection
Échantillon effectif
Poids = inverse du taux de réponse
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STATPLUS 30
Extrapolation par modélisation
Profil
Profil
ModélisationPoids par
modélisation
Échantillon effectif
Population
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STATPLUS 31
Conclusions: on toujours avantage...
• à miser sur les stratégies qui augmentent les taux de réponse;
• à ancrer les échantillons sur le plus grand nombre de variables de contrôle possible.
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STATPLUS 32
Impact sur la précision des estimations
• Analogie avec les estimateurs de régression:
yr = y + β(X – x)
• Les 3 méthodes de pondération donnent des estimateurs qui appartiennent à la famille des estimateurs de régression
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STATPLUS 33
Impact sur la variance des estimations
• Diminution (impact de la régression) :
Var (yr ) = (1-R²) x Var (y)
• Augmentation (impact de la variation des poids) :
(1 + VM)/(1 + VB).
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STATPLUS 34
Impact sur le biais des estimations
• La correction du biais (x - X) apporte une correction proportionnelle sur y :
(yr - y) = ρ σy (X – x)/ σx
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STATPLUS 35
Évolution des taux de réponse
• Études omnibus
• Sondages périodiques (‘Tracking’)
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STATPLUS 36
Impact des efforts pour augmenter les taux de réponse
• Taux de réponse obtenu après x rappels (x=0, 1, 2,…)
• Taux de réponse obtenu avec ou sans récupération de refus
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STATPLUS 37
Caractéristiques des non-répondants
• Enquêtes en deux phases
• Caractéristiques de répondants en fonction des efforts requis pour obtenir une réponse
• Enquête de type panel
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STATPLUS 38
Calcul du taux de réponse
A = Tous les numéros ne correspondant pas à des ménages
B = Tous les ménages rejoints dont aucun membre ne satisfait le critère d’éligibilité
C = Tous les cas pour lesquels on n’a pu établir l’éligibilité
D = Tous les ménages “ éligibles ” dans lesquels on n’a pu réaliser une interview
E = Tous les répondants au questionnaire d’enquête principale
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STATPLUS 39
Taux de réponse
E / [D + E + (T.É.) x C]
(T.É.) = D + E B + D + E