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  1. Information sur le cours

    Rencontrez l'équipe enseignante
  2. Jeu de données du cours 1
  3. Jeu de données du cours 2
  4. MODULE A1: INTRODUCTION AUX STATISTIQUES AVEC R ET STATA
    A1.1 Qu'est-ce que les Statistiques?
  5. A1.2.1a Introduction à Stata
  6. A1.2.2b: Introduction à R
  7. A1.2.2c: Introduction to SPSS
  8. A1.3: Statistiques Descriptives
  9. A1.4: Estimations et Intervalles de Confiance
  10. A1.5: Tests d'Hypothèses
  11. A1.6: Transformation de Variables
  12. Fin du Module A1
    1 Quiz
  13. MODULE A2: CALCULS DE PUISSANCE STATISTIQUE & DE TAILLE D’ÉCHANTILLON
    A2.1 Concepts Clés
  14. A2.2 Calculs de puissance pour une différence de moyennes
  15. A2.3 Calculs de puissance pour une différence de proportions
  16. A2.4 Calcul de taille d’échantillon pour les essais randomisés (RCTs)
  17. A2.5 Calculs de taille d’échantillon pour les études transversales (ou sondages)
  18. A2.6 Calcul de taille d'échantillon pour un devis cas-contrôle
  19. Fin du Module A2
    1 Quiz
  20. MODULE B1: RÉGRESSION LINÉAIRE
    B1.1 Corrélation et Nuages de Points (scatterplots)
  21. B1.2 Différences Entre Moyennes (ANOVA à un facteur)
  22. B1.3 Régression Linéaire Univariée
  23. B1.4 Régression Linéaire Multivariée
  24. B1.5 Sélection de Modèles et Tests F
  25. B1.6 Diagnostics de Régression
  26. Fin du Module B1
    1 Quiz
  27. MODULE B2: COMPARAISONS MULTIPLES & MESURES RÉPÉTÉES
    B2.1 ANOVA Approfondie— Tests Post-Hoc
  28. B2.2 Correction pour Comparaisons Multiples
  29. B2.3 ANOVA à deux facteurs (Two-way ANOVA)
  30. B2.4 Mesures Répétées et Test T Apparié
  31. B2.5 ANOVA pour Mesures Répétées
  32. Fin du Module B2
    1 Quiz
  33. MODULE B3: MÉTHODES NON-PARAMETRIC
    B3.1 Hypothèses des Tests Paramétriques
  34. B3.2 Test U de Mann-Whitney
  35. B3.3 Test de Kruskal-Wallis
  36. B3.4 Test des rangs signés de Wilcoxon
  37. B3.5 Test de Friedman
  38. B3.6 Corrélation des Rangs de Spearman
  39. Fin du Module B3
    1 Quiz
  40. MODULE C1: DONNÉES BINAIRES & RÉGRESSION LOGISTIQUE
    C1.1 Introduction à la prévalence, au Risque, aux Cotes (Odds) et aux Taux
  41. C1.2 Le Test du Chi Carré & le Test de Tendance
  42. C1.3 Régression Logistique Univariée
  43. C1.4 Régression Logistique Multivariée
  44. Fin du Module C1
    1 Quiz
  45. MODULE C2: DONNÉES DE SURVIE
    C2.1 Introduction aux Données de Survie
  46. C2.2 Fonction de Survie de Kaplan-Meier & Test du Log-Rank
  47. C2.3 Régression de Cox à Risque Proportionnel
  48. C2.4 Régression de Poisson
  49. Fin du Module C2
    1 Quiz

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FoSSA Français A2.5 Calculs de taille d’échantillon pour les études transversales (ou sondages)
Lesson 17 of 49
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A2.5 Calculs de taille d’échantillon pour les études transversales (ou sondages)

Learning Outcomes

By the end of this section, students will be able to:

  • Explain the key concept of power and what impacts it
  • Estimate the power of a given study
  • Estimate the sample size needed to test hypotheses in different study designs

You can download a copy of the slides here: A2.5: Sample size calculations for cross-sectional studies (or surveys)

Video A2.5 Calcul de taille d’échantillon pour un devis transversal (3 minutes)

A2.5 PRACTICAL: R

Example of estimating sample size for a hypothesis in a cross-sectional study


You have been asked to help with a power calculation for a cross-sectional study, to estimate the point prevalence of obesity within a population. A study five years ago in this population found that 30% of people were obese, but the government thinks this has increased by 10% (to a point prevalence of 40%). Estimate the sample size needed for this study, assuming that the previous point prevalence of 30% is your `null hypothesis’. You want 80% power.

You are calculating a sample size for one proportion here.

The command is now ‘pwr.p.test’:

> power8<-pwr.p.test(h=ES.h(p1=0.3, p2=0.4), power=0.8, sig.level=0.05)
> power8

proportion power calculation for binomial distribution (arcsine transformation)

          h = 0.2101589
n = 177.7096
sig.level = 0.05
power = 0.8
alternative = two.sided

You need about 178 participants in your study to estimate this prevalence.

Question A2.5: One researcher has suggested that the proportion of the population who is obese may actually have decreased by 10% in the last five years (i.e. to 20%). How would this change your estimate for the sample size needed?

Answer

You are calculating a sample size for one proportion here.

> power9<-pwr.p.test(h=ES.h(p1=0.3, p2=0.2), power=0.8, sig.level=0.05)
> power9

proportion power calculation for binomial distribution (arcsine transformation)

          h = 0.2319843
n = 145.8443
sig.level = 0.05
power = 0.8
alternative = two.sided

The estimated sample size has now reduced slightly, to 146.

Based the outputs above, we can conclude that more data are needed to detect a change in proportion from 0.3 to 0.4 than from 0.3 to 0.2. For a fixed absolute difference (here the absolute difference in proportions is 0.1), larger sample sizes are needed to obtain a given level of power as the proportions approach 0.5. This relationship is symmetrical around 0.5, as shown below:

> power9<-pwr.p.test(h=ES.h(p1=0.1, p2=0.2), power=0.8, sig.level=0.05)
> power9

proportion power calculation for binomial distribution (arcsine transformation)

          h = 0.2837941
n = 97.45404
sig.level = 0.05
power = 0.8
alternative = two.sided

> power10<-pwr.p.test(h=ES.h(p1=0.9, p2=0.8), power=0.8, sig.level=0.05)
> power10     

proportion power calculation for binomial distribution (arcsine transformation)

          h = 0.2837941
n = 97.45404
sig.level = 0.05
power = 0.8
alternative = two.sided

Recall that the standard error (se) of the sampling distribution of p is LaTeX: sqrt{frac{pleft(1-pright)}{n}}.

As p gets closer to 0.5, the amount of variability increases (se is largest when p=0.5) and, therefore, more data are needed to detect a change in proportions of 0.1.

A2.5 PRACTICAL: Stata

Example of estimating sample size for a hypothesis in a cross-sectional study

You have been asked to help with a power calculation for a cross-sectional study, to estimate the point prevalence of obesity within a population. A study five years ago in this population found that 30% of people were obese, but the government thinks this has increased by 10% (to a point prevalence of 40%). Estimate the sample size needed for this study, assuming that the previous point prevalence of 30% is your `null hypothesis’.

You are calculating a sample size for one proportion here.

The command is:

power oneproportion 0.3, diff(0.1)

This could also be calculated using:

power oneproportion 0.3 0.4, power(0.8)

*–Estimated sample size: N = 172

Question A2.5: One researcher has suggested that the proportion of the population who is obese may actually have decreased by 10% in the last five years (i.e. to 20%). How would this change your estimate for the sample size needed?

Answer

You are calculating a sample size for one proportion here.

  power oneproportion 0.3, diff(-0.1)

Or alternatively:

power oneproportion 0.3 0.2

*– Estimated sample size: N = 153

The estimated sample size has now reduced slightly, to 153.

Based the outputs above, we can conclude that more data are needed to detect a change in proportion from 0.3 to 0.4 than from 0.3 to 0.2. For a fixed absolute difference (here the absolute difference in proportions is 0.1), larger sample sizes are needed to obtain a given level of power as the proportions approach 0.5. This relationship is symmetrical around 0.5, as shown below:

power oneproportion 0.1 0.2

*– Estimated sample size: N = 86

power oneproportion 0.9 0.8

*– Estimated sample size: N = 86

Recall that the standard error (se) of the sampling distribution of p is LaTeX: sqrt{frac{pleft(1-pright)}{n}}. As p gets closer to 0.5, the amount of variability increases (se is largest when p=0.5) and, therefore, more data are needed to detect a change in proportions of 0.1.

A2.5 PRACTICAL: SPSS

Example of estimating sample size for a hypothesis in a cross-sectional study

You have been asked to help with a power calculation for a cross-sectional study, to estimate the point prevalence of obesity within a population. A study five years ago in this population found that 30% of people were obese, but the government thinks this has increased by 10% (to a point prevalence of 40%). Estimate the sample size needed for this study, assuming that the previous point prevalence of 30% is your `null hypothesis’.

Select

Analyze >> Power Analysis >> Proportions >> One Sample Binomial Test

Input the values form the scenario into the Power Analysis window as before. In this example the Population proportion is the predicted value of 40% (0.4) and the null value is the previous prevalence of 30% (0.3).

One researcher has suggested that the proportion of the population who is obese may actually have decreased by 10% in the last five years (i.e. to 20%). How would this change your estimate for the sample size needed?

Answer

For the first part of the question, when the hypothesis is that we will see a 40% prevalence, the output table will look like this.

The estimated sample size we need to have a power of 80% is 172.

In the second part of the question, when the hypothesis is that we will see a 20% prevalence, the output table will look like this.

The estimated sample size has now reduced slightly, to 153.

Based the outputs above, we can conclude that more data are needed to detect a change in proportion from 0.3 to 0.4 than from 0.3 to 0.2. For a fixed absolute difference (here the absolute difference in proportions is 0.1), larger sample sizes are needed to obtain a given level of power as the proportions approach 0.5. This relationship is symmetrical around 0.5, as shown below:

Recall that the standard error (se) of the sampling distribution of p is LaTeX: sqrt{frac{pleft(1-pright)}{n}}. As p gets closer to 0.5, the amount of variability increases (se is largest when p=0.5) and, therefore, more data are needed to detect a change in proportions of 0.1

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