Design‐based or Prediction‐based Inference? Stratified Random vs Stratified Balanced Sampling

Early survey statisticians faced a puzzling choice between randomized sampling and purposive selection but, by the early 1950s, Neyman's design‐based or randomization approach had become generally accepted as standard. It remained virtually unchallenged until the early 1970s, when Royall and his co‐authors produced an alternative approach based on statistical modelling. This revived the old idea of purposive selection, under the new name of “balanced sampling”. Suppose that the sampling strategy to be used for a particular survey is required to involve both a stratified sampling design and the classical ratio estimator, but that, within each stratum, a choice is allowed between simple random sampling and simple balanced sampling; then which should the survey statistician choose? The balanced sampling strategy appears preferable in terms of robustness and efficiency, but the randomized design has certain countervailing advantages. These include the simplicity of the selection process and an established public acceptance that randomization is “fair”. It transpires that nearly all the advantages of both schemes can be secured if simple random samples are selected within each stratum and a generalized regression estimator is used instead of the classical ratio estimator. Les statisticiens de sondage ont eu un choix problematique entre l'echantillonage aleatoire et une selection choisie a dessin, mais dansles premieres annees 1950, l'approche de Neyman basee sur les plans d'echantillonage, ou sa methode aleatoire, etait devenue l'etalon generalement; accepte Cet etalon n'a pas eu de concurrence jusqu'aux premieres annees 1970, Iorsque Royall et ses collegues on produit une approche alternative basee sur un modele statistique. Cette approche a reactive l'ancienne idee de selection choisie a dessein, sous le titre d'echantillonage compense. Supposons que la strategie d'echantillonage employee pou un sondage particulier necessite, en meme temps, un plan d'echantillonage stratifie et l'estimateur classique du quotient; mais que dans chaque strate, le choix est permis entre l'echantillonage simple aleatoire et l'echantillonage simple compense. On se demande lequel des deux le statisticien de sondage choisirait? La strategie d'echantillonage compense semple preferable du point de vue de robustesse et d'eficacite, mais le plan aleatoire a, malgre tout, certains avantages. Ceux‐ci comprennent la simplicitfe du processus de selection et l'acceptation publique que la methode ale atoire est equitable. On se rend compte que presque tous les avantages des deux procedes peuvent etre combines si les echantillons aleatoires simples sont choisis parmi chaque strate, et un estimateur de regression generalisee est employe au lieu de l'estimateur classque du quotient.