The Use of Cluster Analysis for Stratification

Abstract

Stratification is a feature of the majority of field sample designs. In the early stages of multi-stagesample procedures the population is often small so that the number of stratification factors which may be employed is limited. The use of cluster analysis allows any number of stratification factors to be incorporated in producing a "specified" or "best" number of strata. An application of the technique in a four-stage design for the selection of a sample of motorists in Birmingham is discussed.

A Procedure for Computing Optimal Stratum Boundaries and Sample Sizes for Multivariate Surveys

“…This approach was introduced by [37] and was also treated by [38]. Thomsen [39] presented an approximation to the variance of the study variable under the assumption of a linear regression on two stratification variables where he demonstrated that under some conditions, one can expect a considerable reduction of the variance using two variables.…”

“…Stratification was also investigated using cluster analysis in [37], [41], and [42]. Following their concepts, [43] proposed the concept of stratification as an optimization problem under the clustering approach which achieved more efficient stratification than other authors in this area.…”

Simple Compromise Strategies in Multivariate Stratification

“…The FPC has been adopted in the literature along with the variance reduction strategy in Section 1 for use in multivariate stratification. See, for example, Hagood and Bernart (1945), Golder and Yeomans (1973), Kish and Anderson (1978) and Jarque (1981). Following Golder and Yeomans (1973), strata can be formed by minimizing V F (U h ) = V str (ȳ 1,str ), whereȳ 1,str is the stratified mean estimator for y 1 with its variance V str (ȳ 1,str ) given as…”

“…See, e.g., Golder and Yeomans (1973) and Jarque (1981). In order to form H (or K as indicated in its nomenclature) strata, the objective function of the K-means clustering algorithm can be written as…”

Structure des peuplements forestiers

“…Très rapidement, on s'est aperçu que les calculs classiques de variance surestimaient les erreurs. L'un des procédés utilisés pour affiner les estimations est la stratification, a priori ou a posteriori, qui consiste à regrouper les placettes par grandes catégories de volume par exemple et à faire les calculs séparément pour chaque strate (Pardé, 1960 ;Singh, 1974 ;Schumacher, 1966 ;Cochran, 1963 ;Loetsch, 1964 ;Arvanitis, 1970 ;Golder, 1973 La plupart des auteurs, devant la difficulté, étudient par simulation directe sur des données les précisions obtenues et comparent à des maillages aléatoires (Finney, 1953 ;Shiue, 1960 ;Matern, 1962 ;Zinger, 1964 ;Grayet, 1977 ;Payandeh, 1970a ;Nyyssônen, 1967 ;Bouchon, 1974 ;Le Goff, 1977) ; ils concluent à la supériorité des maillages systématiques, au moins lorsque la population n'est pas distribuée au hasard.…”