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PROJECT TOPIC- SUB-SAMPLING THE NON-RESPONDENTS IN TWO-STAGE SAMPLING OVER TWO SUCCESSIVE OCCASIONS

PROJECT TOPIC- SUB-SAMPLING THE NON-RESPONDENTS IN TWO-STAGE SAMPLING OVER TWO SUCCESSIVE OCCASIONS

 

Abstract

Severa.1 studies carried out in sampling with partial replacement of units assumed total response from the sample units. The present study looks at the situation where some sample units do not supply the necessary information.
The estimates of the population tota.1 and change in the population total from one occasion to the next have been adjusted for unit non-response using Hansen and Hurwitz (1946) technique. It has been shown empirically that the estimator, T, obtained from partial matching at the first and second sta.ges of sampling is more efficient than the estimator, To, obtained when there is no partial matching of units.
The proposed estimators’ hwe been applied to the estimation of total hectares of land planted in 1999/2000 planting season and change in the land planted between 1998/1999 and 1999/2000 planting seasons in Botswana.

Introduction

In estimating population parameters like the mean, total or ratio, sample survey experts sometimes use; auxiliary information to improve precision
of the estimates. If the survey is repetitive in nature, past values of the variable of interest may be used as an auxiliary to improve on . the precision of the current estimate. In such repetitive surveys, a fraction of the original sample units may be retained for use at the – curreilt occasion, while the remaining fraction is selected afresh. This procedure is called sampling oa successive occasions or sampling with partial replacement of units (Ware and Cunia, 1962; Raj, 1965; Frayer and Furnival, 1967). Other researchers who have worked on successive sampling include Singh (1968), Kathuria (1975) and Arnab (1980). These authors assumed that there is complete response from all the sample units.
It is well known especially in human surveys that information is usually not obtained from all the sample units even after callbacks. Hansen and Hurwitz (1946) proposed a simple procedure of sub-sampling the non-respondents in order to adjust for the non-response in a mail survey. This method has been applied by Okafor and Lee (2000) in double sampling for ratio and regresion estimation. Okafor (2001) extended , this work to the estimation of the population total in element samplivg on two successive occasions. Consider a finite population of N first stage units (fsu’s) in which the i-th fsu (2 = 1,2,. -. , N) consists of Mi second stage units (ssu’s).

Let x i j ( p t j ) be the value of variable of interest at the first (secorid) occasion for the j-th ssu ( j = 1’2, . . . , Mi)in the i-th fsu. Also, let be their respective population totals. In this paper, two-stage sampling Two-Stage Sampling strategies over two successive occasions have been proposed Vor the estimation of the current population total and change in totals when there is non-response on the two occasions. The Hansen and Hurwitz (1946) procedure is used in this case to adjust for non-response. Srinatli (1971) used a procedure different from Hansen and Hurwitz (1946), for selecting the subsample of non- respondent,^ where the subsampling fraction varies according to the nonresponse rates. He applied his procedure in one time element sampling. The variance ob- i tained through his procedure does not involve the population response rate W. However, his procedure is not the subject of my present study.

2 Sampling Strategies

Sampling Scheme 1
First Occasion :
Select n first stage units (

PROJECT TOPIC- SUB-SAMPLING THE NON-RESPONDENTS IN TWO-STAGE SAMPLING OVER TWO SUCCESSIVE OCCASIONS

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