Allocation in Multivariate Stratified Sampling in Presence of Non-Response: A New Approch

7.1 Introduction In mail surveys, it is observed that the data may not be obtained in the first attempt, sometimes due to absenteeism and sometimes due to the refusal of the subject. This problem was first considered by Hansen and Hurwitz (1946), in which the population was divided into the groups of respondents and non respondents. They determine the sample size to be attempted on the first occasion and also the proportion of non-respondents to be attempted on the second occasion. El-Badry (1956), extended Hansen and Hurwitz's technique by sending waves of questionnaire to the non respondents units to increase the response rate. Foradari (1961), generalized El-Badry's approach and studied the use of Hansen and Hurwitz's technique under different designs. Srinath (1971), discussed a rule for the selection of subsample of non respondents under which the sub-sampling rate was not kept constant but taken as the sample non-response rates. Stratified sampling design is the most widely used sampling design for estimating the population parameters of a heterogeneous population. It deals with the properties of the estimates constructed from a stratified random sample and with the optimum choice of the sizes of the samples to be selected from various strata either to maximize the precision of the constructed estimate for a fixed cost or to minimize the cost of the survey for a fixed precision of the estimate. The sample sizes allocated according to either of the above criteria is called an " Optimum Allocation ". Khare (1987), discussed the problem of optimum allocation in stratified sampling in presence of non response for fixed cost as well as for fixed precision of the estimate. Khan et al. (2008), discussed the problem of determining the optimum allocation to