Estimation of Population Mean in Two-Stage Sampling with Systematic Sampling in the Second Stage Sampling
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Abstract
This paper aims at proposing the estimator of the population mean in two-stage sampling when systematic sampling method in the second stage sampling is used instead of the usual simple random sampling method. Its Bias and Mean Square Error (MSE) are derived and its efficiency compared with the usual estimator when simple random sampling is applied at both stages. The theoretical results are validated numerically using the weights and ages of patients in Maternal and Child Health (MCH) Centres across Umuahia North Local Government Area and it is established that the proposed estimator has a greater efficiency than the existing classical estimator.
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References
Chaudhary, M. & Singh, V.K. (2013).Estimating the Population Mean in Two-Stage Sampling with Equal Size Clusters under Non-Response Using Auxiliary Characteristic. Mathematical Journal of Interdisciplinary Sciences, 2 (1), 43-55.
Cochran, W. G. (1977). Sampling Techniques (Third ed.). Wiley. ISBN 0-471-16240-X.
Damon, V. (2018). Advantages and Disadvantages of Multistage Sampling. https://classroom.synonym.com/advantages-disadvantages-multistage-sampling-8544049.html
Dilip, N.C. (2015). Two-stage sampling design for estimation of Total Fertility Rate: with an Illustration for slum dweller married woman. Electronic Journal of Applied Statistical Analysis, 8(1), 112-121.
Knottnerus, P. (2011). Sample Survey Theory: Simple Derivations of Variance Formulas in Two-Stage Simple Random Sampling, Netherland: Statistics Netherland, Henri Faasdreef. http://www.cbs.nl
Monika, S.K. & Nguyen, C.K. (2013).A Review of the Cluster Survey Sampling Method in Humanitarian Emergencies. Public Health Nursing, 25(4). https://doi.org/10.1111/j.1525-1446.2008.00719.x
Okafor, F. C. (2002): Sampling survey theory with application. Afro-Orbis Publications Ltd, Nsukka.
Ravendra, S., Gajendra, K., Gupta, P.C. & Pareek, S. (2013). An Alternative Approach to Estimation of Population Mean in Two-Stage Sampling. Journal of Mathematical Theory and Modeling, 3(13), 48-53.
Shalabh (2003). "Estimation of Bias and Standard Error of An Improved Estimator of Population Mean in Two-stage Sampling", Metrika, 54, 43-51
Srinath, K.P. & Hidiroglou, M.A. (1980). Estimation of Variance in Multi-stage Sampling. International Journal for Theoretical and Applied Statistics, 27(1), 121-125.
Steen, M., Erik, N. & Terje, G. (2013).An Estimator of Variance for Two-Stage Ratio Regression Estimators. Forest Science, 60(4), 663-676.
Sven, B. (1972). Double Sampling for Cluster or Two-stage Sampling. International Statistical Review. 40(1), 13-22.
Cochran, W. G. (1977). Sampling Techniques (Third ed.). Wiley. ISBN 0-471-16240-X.
Damon, V. (2018). Advantages and Disadvantages of Multistage Sampling. https://classroom.synonym.com/advantages-disadvantages-multistage-sampling-8544049.html
Dilip, N.C. (2015). Two-stage sampling design for estimation of Total Fertility Rate: with an Illustration for slum dweller married woman. Electronic Journal of Applied Statistical Analysis, 8(1), 112-121.
Knottnerus, P. (2011). Sample Survey Theory: Simple Derivations of Variance Formulas in Two-Stage Simple Random Sampling, Netherland: Statistics Netherland, Henri Faasdreef. http://www.cbs.nl
Monika, S.K. & Nguyen, C.K. (2013).A Review of the Cluster Survey Sampling Method in Humanitarian Emergencies. Public Health Nursing, 25(4). https://doi.org/10.1111/j.1525-1446.2008.00719.x
Okafor, F. C. (2002): Sampling survey theory with application. Afro-Orbis Publications Ltd, Nsukka.
Ravendra, S., Gajendra, K., Gupta, P.C. & Pareek, S. (2013). An Alternative Approach to Estimation of Population Mean in Two-Stage Sampling. Journal of Mathematical Theory and Modeling, 3(13), 48-53.
Shalabh (2003). "Estimation of Bias and Standard Error of An Improved Estimator of Population Mean in Two-stage Sampling", Metrika, 54, 43-51
Srinath, K.P. & Hidiroglou, M.A. (1980). Estimation of Variance in Multi-stage Sampling. International Journal for Theoretical and Applied Statistics, 27(1), 121-125.
Steen, M., Erik, N. & Terje, G. (2013).An Estimator of Variance for Two-Stage Ratio Regression Estimators. Forest Science, 60(4), 663-676.
Sven, B. (1972). Double Sampling for Cluster or Two-stage Sampling. International Statistical Review. 40(1), 13-22.