A Note on the Precision of Stratified Systematic Sampling
Affiliation(s)
1 Institute for Security Studies, Abuja, Nigeria. 2 Department of Statistics, University of Ilorin, Ilorin, Nigeria.
1 Institute for Security Studies, Abuja, Nigeria. 2 Department of Statistics, University of Ilorin, Ilorin, Nigeria.
ABSTRACT
Conflicting views had greeted the use of systematic sampling for sample selection and estimation in stratified sampling in terms of the precision of the population mean base on the inherent characteristics of the population. These conflicting views were analyzed using Cochran data (1977, p. 211) [1]. When the population units are ordered, variance of systematic sampling for all possible systematic samples provides equal, non-negative and most precise estimates for all the variance functions considered i.e.
, unlike when a single systematic sample is used and when variance of simple random sampling is used to estimate selected systematic samples.
Conflicting views had greeted the use of systematic sampling for sample selection and estimation in stratified sampling in terms of the precision of the population mean base on the inherent characteristics of the population. These conflicting views were analyzed using Cochran data (1977, p. 211) [1]. When the population units are ordered, variance of systematic sampling for all possible systematic samples provides equal, non-negative and most precise estimates for all the variance functions considered i.e.
, unlike when a single systematic sample is used and when variance of simple random sampling is used to estimate selected systematic samples.
KEYWORDS
Precision, Systematic Sampling, Stratified Systematic Sampling, Systematic Random Estimator
Precision, Systematic Sampling, Stratified Systematic Sampling, Systematic Random Estimator
Cite this paper
Kareem, A. , Oshungade, I. and Oyeyemi, G. (2015) A Note on the Precision of Stratified Systematic Sampling. Open Journal of Statistics, 5, 104-112. doi: 10.4236/ojs.2015.52013.
Kareem, A. , Oshungade, I. and Oyeyemi, G. (2015) A Note on the Precision of Stratified Systematic Sampling. Open Journal of Statistics, 5, 104-112. doi: 10.4236/ojs.2015.52013.
References
[1] Cochran, W.G. (1977) Sampling Techniques. 3rd Edition, John Wiley and Sons, New York. [2] Murthy, M.N. (1967) Sampling Theory and Methods. 2nd Edition, Statistical Publishing Society, Calcutta. [3] Raj, D. and Chandhok, P. (1998) Sample Survey Theory. Narosa Publishing House, New Delhi. [4] Madow, W.G. (1953) On the Theory of Systematic Sampling III. Annals of Mathematical Statistics, 24, 101-106.
http://dx.doi.org/10.1214/aoms/1177729087 [5] Gautschi, W. (1957) Some Remarks on Systematic Sampling. Annals of Mathematical Statistics, 28, 385-394.
http://dx.doi.org/10.1214/aoms/1177706966 [6] Okafor, F.C. (2002) Sample Survey Theory with Applications. Afro-Orbis Publications Ltd., Nsukka. [7] Lahiri, D.B. (1952) NSE Instruction to Field Workers. See Murthy (1967, p. 140). [8] Leu, C.-H. and Tsui, K.-W. (1996) New Partially Systematic Sampling. Statistica Sinica, 6, 617-630. [9] Chang, H.J. and Huang, K.C. (2000) Reminder Linear Systematic Sampling Sankya. The Indian Journal of Statistics, 62 (Series B), 249-256. [10] Kareem, A.O, Oyeyemi, G.M. and Adewara, A.A (2015) On the Choice of an Efficient Sampling Scheme within Strata ICASTOR. Indian Journal of Mathematical Science, 9. (In Press) [11] Mendehall, W., Ott, L. and Scheafffer, R.L. (1971) Elementary Survey Sampling. Duxbary Press, Belmont.
[1] Cochran, W.G. (1977) Sampling Techniques. 3rd Edition, John Wiley and Sons, New York. [2] Murthy, M.N. (1967) Sampling Theory and Methods. 2nd Edition, Statistical Publishing Society, Calcutta. [3] Raj, D. and Chandhok, P. (1998) Sample Survey Theory. Narosa Publishing House, New Delhi. [4] Madow, W.G. (1953) On the Theory of Systematic Sampling III. Annals of Mathematical Statistics, 24, 101-106.
http://dx.doi.org/10.1214/aoms/1177729087 [5] Gautschi, W. (1957) Some Remarks on Systematic Sampling. Annals of Mathematical Statistics, 28, 385-394.
http://dx.doi.org/10.1214/aoms/1177706966 [6] Okafor, F.C. (2002) Sample Survey Theory with Applications. Afro-Orbis Publications Ltd., Nsukka. [7] Lahiri, D.B. (1952) NSE Instruction to Field Workers. See Murthy (1967, p. 140). [8] Leu, C.-H. and Tsui, K.-W. (1996) New Partially Systematic Sampling. Statistica Sinica, 6, 617-630. [9] Chang, H.J. and Huang, K.C. (2000) Reminder Linear Systematic Sampling Sankya. The Indian Journal of Statistics, 62 (Series B), 249-256. [10] Kareem, A.O, Oyeyemi, G.M. and Adewara, A.A (2015) On the Choice of an Efficient Sampling Scheme within Strata ICASTOR. Indian Journal of Mathematical Science, 9. (In Press) [11] Mendehall, W., Ott, L. and Scheafffer, R.L. (1971) Elementary Survey Sampling. Duxbary Press, Belmont.