Efficiency of Neyman Allocation Procedure over other Allocation Procedures in Stratified Random Sampling
American Journal of Theoretical and Applied Statistics
Volume 2, Issue 5, September 2013, Pages: 122-127
Received: Aug. 6, 2013;
Published: Aug. 30, 2013
Views 3570 Downloads 723
Olayiwola Olaniyi Mathew, Department of Statistics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria
Apantaku Fadeke Sola, Department of Statistics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria
Bisira Hammed Oladiran, Department of Mathematics, Lagos State Polytechnic, Ikorodu, Lagos State, Nigeria
Adewara Adedayo Amos, Department of Statistics, University of Ilorin
Follow on us
In sampling, we have interest in precision and in order to create the precision, we make use of prior knowledge of the population. We try to put the population into series of homogeneous groups and by this, the precision will be increased. When the population of interest can be divided into k homogeneous groups and the sample of observation is taken from each group, we have a stratified random sample and each group is called a stratum. The study was therefore designed to investigate the efficiency of Neyman allocation procedure over equal and proportional allocations. The data used for this research were primary data collected from ten Markets in Abeokuta, Ogun State, Nigeria on the prices of Peak Milk (Nigeria made). A stratified random sampling scheme was used in selecting 10 markets in Abeokuta, Ogun State, Nigeria. Each market stands as a stratum. From each stratum, independent sample was selected randomly based on equal, proportional and Neyman/Optimum allocation procedures. Statistic was obtained from each stratum and combined estimate of the separate statistic was also obtained for each of the allocation procedure. Considering the analysis and estimates obtained, the mean and variance under Neyman allocation procedure were 1356.672 and 21.45 respectively. For proportional allocation, the mean was 1349.3069 and variance was 38.98 while equal allocation gave mean of 1352 and variance of 170.3238. Neyman/Optimum allocation procedure gave the least variance. This was followed by Proportional allocation and Equal allocation. Neyman allocation procedure is the best selection procedure. Hence, for estimating the average and the variance of the prices of Peak Milk (Nigeria Made) in the markets in Abeokuta, of all the three sample allocation procedures considered in this paper, Neyman allocation procedure is the best and hence the most efficient.
Efficiency, Stratified Random Sampling, Neyman Allocation, Procedure
To cite this article
Olayiwola Olaniyi Mathew,
Apantaku Fadeke Sola,
Bisira Hammed Oladiran,
Adewara Adedayo Amos,
Efficiency of Neyman Allocation Procedure over other Allocation Procedures in Stratified Random Sampling, American Journal of Theoretical and Applied Statistics.
Vol. 2, No. 5,
2013, pp. 122-127.
Kish, L. 1965. Survey sampling. New York, Wiley.
Hunt, N. and Tyrell, S. (2004), Stratified sampling. Coventry UniversityPress. http://www.coventry.ac.uk/ec/¬nhunt/meths/strati.html (accessed February 28, 2011)
Arthanari, T.S and Dodge, Y. 1981. Mathematical programming on statistics. A Wiley-Interscience, Publication, John Wiley & Sons Inc.
Bethel, F. 1989. Bayes and Minimax prediction in finite population. Journal of Statistical Planning, 60, 127 – 135.
Chatterjee, S. 1972. A study of optimal allocation in multivariate stratified surveys. Skand Akt. 73, 55 – 57.
Cochran, W. G. 1977. Sampling Techniques (3rd Edition), New York, Wiley.
Dalenius, T. 1957. Sampling in Sweden: Contributions to the methods and theories of sample survey practice, Almavist and wicksell, Stockholm.
Diaz-Garcia, J.A and Cortez, L.U. 2008. Multi-objective optimisation for optimum allocation in multivariate stratified sampling. Survey Methodology, Vol. 34, No 2, 215-222.
Ghosh, S.P., 1958. A note on Stratified Random Sampling with Multiple Characters. Col.Stat. Bull, 8, 81-89.
Hunt, N. And Tyrell, S. 2004. Stratified sampling. Coventry UniversityPress. http://www.coventry.ac.uk/ec/~nhunt/meths/strati.html (accessed February 28, 2011).
Khan, M.G.M and Ahsan, M.J. 2003. A note on Optimum Allocation in Multivariate Stratified Sampling. South Pacific Journal Natural Science, 21, 91-95.
Khan, M.G.M, Jahan, N. and Ahsan, M.J. 1997. Determining the optimum cluster size. Journal of the Indian Society of Agricultural Statistics. Vol. 50 (2), 121-129.
Kish, L. 1965. Survey sampling. New York, Wiley.
Kokan, A.R and Khan, S.U., 1967. Optimum allocation in mutivariate surveys. An analytical solution. Journal of Royal Statistical Society. Series B, 29, 115-125.
Neymaan, J. 1934. On the two different aspects of the representative methods. The method stratified sampling and the method of purposive selection. Journal of Royal Statistical Society, 97, 558-606.
Sukhatme, P.V, Sukhatme, B.V, Sukhatme, S., and Asok, C. 1984. Sampling Theory of Survey with Applications. 3rd Edition. Ames, Iowa: Iowa State University Press.