Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling
American Journal of Theoretical and Applied Statistics
Volume 6, Issue 6, November 2017, Pages: 270-277
Received: Sep. 17, 2017; Accepted: Oct. 4, 2017; Published: Nov. 10, 2017
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Oloo Odhiambo Erick, Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
James Kahiri, Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
Wafula Mike Erick, Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
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The study involves investigating the impact of measurement errors on estimators of parameters of a finite population with linear trend among population values, under systematic sampling. The study provides deep understanding on the amount and nature of deviation introduced by errors and how these errors affect estimators of parameters of a population with linear trend. Consideration is given to measurement errors that assume a normal distribution. Systematic sampling technique is used where a sample of size n is selected randomly from a finite population with a fixed interval a. Systematic sampling is considered instead of simple random sampling in this case because of its effectiveness in dealing with linear trend. The explicit values of population totals, means and variances together with their estimates are derived. The results indicate that there can be overestimate of the population mean if the expected systematic errors tend towards positive values and underestimate if the expected systematic error tend towards negative values. When random errors are considered, there is no effect on estimated population parameters.
Finite Population with Linear Trend, Systematic Sampling, Measurement Errors
To cite this article
Oloo Odhiambo Erick, James Kahiri, Wafula Mike Erick, Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling, American Journal of Theoretical and Applied Statistics. Vol. 6, No. 6, 2017, pp. 270-277. doi: 10.11648/j.ajtas.20170606.12
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This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Fuller, W. (1987). Measurement Error Models. Wiley and Sons.
Carroll, R., J, R. D. and Stefanski, L. (1994). Measurement Error in nonlinear models, Chapman and Hall, London.
Bound, J., Brown, C., and Mathiowetz, N (2001). Measurement Error in Survey data. American Journal of Theoretical and Applied Statistics, 5.
Pischke, J. (1995). Measurement error and earnings dynamics: some estimates from the psid validation study. Journal Business of Econmics Statistics, 13(3):305-314.
O’ Neil, D., Sweetman, O., and Van der gaer, D. (2007). The effects of measurement error and omitted variables when using transition matrices to measure intergenerational mobility. Journal of Economic Inequality, 5(2):159-178.
Gottschalk, P. and Huynh, M. (2010). Are earnings inequality and morbility overstated? The Impact of Nonclassical Measurement Error. Review of Economics and Statistics, 92(2): 302-315.
Conor, G., Temblay, M., Moher, D., and Gorver, B. (2007). A comparison of Direct vs Self-reported Measures for Assessing Height, Weight and Body Mass Index: a systematic review. Obesity Rev. 8:307-326.
Plankey, M., Stevens, J., Flegal, K., and Rust, P. (1997). Prediction equations do not eliminate systematic error in self-reported body mass index. Obesity Research, 5(4):308-314.
Stommel, M. Schoenborn, C. (2009). Accuracy and usefulness of BMI measures based on self-reported weight and height: findings from the nhanes and nhis 20012006, BMC Public Health, 9(421).
Belloc, N. (1954). Validation of morbidity survey data by comparison with hospital records, Journal of American Statistics Associations, 49:832-846.
Gray, P. (1955). The Memory Factor in Social Survey. Journal of American Statistics Associations, 50:344-363.
Sagen, O. K, D. R and Simmons, W (1959). Health Statistics from record sources and household interview compared. Proceedings of the social Statistics election of American Statistics Associations, pages 6-15.
Trusell, R and Elinson, J. (1959). Chronic Illness in a Large City. Harvard University Press Cambridge Mass.
Särndal, C. (1992). Model assisted Survey Sampling. Springer-verlag New York, Inc, USA.
Nyabwanga, R. (2010). Effect of measurement errors on population in random order when sampling systematically. Unpublished project department of Mathematics Kenyatta University.
Rosella, L. C. Corey, P. Stukel, T. Mustard, C. Hux, J. and Manuel, D. G. (2012). The influence of measurement error on calibration, discrimination and overall estimation of a risk prediction model. Population Health Metr; 10:20. doi:10:1186/1478-7954-10-20. [PMC 3545925].
O’ Neil, D. and Olive, S. (2013). The consequences of measurment error when estimating the impact of obesity on income. IZA Journal of Labor Economics, 2(3).
Subramani, J. and Singh, S. (2014). Estimation of population mean in the presence of linear trend. Communications in the Statistics-Theory and Methods, 43.
Ouko, A., Cheruiyot, W., and Emily, K. (2014). Effects of measurement errors on population estimates from samples generated from a stratified population through systematic sampling technique. Expert Journal of Economics, 2:120-132.
Grellety, E. Golden, M. H (2016). The effect of Random error on diagnosis accuracy illustrated with the anthropometric diagnosis of malnutrition. PLoS ONE 11(12): e0168585 doi 10.1371.
Mukhopadhyay, P. (1998). Theory and Methods of Survey Sampling. Prentice-Hall of India Private Ltd.
Horvitz, D. and Thompson, D. (1952). A generalization of Sampling Without Replacement From a Finite Universe. Journal of American Statistics Associations, 47:663-685.
Daroga, S. and Chaudhary, F. S (1986). Theory and Analysis of Sample Survey Designs. New Age Inernational (P) Ltd.
Wolter, K. (1985). Introduction to Variance Estimation, Springer-Verlag, New York.
Cochran, W. G. (1977). Sampling Techniques, John Wiley and Sons, third edition.
Yates, F. (1948). Systematic sampling, Philosophical Transaction of the Royal society of London, A241:345-377.
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