An Optimum Sample Size in Cross Sectional Studies

J. Sreedharan¹ , S. Chandrasekharan² , A. Gopakumar³

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.1 , pp.122-130, Feb-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.122130

Online published on Feb 28, 2019

Copyright © J. Sreedharan, S. Chandrasekharan, A. Gopakumar . This 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.
 

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Abstract :
Sample size plays a vital role in any research as very less sample and very large sample may lead to false conclusions. There are many formulas available for the calculation of sample size according to the design of the study or/and statistical tool. These formulas generally give a minimum sample size but not provide solution for finding the required upper limit. Studies which include large sample give estimates with higher precision but may lead to large sample fallacy with statistical significance even for insignificant effects. This paper aimed to develop a formula for optimum sample size in the context of cross sectional study design. Pattern of changes in the results at minimum, optimum, large and extreme large sample size is discussed. Also we compare the result of cross sectional study with the result of a case control study. This study observed that an additional factor (m-factor) to be multiplied with the existing formula, that gives an optimum large sample in a cross-sectional study. The m-factor is a function of Zα and Zβ.

Key-Words / Index Term :
Minimum sample size, Optimum sample size, Large sample size, Cross sectional study, Power

References :
[1] H. Shah, “How to calculate sample size in animal studies?”, National Journal of Physiology, Pharmacy and Pharmacology, Vol.1,Issue.1,pp.35–39, 2011.
[2] P. Patra, “Sample size in clinical research, the number we need”, International Journal of Medical Science and Public Health, Vol.1,Issue.1,pp.5–9, 2012.
[3] J. Cai, D. Zeng, “Sample size/power calculation for case-cohort studies”, Biometrics, Vol.60,Issue.4,pp.1015–24, 2004.
[4] V. Kasiulevicius, V. Sapoka, R. Filipaviciute, “Sample size calculation in epidemiological studies, Gerontology, Vol.7,Issue.4,pp.225–31, 2006.
[5] M. Puopolo, “Biostatistical approaches to reducing the number of animals used in biomedical research”,Annali dell`Istituto Superiore di Sanità, Vol.40,pp.157–63, 2004.
[6] P.R. Burton, A.L. Hansell, I. Fortier, T.A. Manolio, M.J. Khoury, J. Little, P. Elliott, “Size matters: Just how big is BIG? Quantifying realistic sample size requirements for human genome epidemiology”, International Journal of Epidemiology, Vol.38,Issue.1,pp.263–73, 2009.
[7] J. Charan, T. Biswas, “How to Calculate Sample Size for Different Study Designs in Medical Research?”, Indian Journal of Psychological Medicine, Vol.35,Issue.2,pp.121-126, 2013.
[8] M.S. Setia, “Methodology Series Module 3: Cross-sectional Studies”, Indian Journal of Dermatology, Vol.61,Issue.3,pp.261-264, 2016.
[9] M. Szklo, F.J. Nieto, “Epidemiology: Beyond the Basics”, MA: Jones and Bartlett Publishers, Sudbury, 2004.
[10] L. Naing,, T. Winn, B.N. Rusli, “Practical issues in calculating the sample size for prevalence studies”, Archives of Orofacial Sciences, Vol.1,pp.9–14, 2006.
[11] T. Dahiru, T.S. Kene, A.A. Aliyu, “Statistics in medical research: misuse of sampling and sample size determination”, Annals of African Medicine, Vol.5,Issue.3,pp.158-61, 2006.
[12] M. Noordzij, G. Tripepi, F.W. Dekker, C. Zoccali, M.W. Tanck, K.J Jager, “Sample size calculations: basic principles and common pitfalls”, Nephrology Dialysis Transplant, Vol.25,Issue.5,pp.1388-93, 2010.
[13] R.K. Malhotra, A. Indrayan, “Simple nomogram for estimating sample size for sensitivity and specificity of medical tests”’, Indian Journal of Ophthalmology, Vol.58,Issue.6,pp.519–22, 2010.
[14] T.J. Naduvilath, R.K. John, L. Dandona, “Sample size for ophthalmology studies”, Indian Journal of Ophthalmology, Vol.48,Issue.3,pp.245-50, 2000.
[15] S.B. Hulley, S.R. Cumming, W.S. Browner, D. Grady, N. Hearst, T.B. Newman. “Designing Clinical Research”, 2nd ed., Lippincot Williams & Wilkins, Philadelphia, USA, 2001.
[16] R.B Dell, S. Holleran, R. Ramakrishnan, “Sample Size Determination”, Institute for Laboratory Animal Research Journal, Vol.43,Issue.4,pp.207-213, 2002.
[17] D.J. Biau, S. Kerneis, R. Porcher, “Statistics in brief: The importance of sample size in the planning and interpretation of medical research”, Clinical Orthopaedics and Related Research, Vol.466,Issue.9,pp.2282–8, 2008.
[18] P. Kadam, S. Bhalerao, “Sample size calculation”, International Journal of Ayurveda Research, Vol.1,Issue.2,pp.55-57, 2010.
[19] P. Bacchetti, “Current sample size conventions: Flaws, harms, and alternatives”, BMC Medicine, Vol.8,Issue.17, 2010.
[20] G.T Fosgate, “Practical sample size calculations for surveillance and diagnostic investigations”, Journal of Veterinary Diagnostic Investigation, Vol.21,Issue.1,pp.3–14, 2009.
[21] E. Whitley, J. Ball, “Statistics review 4: Sample size calculations”, Critical Care, Vol.6,Issue.4,pp.335–41, 2002.
[22] Hazra, N. Gogtay, “Biostatistics series module 5: Determining sample size”, Indian Journal of Dermatology, Vol.61,Issue.5,pp.496-504, 2016.
[23] F. Farrokhyar, D. Reddy, R.W. Poolman, M. Bhandari. “Why perform a priori sample size calculation?”, Canadian Journal of Surgery, Vol.56,Issue.3,pp.207-213, 2013.
[24] K. Malterud, V.D. Siersma, A.D. Guassora, “Sample Size in Qualitative Interview Studies: Guided by Information Power” Qualitative health research, Vol.26,pp.1753-60, 2015.
[25] N. Gogate, “Principles of sample size calculation,” Indian Journal of Ophthalmology, Vol.58, Issue.6, pp.517–8, 2010.
[26] K. Sivasakthi, M.L. William, “A Class of Super-Efficient Estimators of the Normal Variance: A Study on Sample Size Preference", International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.212-221, 2018.
[27] S. Lemeshow, D.W. Hosmer, K. Janelle, K.L. Stephen, “Adequacy of sample size in health studies”, John Wiley & Sons Ltd., World Health Organization, Englan, 1990. Available at: http://www.who.int/iris/handle/10665/41607
[28] M.A. Pourhoseingholi, M. Vahedi, M. Rahimzadeh. “Sample size calculation in medical studies”, Gastroenterology and Hepatology from Bed to Bench, Vol.6,Issue.1,pp.14-17, 2013.
[29] N.N. Naing, “Determination of Sample Size”, The Malaysian Journal of Medical Sciences, Vol. 10,Issue.2,pp.84-86, 2003.
[30] G.T. Fosgate, “Practical sample size calculations for surveillance and diagnostic investigations”, Journal of Veterinary Diagnostic Investigation, Vol.21,Issue.1,pp.3–14, 2009.
[31] D.I. Glenn, “Determining Sample Size”, Institute of Food and Agricultural Sciences, University of Florida, IFAS extension (PEOD6; Reviewed 2003), 1992. Available at: https://www.tarleton.edu/academicassessment/documents/Samplesize.pdf
[32] N Pandis, “Sample calculations for comparing proportions”, American Journal of Orthodontics and Dentofacial Orthopedics, Vol.141,Issue.5,pp.666-7, 2012.
[33] R Rana, Singhal, R, “Chi-square test and its application in hypothesis testing”, Journal of the Practice of Cardiovascular Sciences, Vol.1,Issue.1, pp.69-71, 2015.
[34] Demographic and Health Surveys (DHS), “National Family Health Survey (NFHS-4), Latest Publication, 2015-2016. India. Available at: http://rchiips.org/nfhs/