Sampling in surveys with reduced populations: a simplified method for the water, sanitation, and hygiene sector
Making decisions efficiently and equitably requires up-to-date and reliable information. In the water, sanitation, and hygiene sector, devolving decision-making to local governments is increasingly promoted to stimulate local development. However, too few data are available at a level of disaggregation that is appropriate to allow decisions to be made about local-level allocations or for monitoring equitable outcomes across communities. Collecting robust data through cost-effective methodologies is therefore a key element of planning and programming, and for this correct sampling methods are of primary importance. Although different sampling strategies are currently being used to support national-level interventions, none have been optimized for data collection at the local level with only small populations, and standard approaches are usually overly expensive and time consuming. Against this background, we used simplified linear piecewise approximations in this paper to calculate the sample size for proportions in terms of given precision, confidence levels, and population size. To support the use of this proposed approach by practitioners in the field, easy-to-use pre-calculated tables have been included. For sampling, easy-to-follow practical guidelines for household selection and transect walk planning are also provided. Further, six rural communities in Honduras are presented as an initial case study, with total populations ranging from 11 to 44 households. The results illustrate the validity and applicability of this approach for sampling design and sample size determination.Anderson, T.W. and Burstein, H. (1967) ‘Approximating the upper binomial confidence limit’, Journal of the American Statistical Association 62(319): 857–61 <http://www.jstor.org/stable/2283675> [accessed 30 May 2018].
Anderson, T.W. and Burstein, H. (1968) ‘Approximating the lower binomial confidence limit’, Journal of the American Statistical Association 63(324): 1413–15.
Bartram, J., Corrales, L., Davison, A., Deere, D., Drury, D., Gordon, B., Howard, G., Rinehold, A. and Stevens, M. (2009) Water Safety Plan Manual: Step-by-step Risk Management for Drinking-water Suppliers, World Health Organization and International Water Association, Geneva.
Bennett, S., Woods, T., Liyanage, W.M. and Smith, D.L. (1991) ‘A simplified general method for cluster-sample surveys of health in developing countries’, World Health Stat Q, 1991/01/01, 44(3): 98–106.
Burstein, H. (1975) ‘Finite population correction for binomial confidence limits’, Journal of the American Statistical Association, 70(349): 67–9 <http://dx.doi.org/10.2307/2285378>.
Chadha, V.K. (2006) ‘Sample size determination in health studies’, NTI Bulletin, 42(3&4): 55–62.
Cochran, W.G. (1977) Sampling Techniques, 3rd edn, John Wiley and Sons, New York.
Giné-Garriga, R., Jiménez, A. and Pérez-Foguet, A. (2013) ‘Water-sanitation-hygiene mapping: An improved approach for data collection at local level’, Science of the Total Environment, 463–64: 700–11 <http://dx.doi.org/10.1016/j.scitotenv.2013.06.005>.
Grosh, M.E. (1997) ‘The policymaking uses of multitopic household survey data: A primer’, World Bank Research Observer, 12(2): 137–60.
Howard, G., Ince, M., Schmoll, O. and Smith, M. (2012) Rapid Assessment of Drinking-water Quality: A Handbook for Implementation, World Health Organization and United Nations Children’s Fund, Geneva.
Israel, G.D. (2013) Determining Sample Size, Agricultural Education and Communication Department, UF/IFAS Extension, PEOD6, Gainesville. Available from <https://www.gjimt.ac.in/wp-content/uploads/2017/10/2_Glenn-D.-Israel_Determining-Sample-Size.pdf> [accessed 30 May 2018].
Joint Monitoring Programme (2006) Core Questions on Drinking-water and Sanitation for Household Surveys, World Health Organization and United Nations Children’s Fund, Geneva/New York. Available from <http://www.who.int/water_sanitation_health/monitoring/oms_brochure_core_questionsfinal24608.pdf> [accessed 30 May 2018].
Joint Monitoring Programme (2008) Progress on Drinking Water and Sanitation: Special Focus on Sanitation, Joint Monitoring Programme for Water Supply and Sanitation, World Health Organization and United Nations Children’s Fund, Geneva/New York. Available from <http://www.wssinfo.org> [accessed 30 May 2018].
Lwanga, S.K. and Lemeshow, S. (1991) Sample Size Determination in Health Studies: A Practical Manual, World Health Organization, Geneva.
Macro International Inc. (1996) Sampling Manual, DMacro lnternational Inc. 1996. Sampling Manual. DHS-III Basic Documentation No.6. Calverton, Maryland, USA. Available from <https://dhsprogram.com/pubs/pdf/AISM5/DHS_III_Sampling_Manual.pdf> [accessed 30 May 2018].
Reiczigel, J. (2003) ‘Confidence intervals for the binomial parameter: some new considerations’, Statistics in Medicine, 22(4): 611–21 <http://dx.doi.org/10.1002/sim.1320>.
United Nations Children’s Fund (2006) Multiple Indicator Cluster Survey Manual 2005, United Nations Children’s Fund, Division of Policy and Planning, New York.
WaterAid and Overseas Development Institute (ODI) (2005) Learning for Advocacy and Good Practice – WaterAid Water Point Mapping, ODI, London.
Anderson, T.W. and Burstein, H. (1967) ‘Approximating the upper binomial confidence limit’, Journal of the American Statistical Association 62(319): 857–61 <http://www.jstor.org/stable/2283675> [accessed 30 May 2018].
Anderson, T.W. and Burstein, H. (1968) ‘Approximating the lower binomial confidence limit’, Journal of the American Statistical Association 63(324): 1413–15.
Bartram, J., Corrales, L., Davison, A., Deere, D., Drury, D., Gordon, B., Howard, G., Rinehold, A. and Stevens, M. (2009) Water Safety Plan Manual: Step-by-step Risk Management for Drinking-water Suppliers, World Health Organization and International Water Association, Geneva.
Bennett, S., Woods, T., Liyanage, W.M. and Smith, D.L. (1991) ‘A simplified general method for cluster-sample surveys of health in developing countries’, World Health Stat Q, 1991/01/01, 44(3): 98–106.
Burstein, H. (1975) ‘Finite population correction for binomial confidence limits’, Journal of the American Statistical Association, 70(349): 67–9 <http://dx.doi.org/10.2307/2285378>.
Chadha, V.K. (2006) ‘Sample size determination in health studies’, NTI Bulletin, 42(3&4): 55–62.
Cochran, W.G. (1977) Sampling Techniques, 3rd edn, John Wiley and Sons, New York.
Giné-Garriga, R., Jiménez, A. and Pérez-Foguet, A. (2013) ‘Water-sanitation-hygiene mapping: An improved approach for data collection at local level’, Science of the Total Environment, 463–64: 700–11 <http://dx.doi.org/10.1016/j.scitotenv.2013.06.005>.
Grosh, M.E. (1997) ‘The policymaking uses of multitopic household survey data: A primer’, World Bank Research Observer, 12(2): 137–60.
Howard, G., Ince, M., Schmoll, O. and Smith, M. (2012) Rapid Assessment of Drinking-water Quality: A Handbook for Implementation, World Health Organization and United Nations Children’s Fund, Geneva.
Israel, G.D. (2013) Determining Sample Size, Agricultural Education and Communication Department, UF/IFAS Extension, PEOD6, Gainesville. Available from <https://www.gjimt.ac.in/wp-content/uploads/2017/10/2_Glenn-D.-Israel_Determining-Sample-Size.pdf> [accessed 30 May 2018].
Joint Monitoring Programme (2006) Core Questions on Drinking-water and Sanitation for Household Surveys, World Health Organization and United Nations Children’s Fund, Geneva/New York. Available from <http://www.who.int/water_sanitation_health/monitoring/oms_brochure_core_questionsfinal24608.pdf> [accessed 30 May 2018].
Joint Monitoring Programme (2008) Progress on Drinking Water and Sanitation: Special Focus on Sanitation, Joint Monitoring Programme for Water Supply and Sanitation, World Health Organization and United Nations Children’s Fund, Geneva/New York. Available from <http://www.wssinfo.org> [accessed 30 May 2018].
Lwanga, S.K. and Lemeshow, S. (1991) Sample Size Determination in Health Studies: A Practical Manual, World Health Organization, Geneva.
Macro International Inc. (1996) Sampling Manual, DMacro lnternational Inc. 1996. Sampling Manual. DHS-III Basic Documentation No.6. Calverton, Maryland, USA. Available from <https://dhsprogram.com/pubs/pdf/AISM5/DHS_III_Sampling_Manual.pdf> [accessed 30 May 2018].
Reiczigel, J. (2003) ‘Confidence intervals for the binomial parameter: some new considerations’, Statistics in Medicine, 22(4): 611–21 <http://dx.doi.org/10.1002/sim.1320>.
United Nations Children’s Fund (2006) Multiple Indicator Cluster Survey Manual 2005, United Nations Children’s Fund, Division of Policy and Planning, New York.
WaterAid and Overseas Development Institute (ODI) (2005) Learning for Advocacy and Good Practice – WaterAid Water Point Mapping, ODI, London.
Anderson, T.W. and Burstein, H. (1967) ‘Approximating the upper binomial confidence limit’, Journal of the American Statistical Association 62(319): 857–61 <http://www.jstor.org/stable/2283675> [accessed 30 May 2018].
Anderson, T.W. and Burstein, H. (1968) ‘Approximating the lower binomial confidence limit’, Journal of the American Statistical Association 63(324): 1413–15.
Bartram, J., Corrales, L., Davison, A., Deere, D., Drury, D., Gordon, B., Howard, G., Rinehold, A. and Stevens, M. (2009) Water Safety Plan Manual: Step-by-step Risk Management for Drinking-water Suppliers, World Health Organization and International Water Association, Geneva.
Bennett, S., Woods, T., Liyanage, W.M. and Smith, D.L. (1991) ‘A simplified general method for cluster-sample surveys of health in developing countries’, World Health Stat Q, 1991/01/01, 44(3): 98–106.
Burstein, H. (1975) ‘Finite population correction for binomial confidence limits’, Journal of the American Statistical Association, 70(349): 67–9 <http://dx.doi.org/10.2307/2285378>.
Chadha, V.K. (2006) ‘Sample size determination in health studies’, NTI Bulletin, 42(3&4): 55–62.
Cochran, W.G. (1977) Sampling Techniques, 3rd edn, John Wiley and Sons, New York.
Giné-Garriga, R., Jiménez, A. and Pérez-Foguet, A. (2013) ‘Water-sanitation-hygiene mapping: An improved approach for data collection at local level’, Science of the Total Environment, 463–64: 700–11 <http://dx.doi.org/10.1016/j.scitotenv.2013.06.005>.
Grosh, M.E. (1997) ‘The policymaking uses of multitopic household survey data: A primer’, World Bank Research Observer, 12(2): 137–60.
Howard, G., Ince, M., Schmoll, O. and Smith, M. (2012) Rapid Assessment of Drinking-water Quality: A Handbook for Implementation, World Health Organization and United Nations Children’s Fund, Geneva.
Israel, G.D. (2013) Determining Sample Size, Agricultural Education and Communication Department, UF/IFAS Extension, PEOD6, Gainesville. Available from <https://www.gjimt.ac.in/wp-content/uploads/2017/10/2_Glenn-D.-Israel_Determining-Sample-Size.pdf> [accessed 30 May 2018].
Joint Monitoring Programme (2006) Core Questions on Drinking-water and Sanitation for Household Surveys, World Health Organization and United Nations Children’s Fund, Geneva/New York. Available from <http://www.who.int/water_sanitation_health/monitoring/oms_brochure_core_questionsfinal24608.pdf> [accessed 30 May 2018].
Joint Monitoring Programme (2008) Progress on Drinking Water and Sanitation: Special Focus on Sanitation, Joint Monitoring Programme for Water Supply and Sanitation, World Health Organization and United Nations Children’s Fund, Geneva/New York. Available from <http://www.wssinfo.org> [accessed 30 May 2018].
Lwanga, S.K. and Lemeshow, S. (1991) Sample Size Determination in Health Studies: A Practical Manual, World Health Organization, Geneva.
Macro International Inc. (1996) Sampling Manual, DMacro lnternational Inc. 1996. Sampling Manual. DHS-III Basic Documentation No.6. Calverton, Maryland, USA. Available from <https://dhsprogram.com/pubs/pdf/AISM5/DHS_III_Sampling_Manual.pdf> [accessed 30 May 2018].
Reiczigel, J. (2003) ‘Confidence intervals for the binomial parameter: some new considerations’, Statistics in Medicine, 22(4): 611–21 <http://dx.doi.org/10.1002/sim.1320>.
United Nations Children’s Fund (2006) Multiple Indicator Cluster Survey Manual 2005, United Nations Children’s Fund, Division of Policy and Planning, New York.
WaterAid and Overseas Development Institute (ODI) (2005) Learning for Advocacy and Good Practice – WaterAid Water Point Mapping, ODI, London.
Anderson, T.W. and Burstein, H. (1967) ‘Approximating the upper binomial confidence limit’, Journal of the American Statistical Association 62(319): 857–61 <http://www.jstor.org/stable/2283675> [accessed 30 May 2018].
Anderson, T.W. and Burstein, H. (1968) ‘Approximating the lower binomial confidence limit’, Journal of the American Statistical Association 63(324): 1413–15.
Bartram, J., Corrales, L., Davison, A., Deere, D., Drury, D., Gordon, B., Howard, G., Rinehold, A. and Stevens, M. (2009) Water Safety Plan Manual: Step-by-step Risk Management for Drinking-water Suppliers, World Health Organization and International Water Association, Geneva.
Bennett, S., Woods, T., Liyanage, W.M. and Smith, D.L. (1991) ‘A simplified general method for cluster-sample surveys of health in developing countries’, World Health Stat Q, 1991/01/01, 44(3): 98–106.
Burstein, H. (1975) ‘Finite population correction for binomial confidence limits’, Journal of the American Statistical Association, 70(349): 67–9 <http://dx.doi.org/10.2307/2285378>.
Chadha, V.K. (2006) ‘Sample size determination in health studies’, NTI Bulletin, 42(3&4): 55–62.
Cochran, W.G. (1977) Sampling Techniques, 3rd edn, John Wiley and Sons, New York.
Giné-Garriga, R., Jiménez, A. and Pérez-Foguet, A. (2013) ‘Water-sanitation-hygiene mapping: An improved approach for data collection at local level’, Science of the Total Environment, 463–64: 700–11 <http://dx.doi.org/10.1016/j.scitotenv.2013.06.005>.
Grosh, M.E. (1997) ‘The policymaking uses of multitopic household survey data: A primer’, World Bank Research Observer, 12(2): 137–60.
Howard, G., Ince, M., Schmoll, O. and Smith, M. (2012) Rapid Assessment of Drinking-water Quality: A Handbook for Implementation, World Health Organization and United Nations Children’s Fund, Geneva.
Israel, G.D. (2013) Determining Sample Size, Agricultural Education and Communication Department, UF/IFAS Extension, PEOD6, Gainesville. Available from <https://www.gjimt.ac.in/wp-content/uploads/2017/10/2_Glenn-D.-Israel_Determining-Sample-Size.pdf> [accessed 30 May 2018].
Joint Monitoring Programme (2006) Core Questions on Drinking-water and Sanitation for Household Surveys, World Health Organization and United Nations Children’s Fund, Geneva/New York. Available from <http://www.who.int/water_sanitation_health/monitoring/oms_brochure_core_questionsfinal24608.pdf> [accessed 30 May 2018].
Joint Monitoring Programme (2008) Progress on Drinking Water and Sanitation: Special Focus on Sanitation, Joint Monitoring Programme for Water Supply and Sanitation, World Health Organization and United Nations Children’s Fund, Geneva/New York. Available from <http://www.wssinfo.org> [accessed 30 May 2018].
Lwanga, S.K. and Lemeshow, S. (1991) Sample Size Determination in Health Studies: A Practical Manual, World Health Organization, Geneva.
Macro International Inc. (1996) Sampling Manual, DMacro lnternational Inc. 1996. Sampling Manual. DHS-III Basic Documentation No.6. Calverton, Maryland, USA. Available from <https://dhsprogram.com/pubs/pdf/AISM5/DHS_III_Sampling_Manual.pdf> [accessed 30 May 2018].
Reiczigel, J. (2003) ‘Confidence intervals for the binomial parameter: some new considerations’, Statistics in Medicine, 22(4): 611–21 <http://dx.doi.org/10.1002/sim.1320>.
United Nations Children’s Fund (2006) Multiple Indicator Cluster Survey Manual 2005, United Nations Children’s Fund, Division of Policy and Planning, New York.
WaterAid and Overseas Development Institute (ODI) (2005) Learning for Advocacy and Good Practice – WaterAid Water Point Mapping, ODI, London.
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