I have 43000 farmers in my study area encompassing 5 administrative blocks. Please suggest, what should be the appropriate sample size to be considered for survey study, that could represent the entire farming community in my study area?
Your sample size, for each question on a quantitative survey, depends upon (1) sample design - say perhaps stratified random, or perhaps multistage sampling in each administrative block, (2) population standard deviation or subpopulation standard deviations, (3) whether or not good auxiliary data are available for model-assisted design-based sampling and estimation or even completely model-based methods, and (4) your goals regarding required accuracy. The ideal for each of the above may be different for each question. The survey sample size used needs to be big enough (and with high enough quality data) to accommodate the key questions/'target variables' using whatever method/design you choose. The choice may be influenced by logistics. Cluster sampling is less efficient than stratification, but randomized cluster sampling may be more practical if you need to dispatch data collectors.
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Good books to consider may be as follows:
Thompson, S.K.(2012), Sampling, 3rd ed, John Wiley & Sons.
Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons.
Blair, E. and Blair, J(2015), Applied Survey Sampling, Sage Publications.
Lohr, S.L(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.
Särndal, CE, Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlang.
Snijkers, G., Haraldsen, G., Jones, J., and Willimack, D.K.(2013), Designing and Conducting Business Surveys, John Wiley & Sons, Inc.
Brewer, KRW (2002), Combined survey sampling inference: Weighing Basu's elephants, Arnold: London and Oxford University Press.
An Introduction to Model-Based Survey Sampling with Applications, 2012,
Ray Chambers and Robert Clark, Oxford Statistical Science Series
Finite Population Sampling and Inference: A Prediction Approach, 2000,
Richard Valliant, Alan H. Dorfman, Richard M. Royall,
Wiley Series in Probability and Statistics.
Survey Sampling: Theory and Methods, Second Edition
Arijit Chaudhuri, Horst Stenger
March 29, 2005 by CRC Press -
2nd ed by Marcel Dekker, Inc., 1992.
Hansen, M.H., Hurwitz W.N. and Madow, W.G. (1953). Sample Survey Methods and Theory (2 vols.) (Republished 1993) Wiley, New York.
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A paper for an often used model:
"Projected Variance for the Model-based Classical Ratio Estimator: Estimating Sample Size Requirements" (for a single given stratum/model-based group or subpopulation):
A pilot study may help you decide how to group your data/population (design: probability-of-selection, or model-based), and obtain estimates of standard deviations. This could help you decide upon your sample size requirements. A pilot study may have other benefits regarding your data collection planning.
For qualitative surveys (not an area for me), I suppose that a pilot study would also help plan the sample design and size needed to study and/or discover what you wish.
Cheers - Jim
PS - The following may be of interest:
Brewer, K.R.W. (2014), “Three controversies in the history of survey sampling,” Survey Methodology (December 2013/January 2014), Vol 39, No 2, pp. 249-262. Statistics Canada, Catalogue No. 12-001-X. http://www.statcan.gc.ca/pub/12-001-x/2013002/article/11883-eng.htm
There are a number of online calculators. They are generally for yes/no questions only. They often assume the worst case of p=q=0.5. They generally assume simple random sampling with no finite population correction factor. In short, they can be helpful if your circumstances apply, but I suspect that far more often, people try to use them where they do not apply. Use with caution.
There is no substitute for knowing what your software is doing and knowing what you want it to do. That applies to online calculators as well.
A sample size cannot be provided without much more information. Even if one thought that the data are distributed in such a way that simple random sampling would suffice, without an estimated standard deviation and a goal for standard error, all for each key item/question/variable, one cannot say what sample size will likely provide you with what you want.
Even for qualitative surveys you would need more inforation to decide what would be adequate. Not my area, but perhaps that is especially important for qualitative surveys.
One way to obtain the needed information, as I noted above, is a pilot study. Also, perhaps other, past related studies may provide a clue. See Cochran(1977) and other references I gave above for quantitative surveys.
Dr Sharma, I believe sample size of 100 is too small for a large population of 43000. A sample size of 100 may not be a true representative of the entire population. What you think sir?
Dear Dr. Pritpal, Your sample size from given population depends on confidence level and confidence interval. In this situation, at 95% confidence level with confidence interval of 5%, sample size can be 381. At the same, at 99% confidence level with 5% confidence interval, sample size comes to be 656.
There are several research publications wherein authors had calculated no of samples which needs to be surveyed that are representative of the population. It is based on total population count, standard deviation etc.
It should be at least 1 per cent of the population. I.e. a sample size of 430 farmers for your case. divide this sample among block proportionately. i.e. higher sample from higher population block and lower sample from low population blocks.