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The Importance of Sample Size and Its Varying Effects on Precision in Large-Scale Surveys

The Importance of Sample Size and Its Varying Effects on Precision in Large-Scale Surveys. Dipankar Roy, PhD Bangladesh Bureau of Statistics dr.droy69@gmail.com Presented at the International Seminar at Rajshahi University 18-19 October 2012 Rajshahi, Bangladesh.

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The Importance of Sample Size and Its Varying Effects on Precision in Large-Scale Surveys

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  1. The Importance of Sample Size and Its Varying Effects on Precision in Large-Scale Surveys Dipankar Roy, PhD Bangladesh Bureau of Statistics dr.droy69@gmail.com Presented at the International Seminar at Rajshahi University 18-19 October 2012 Rajshahi, Bangladesh

  2. Sample size determination • the act of choosing the number of observations to be surveyed • The way should be statistically sound and formulae-oriented • Samples should be selected with selection probability (base weight) • Samples should be allocated scientifically (need based)

  3. Sampling • The process of selecting units • Study them • Generalize the result (estimate/statistic) • Back to population (parameter) • Infer about population through sample

  4. A major goal of data analysis • sample mean (or proportion) to estimate the corresponding parameters in the respective population • Statistical inference about a population NOT for sample

  5. Two approaches • Precision-based approach • Power-based approach

  6. How large a sample is needed to • enable statistical judgments that are accurate and reliable? AND • to attain a desirable level of precision?

  7. Sample size should not be determined • arbitrarily • without solving the equation • Required/optimum samples can ensure accurate, precise and reliable estimates • Too low samples lack the precision • Unnecessary larger samples yield minimal gain

  8. Sampling Error • Standard Error (SE) • Margin of Error (MOE) • Confidence Interval (CI)

  9. MOE Indicates that a data user can be certain that the estimate (statistic) and the population value (parameter) differ by no more than the value of the MOE

  10. There is some margin of error d in the estimated proportion p in relation to the true proportion P • There is some risk α that the actual error is larger than d Pr(|p-P|>d)= α OR Pr(|p-P|<=d)=1-α

  11. n=[z^2*P*(1-P)]/d^2 • the level of precision, • the level of confidence or risk, and • the degree of variability in the attributes

  12. Sample of size n is required to • estimate an event of p • within d of its true value • with 100(1-α)% confidence level

  13. Formulae for MICS Sample Size

  14. HIES • Coefficient of variation should have been used in determining sample size for a study variable like income • Household income, by its nature, seems to be heterogeneous within and/or between localities

  15. Template

  16. Sample size vs. coverage rate

  17. Sample size vs. margin of error

  18. n vs. N

  19. Interval width is equal to twice the margin of error and it is directly proportional to • If the sample size is increased by a factor of 4, the interval width will be reduced by half • High levels of precision require larger sample sizes • Higher confidence levels require larger sample sizes

  20. Sample size depends on domain-level estimation • Sample size does not necessarily depend on how large the population • In a certain stage there is no necessity for increasing the sample size for population becoming any larger • For any complex design, sample size should be inflated by the design effect.

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