Abstract
In Chap. we calculated sample sizes based on targets for coefficients of variation (CV s), margins of error, and cost constraints. Another method is to determine the sample size needed to detect a particular alternative value when testing a hypothesis. For example, when comparing the means for two groups, one way of determining sample size is through a power calculation. Roughly speaking, power is a measure of how likely you are to recognize a certain size of difference in the means. A sample size is determined that will allow that difference to be detected with high probability (i.e., a detectable difference). Power can also be determined in a one-sample case where a simple hypothesis is being tested versus a simple alternative. Using power to determine sample sizes is especially useful when some important analytic comparisons can be identified in advance of selecting the sample. Although not covered in most books on sample design, most practitioners will inevitably have applications where power calculations are needed.
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Notes
- 1.
Roughly speaking, an estimator is said to be consistent if it gets closer and closer to the value it is supposed to be estimating as the sample size increases. A variance estimator \(\mathit{v}\left (\hat{\bar{y}}\right )\) is a consistent estimator of the true variance \(\mathit{V}\left (\hat{\bar{y}}\right )\) if \(\mathit{v}\left (\hat{\bar{y}}\right )\left /\mathit{V}\left (\hat{\bar{y}}\right )\right.\stackrel{p} \rightarrow 1\) as n → ∞. In survey samples, n is the number of sample units in a single-stage sample or the number of primary sampling units (PSUs) in a multistage sample. A ratio is used in this definition because both the estimator and its target approach 0 as the sample size increases.
- 2.
A standard normal distribution is a normal distribution with mean = 0 and standard deviation = 1, i.e., N(0, 1).
- 3.
References
Armitage P., Berry G. (1987). Statistical Methods in Medical Research, 2nd edn. Blackwell, Oxford
Brown L., Cai T., Das Gupta A. (2001). Interval estimation for a binomial proportion. Statistical Science 16:101–133
Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. Lawrence Erlbaum Associates, New Jersey
Hedges L.V., Olkin I. (1985). Statistical Methods for Meta-analysis. Academic Press, Orlando
Heiberger R.M., Neuwirth E. (2009) R Through Excel: A Spreadsheet Interface for Statistics, Data Analysis, and Graphics. Springer, New York
Korn E.L. (1986). Sample size tables for bounding small proportions. Biometrics 42:213–216
Lemeshow S., Hosmer D., Klar J., Lwanga S. (1990). Adequacy of Sample Size in Health Studies. John Wiley & Sons, Inc., Chichester
R Core Team and contributors worldwide (2012c). stats: R statistical functions. URL http://finzi.psych.upenn.edu/R/library/stats/html/00Index.html
Royall R.M. (1986). The effect of sample size on the meaning of significance tests. The American Statistician 40:313–315
Rust K.F. (1984). Techniques for estimating variances for sample surveys. PhD thesis, University of Michigan, Ann Arbor MI, unpublished
Rust K.F. (1985). Variance estimation for complex estimators in sample surveys. Journal of Official Statistics 1:381–397
Schlesselman J. (1982). Case-Control Studies: Design, Conduct, and Analysis. Oxford University Press, New York
Valliant R., Rust K.F. (2010). Degrees of freedom approximations and rules-of-thumb. Journal of Official Statistics 26:585–602
Woodward M. (1992). Formulas for sample size, power, and minimum detectable relative risk in medical studies. The Statistician 41:185–196
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Valliant, R., Dever, J.A., Kreuter, F. (2013). Power Calculations and Sample Size Determination. In: Practical Tools for Designing and Weighting Survey Samples. Statistics for Social and Behavioral Sciences, vol 51. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6449-5_4
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