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2013 | OriginalPaper | Buchkapitel

4. Power Calculations and Sample Size Determination

verfasst von : Richard Valliant, Jill A. Dever, Frauke Kreuter

Erschienen in: Practical Tools for Designing and Weighting Survey Samples

Verlag: Springer New York

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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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Fußnoten
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).
 
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Metadaten
Titel
Power Calculations and Sample Size Determination
verfasst von
Richard Valliant
Jill A. Dever
Frauke Kreuter
Copyright-Jahr
2013
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-6449-5_4