Handbook of Anthropometry pp 3-27 | Cite as

# Calculating Sample Size in Anthropometry

## Abstract

Sample size estimation is a fundamental step when designing clinical trials and epidemiological studies for which the primary objective is the estimation or the comparison of parameters. One may be interested in the prevalence of overweight children in a given population; however, the true prevalence will remain unknown and cannot be observed unless the whole population is studied. Statistical inference is the use of statistics and random sampling to make inferences concerning the true parameters of a population. By choosing a representative sample, inference based on the observed prevalence leads to an estimation of the true parameter. But how many subjects should be sampled to obtain an accurate estimate of the prevalence? Similarly, how many subjects should we sample to show that this parameter is different from some fixed value? We first review basic statistical concepts including random variables, population and sample statistics, as well as probability distributions such as the binomial and normal distributions. Principles of point and interval estimation, as well as hypothesis testing, are presented. We consider several commonly used statistics: single proportions, differences between two proportions, single means, differences between two means, and reference limits. For each parameter, point estimators are presented as well as methods for constructing confidence intervals. We then review general methods for calculating sample sizes. We first consider precision-based estimation procedures, where the sample size is estimated as a function of the desired degree of precision. Next, although there is greater emphasis on precision-driven estimation procedures, we also briefly describe power-based estimation methods. This approach requires defining a priori the difference one wishes to detect, the desired significance level, and the desired power of the test. Sample size estimation procedures are presented for each parameter, and examples are systematically provided.

### Keywords

Cholesterol Obesity Cytel### Abbreviations and Notations

- N
Population size

- n
Sample size

- ME
Margin of error

- e
Precision

- m
Population mean

- m
Sample mean

- s 2
Population variance

- s2
Sample variance

- p
Population proportion

- p
Sample proportion

- H0
Null hypothesis

- HA
Alternative hypothesis

- a
Type I error rate

- b
Type II error rate

- zp
100p% standard normal deviate

- BMI
Body mass index

- DBP
Diastolic blood pressure

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