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Sample size calculations
This utility calculates the sample size required to estimate a proportion (or prevalence) with a specified level of confidence and precision.
Inputs are the assumed or estimated value for the proportion, the desired level of confidence, the desired precision of the estimate and the size of the population for limited population sizes. The desired precision of the estimate (also sometimes called the allowable or acceptable error in the estimate) is half the width of the desired confidence interval. For example if you would like the confidence interval width to be about 0.1 (10%) you would enter a precision of +/- 0.05 (5%).
The program outputs the sample sizes required to estimate the true value with the desired precision and confidence, for both an infinite population and for a population of the specified size. If population size is left blank or zero, only the sample size for an infinite population is calculated.
Note: Adjustment for finite population size may underestimate required sample size unless this is also taken into account when estimating variance and resulting confidence interval.
Sample size is calculated using the formula: n = (Z2 x P x (1 - P))/e2
Where:
- Z = value from standard normal distribution corresponding to desired confidence level (Z=1.96 for 95% CI)
- P is expected true proportion
- e is desired precision (half desired CI width).
For small populations n can be adjusted so that n(adj) = (Nxn)/(N+n). Adjustment for finite population size is described by Thrusfield M, 2005. Veterinary Epidemiology, 2nd Edition, Blackwell Science, Oxford, UK (p 183).
Sample size to estimate a proportion or apparent prevalence with specified precision
This utility calculates the sample size required to estimate a proportion (or prevalence) with a specified level of confidence and precision.
Inputs are the assumed or estimated value for the proportion, the desired level of confidence, the desired precision of the estimate and the size of the population for limited population sizes. The desired precision of the estimate (also sometimes called the allowable or acceptable error in the estimate) is half the width of the desired confidence interval. For example if you would like the confidence interval width to be about 0.1 (10%) you would enter a precision of +/- 0.05 (5%).
The program outputs the sample sizes required to estimate the true value with the desired precision and confidence, for both an infinite population and for a population of the specified size. If population size is left blank or zero, only the sample size for an infinite population is calculated.
Note: Adjustment for finite population size may underestimate required sample size unless this is also taken into account when estimating variance and resulting confidence interval.
Sample size is calculated using the formula: n = (Z2 x P x (1 - P))/e2
Where:
- Z = value from standard normal distribution corresponding to desired confidence level (Z=1.96 for 95% CI)
- P is expected true proportion
- e is desired precision (half desired CI width).
For small populations n can be adjusted so that n(adj) = (Nxn)/(N+n). Adjustment for finite population size is described by Thrusfield M, 2005. Veterinary Epidemiology, 2nd Edition, Blackwell Science, Oxford, UK (p 183).