Sample size: simple random sample

Theory

The calculation of the sample size (n) required for the estimation of the prevalence of an event in an infinite population is based on the following formula:

Where:

p The assumed prevalence of the event in the population under study.

z The critical value obtained from a standard normal distribution. For each level of confidence there is a corresponding value of z. The levels of confidence frequently used in biological studies are 90%, 95%, and 99%. The corresponding z values are 1.64, 1.96, and 2.58 respectively.

e The maximum absolute error that the user is willing to accept. For example: if one assumes a prevalence of 0.40 and a relative error of 0.10 the absolute error will be 0.04 (that is, 0.40 × 0.10). In general, the relative error should be ≤ 0.20.

Sample size may be adjusted (n_a) according to the size of the study population (N), as follows:

Where:

n The sample size calculated for an infinite population.

N The size of the population under study.

Practice

Expected prevalence The assumed prevalence of the event in the population under study (usually based on previous studies, field data or the literature). When no information is available a value of 0.50 will yield the maximum sample size.
Acceptable values: ≥ 0 and ≤ 1.

Acceptible relative error A measure of the desired precision. For example, if you assume a prevalence of 0.40 and a relative error of 0.10, the result will have a precision of ± 0.04 (that is, 0.40 × 0.10). In this case 0.04 is the absolute error. In general, the relative error should be ≤ 0.20.
Acceptable values: ≥ 0 and ≤ 1.

Level of confidence The confidence that the user wants to have in the results.
Acceptable values: 90%, 95% or 99%.

Population size The number of individuals in the population under study.
Acceptable values: any positive whole number.


Instituto Nacional de Tecnología Agropecuaria	EpiCentre, IVABS, Massey University

p	The assumed prevalence of the event in the population under study.
z	The critical value obtained from a standard normal distribution. For each level of confidence there is a corresponding value of z. The levels of confidence frequently used in biological studies are 90%, 95%, and 99%. The corresponding z values are 1.64, 1.96, and 2.58 respectively.
e	The maximum absolute error that the user is willing to accept. For example: if one assumes a prevalence of 0.40 and a relative error of 0.10 the absolute error will be 0.04 (that is, 0.40 × 0.10). In general, the relative error should be ≤ 0.20.

n	The sample size calculated for an infinite population.
N	The size of the population under study.

Expected prevalence	The assumed prevalence of the event in the population under study (usually based on previous studies, field data or the literature). When no information is available a value of 0.50 will yield the maximum sample size. Acceptable values: ≥ 0 and ≤ 1.
Acceptible relative error	A measure of the desired precision. For example, if you assume a prevalence of 0.40 and a relative error of 0.10, the result will have a precision of ± 0.04 (that is, 0.40 × 0.10). In this case 0.04 is the absolute error. In general, the relative error should be ≤ 0.20. Acceptable values: ≥ 0 and ≤ 1.
Level of confidence	The confidence that the user wants to have in the results. Acceptable values: 90%, 95% or 99%.
Population size	The number of individuals in the population under study. Acceptable values: any positive whole number.