Estimate prevalence: confidence interval for a stratified random sample

Theory

To determine the confidence interval of a proportion estimated from stratified random sampling, the standard error (SE) of the proportion must be firstly calculated, based on the following equation:

Where:

e The number of defined strata.

N_i The number of individuals from the population that form part of strata i.

n_i The number of individuals from the sample that form part of strata i.

p_i The estimated proportion of individuals with the event in strata i.

N The number of individuals in the population.

The confidence interval is calculated as follows:

Where:

z The value obtained from the standard normal distribution. To each value of confidence there is a correspondent value of z. The levels of confidence more frequently used in biological studies are 90%, 95% and 99%. The values of z correspondent to them are 1.64, 1.96, and 2.58 respectively.

p The estimated prevalence in the population. It is calculated as follows:


Instituto Nacional de Tecnología Agropecuaria	EpiCentre, IVABS, Massey University

e	The number of defined strata.
N_i	The number of individuals from the population that form part of strata i.
n_i	The number of individuals from the sample that form part of strata i.
p_i	The estimated proportion of individuals with the event in strata i.
N	The number of individuals in the population.

z	The value obtained from the standard normal distribution. To each value of confidence there is a correspondent value of z. The levels of confidence more frequently used in biological studies are 90%, 95% and 99%. The values of z correspondent to them are 1.64, 1.96, and 2.58 respectively.
p	The estimated prevalence in the population. It is calculated as follows: