Results

If the prevalence used in the above calculation is an estimate then plot below will give you an idea of possible sample size required. If you hover over the individual points you will see the sample size.

This sample size calculator is designed to calculate the minimum sample size required to detect a disease within a population. The formula used is:

$$n = \left(1 - \left(1 - p\right) ^ {\frac{1}{NP}}\right) \times \left(N - \frac{NP - 1}{2}\right)$$

and then \(\lceil n \rceil\) (the next largest integer) is returned. In the calculation

• \(p\) is the confidence level
• \(N\) is population size
• \(P\) is the prevalence

Results

Minimum sample size:

If the proportion used in the above calculation is an estimate then plot below will give you an idea of possible sample size required. If you hover over the individual points you will see the sample size.

The formula used for this sample size calculation is:

$$n = \frac{Z_\alpha^2 p (1 - p)}{L^2}$$

and then \(\lceil n \rceil\) (the next largest integer) is returned. In the calculation

• \(Z_\alpha\) is the two-tailed \(Z\)-value from the confidence level.
• \(p\) is the expected proportion of animals that will test positive.
• \(L\) is the precision on the expected proportion. If the expected proportion is \(p = 50\)% (or 0.5) and \(L = 5\)% then we are estimating a sample size to be \(95\)% sure that our result is between \(45\)% and \(55\)%.

Results

Minimum sample size:

The formula used for this sample size calculation is:

$$n = \frac{Z_\alpha^2 \sigma^2}{L^2}$$

and then \(\lceil n \rceil\) (the next largest integer) is returned. In the calculation

• \(Z_\alpha\) is the two-tailed Z-value from the confidence level.
• \(\sigma\) is the population variance.
• \(L\) is the precision on the estimated population mean. If the mean is \(100\) with a confidence interval of \(95\)% and \(L = 5\) then we are estimating a sample size to be \(95\)% sure that our result is between \(95\) and \(105\).

Results

Minimum sample size (per group):

If either proportion used in the above calculation is an estimate then the plots below will give you an idea of possible sample size required. If you hover over the individual points you will see the sample size.

The formula used for this sample size calculation is:

$$n = \frac{\left(Z_\alpha\sqrt{2p(1 - p)} - Z_\beta\sqrt{p_1(1 - p_1) + p_2(1 - p_2)}\right)^2}{\left(p_1 - p_2\right)^2}$$

and then \(\lceil n \rceil\) (the next largest integer) is returned. In the calculation

• \(Z_\alpha\) is the two-tailed \(Z\)-value from the confidence level.
• \(Z_\beta\) is the one-tailed \(Z\)-value from the power.
• \(p_1\) is the proportion from group 1.
• \(p_2\) is the proportion from group 2. Note that it is assumed that \(p_2 < p_1\) and the calculator will force value changes to control this.
• \(p = \frac{p_1 + p_2}{2}\) the mean proportion.

Results

The formula used for this sample size calculation is:

$$n = 2\frac{\left(Z_\alpha - Z_\beta\right)^2\sigma^2}{\left(\mu_1 - \mu_2\right)^2}$$

and then \(\lceil n \rceil\) (the next largest integer) is returned. In the calculation

• \(Z_\alpha\) is the two-tailed \(Z\)-value from the confidence level.
• \(Z_\beta\) is the one-tailed \(Z\)-value from the power.
• \(\mu_1\) is the mean from group 1.
• \(\mu_2\) is the mean from group 2. Note the test assumes that the means are different.
• \(\sigma\) is the population standard deviation (the test assumes that both groups have the same variance).