Effective Sample Size Calculator

Calculate Effective Sample Size



Formula

To calculate the Effective Sample Size:

\[ n_e = \frac{n}{1 + (n - 1) \cdot \rho} \]

Where:

What is Effective Sample Size?

Effective sample size is a concept used in statistics to describe the number of independent observations in a sample. It accounts for the design effect, which is the loss of statistical efficiency due to the sampling design, such as clustering or stratification. The effective sample size is often smaller than the actual sample size because the observations within clusters or strata are not completely independent. This adjustment is crucial for accurate statistical inference and ensures that the calculated sample size reflects the true amount of information available.

Example Calculation 1

Let's assume the following values:

Using the formula:

\[ n_e = \frac{100}{1 + (100 - 1) \cdot 0.05} = \frac{100}{1 + 4.95} = \frac{100}{5.95} = 16.81 \]

The Effective Sample Size is approximately 16.81.

Example Calculation 2

Let's assume the following values:

Using the formula:

\[ n_e = \frac{200}{1 + (200 - 1) \cdot 0.10} = \frac{200}{1 + 19.9} = \frac{200}{20.9} = 9.57 \]

The Effective Sample Size is approximately 9.57.