To calculate the Effective Sample Size:
\[ n_e = \frac{n}{1 + (n - 1) \cdot \rho} \]
Where:
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.
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.
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.
