What is the design effect in school-based research?

Students in the same classroom are more similar to each other than to randomly selected students (intraclass correlation, ICC). The design effect DEFF = 1 + (cluster size – 1) × ICC multiplies the required sample size. Typical school ICC for achievement is 0.10–0.25, requiring 20–50% larger samples.

How large a sample is needed for a classroom study?

For a medium effect size (d=0.5), 80% power, and α=0.05 (two-tailed), you need approximately 64 students per group. With a design effect of 1.5 for clustering, this becomes 96 students per condition. For a small effect (d=0.2), 393 per group is required.

Sample Size Calculator for Education Research (n = Z²σ²/E²)

Formula Definitions

The Sample Size Calculator for Education Research (n = Z²σ²/E²) works by applying a well-defined formula to the values you enter. Understanding the formula behind the calculation helps you interpret the result and check that your inputs are correct. Below we break down the key components that drive the Sample Size n.

The core formula used by this calculator is:

Result = f(inputs, settings)

Each variable in the formula has a specific meaning:

inputs — Values entered into the Sample Size n.
settings — Options, units, or parameters that adjust how the calculation is performed.
Result — Computed output for the chosen inputs and settings.

How to Use This Calculator

Enter the required values. Enter the required values into the Sample Size Calculator for Education Research (n = Z²σ²/E²) input fields.
Adjust settings. Adjust any settings, select applicable options, or choose units as needed.
Calculate the result. Press Calculate to compute the result using the underlying formula.
Interpret the output. Review and interpret your result using the provided context, reference ranges, or explanatory notes.

Glossary and Definitions

Input: A value entered into the calculator to be processed.
Output: The computed result returned by the calculator for the given inputs.
Setting: An option that adjusts how the calculation is performed, such as unit selection or mode.
Sample size: A key concept referenced by the Sample Size n: Calculate required sample size for education research using n = Z²σ²/E² for continuous measures or n = Z²p(1−p)/E² for proportions. Accounts for design effect for cluster-sampled school surveys.
Education research: A key concept referenced by the Sample Size n: Calculate required sample size for education research using n = Z²σ²/E² for continuous measures or n = Z²p(1−p)/E² for proportions. Accounts for design effect for cluster-sampled school surveys.
Survey design: A key concept referenced by the Sample Size n: Calculate required sample size for education research using n = Z²σ²/E² for continuous measures or n = Z²p(1−p)/E² for proportions. Accounts for design effect for cluster-sampled school surveys.
Research methodology: A key concept referenced by the Sample Size n: Calculate required sample size for education research using n = Z²σ²/E² for continuous measures or n = Z²p(1−p)/E² for proportions. Accounts for design effect for cluster-sampled school surveys.
Confidence interval: A key concept referenced by the Sample Size n: Calculate required sample size for education research using n = Z²σ²/E² for continuous measures or n = Z²p(1−p)/E² for proportions. Accounts for design effect for cluster-sampled school surveys.
Design effect: A key concept referenced by the Sample Size n: Calculate required sample size for education research using n = Z²σ²/E² for continuous measures or n = Z²p(1−p)/E² for proportions. Accounts for design effect for cluster-sampled school surveys.