What sample size is needed for a 95% confidence interval with ±5% margin of error?

For a proportion (p=0.5 gives maximum variance), Z=1.96, E=0.05: n = (1.96)² × 0.25 / (0.05)² = 384. Adding 10% non-response buffer gives 423. For continuous outcomes, you need an estimated standard deviation; if unknown, use a pilot sample of n=30–50 to estimate σ.

Why does increasing sample size yield diminishing returns for precision?

Precision (margin of error) is proportional to 1/√n. To halve the margin of error, you must quadruple the sample size. Going from n=100 to n=400 doubles precision; going from n=400 to n=1,600 doubles it again. This is the key principle behind cost-effective sampling strategy: after n≈1,500, precision gains become minimal.

Research Methodology Sample Size Calculator

How It Works

Calculate required sample size using the fundamental formula n = Z²σ²/E² for continuous outcomes or n = Z²p(1−p)/E² for proportions. Includes finite population correction and design effect adjustment for clustered samples

Each component has a specific meaning:

Fundamental formula n = Z²σ²/E² — The fundamental formula n = z²σ²/e² recorded for the patient or scenario being assessed.

Note: Interpret the research sample size result against the clinical thresholds and context described above.

How to Use

Enter the fundamental formula n = Z²σ²/E² for the patient or scenario you are assessing. Calculate required sample size using the fundamental formula n = Z²σ²/E² for continuous outcomes or n = Z²p(1−p)/E² for proportions. Includes finite population correction and design effect adjustment for clustered samples. Use the research sample size result to inform your clinical assessment.

Glossary and Definitions

Sample size formula: A key concept in Research Sample Size: Calculate required sample size using the fundamental formula n = Z²σ²/E² for continuous outcomes or n = Z²p(1−p)/E² for proportions. Includes finite population correction and design effect adjustment for clustered samples.
Research methodology: A key concept in Research Sample Size: Calculate required sample size using the fundamental formula n = Z²σ²/E² for continuous outcomes or n = Z²p(1−p)/E² for proportions. Includes finite population correction and design effect adjustment for clustered samples.
Confidence interval: A key concept in Research Sample Size: Calculate required sample size using the fundamental formula n = Z²σ²/E² for continuous outcomes or n = Z²p(1−p)/E² for proportions. Includes finite population correction and design effect adjustment for clustered samples.
Margin of error: A key concept in Research Sample Size: Calculate required sample size using the fundamental formula n = Z²σ²/E² for continuous outcomes or n = Z²p(1−p)/E² for proportions. Includes finite population correction and design effect adjustment for clustered samples.
Z score: A key concept in Research Sample Size: Calculate required sample size using the fundamental formula n = Z²σ²/E² for continuous outcomes or n = Z²p(1−p)/E² for proportions. Includes finite population correction and design effect adjustment for clustered samples.
Population sampling: A key concept in Research Sample Size: Calculate required sample size using the fundamental formula n = Z²σ²/E² for continuous outcomes or n = Z²p(1−p)/E² for proportions. Includes finite population correction and design effect adjustment for clustered samples.
Research Sample Size: The Research Sample Size computes a result from the inputs you provide, based on the method described above.

Research Methodology Sample Size Calculator (Z²σ²/E²)

How It Works

How to Use

Glossary and Definitions

Frequently Asked Questions