Sample Size Calculator For Proportion

Sample Size Formula for Proportion:

\[ n = \frac{Z^2 \times p \times (1-p)}{E^2} \times \left(1 + \frac{1}{N}\right) \]

Z-Score (Z):

(e.g., 1.96 for 95% CI)

Proportion (p):

(0 to 1)

Margin of Error (E):

(0 to 1)

Population Size (N):

individuals

Required Sample Size (n):

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1. What is Sample Size Calculation for Proportion?

The sample size calculation for proportion determines the number of participants needed in a study to estimate a population proportion with specified precision and confidence level, using finite population correction for more accurate results.

2. How Does the Calculator Work?

The calculator uses the sample size formula for proportion with finite population correction:

\[ n = \frac{Z^2 \times p \times (1-p)}{E^2} \times \left(1 + \frac{1}{N}\right) \]

Where:

\( Z \) — Z-score corresponding to desired confidence level
\( p \) — Estimated population proportion (0 to 1)
\( E \) — Margin of error (precision level)
\( N \) — Total population size

Explanation: The formula calculates the minimum sample size needed to estimate a population proportion within a specified margin of error at a given confidence level, with finite population correction for more accurate results when sampling from finite populations.

3. Importance of Sample Size Determination

Details: Proper sample size calculation ensures studies have adequate statistical power, prevents wasted resources on underpowered studies, and provides reliable estimates of population parameters with known precision.

4. Using the Calculator

Tips: Enter Z-score (1.96 for 95% CI, 2.58 for 99% CI), estimated proportion (use 0.5 for maximum variability), desired margin of error, and total population size. All values must be valid and positive.

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Use 1.96 for 95% confidence level, 2.58 for 99% confidence level, or 1.645 for 90% confidence level.

Q2: Why use 0.5 for proportion when unknown?
A: Using p=0.5 maximizes the product p×(1-p), giving the most conservative (largest) sample size estimate, ensuring adequate power regardless of the true proportion.

Q3: When is finite population correction important?
A: When sampling from small populations (typically when sample size exceeds 5-10% of population), finite population correction provides more accurate sample size estimates.

Q4: What is a reasonable margin of error?
A: Common margins are 0.05 (5%) or 0.03 (3%), but this depends on research requirements and acceptable precision level.

Q5: Can this calculator be used for clinical trials?
A: This calculator is for estimating proportions. Clinical trials typically require sample size calculations based on effect sizes and power analysis for hypothesis testing.