Sample Size Calculation Proportion

Sample Size Formula for Proportion:

\[ n = \frac{z^2 \times p \times (1-p)}{e^2} \]

Z-score (z):

dimensionless

Expected Proportion (p):

dimensionless

Margin of Error (e):

dimensionless

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 a specified margin of error and confidence level. It's essential for designing surveys and clinical trials.

2. How Does the Calculator Work?

The calculator uses the sample size formula for proportion:

\[ n = \frac{z^2 \times p \times (1-p)}{e^2} \]

Where:

\( z \) — Z-score corresponding to the desired confidence level
\( p \) — Expected proportion (0-1)
\( e \) — Margin of error (0-1)
\( n \) — Required sample size

Explanation: The formula accounts for the relationship between confidence level (z), expected variability (p), and desired precision (e) to determine the minimum number of observations needed.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures studies have adequate power to detect effects while avoiding unnecessary resource expenditure. Underpowered studies may miss important findings, while overpowered studies waste resources.

4. Using the Calculator

Tips: Enter z-score (e.g., 1.96 for 95% CI), expected proportion (0-1), and margin of error (0-1). All values must be valid (z > 0, 0 ≤ p ≤ 1, 0 < e ≤ 1).

5. Frequently Asked Questions (FAQ)

Q1: What z-score should I use?
A: Common values are 1.645 (90% CI), 1.96 (95% CI), and 2.576 (99% CI). Choose based on desired confidence level.

Q2: What if I don't know the expected proportion?
A: Use p = 0.5 for maximum variability, which gives the most conservative (largest) sample size estimate.

Q3: How does margin of error affect sample size?
A: Smaller margins require dramatically larger samples (n ∝ 1/e²). Halving the margin quadruples the required sample size.

Q4: When is this formula appropriate?
A: For estimating a single proportion with a simple random sample. Different formulas are needed for other designs (e.g., comparing proportions).

Q5: Should I adjust for expected response rate?
A: Yes, divide calculated n by expected response rate (e.g., if n=385 and you expect 70% response, plan to contact 385/0.7 ≈ 550 subjects).