Sample Size Calculator

Sample Size Formula:

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

Z-score (confidence level):

Expected proportion (p):

(decimal, 0-1)

Margin of error (e):

(decimal, 0-1)

Required Sample Size:

1. What is the Sample Size Formula?

The sample size formula calculates the number of participants needed in a study to achieve statistically significant results. It accounts for confidence level, expected proportion, and margin of error.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula:

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

Where:

\( n \) — Required sample size
\( Z \) — Z-score (determined by confidence level)
\( p \) — Expected proportion (decimal between 0 and 1)
\( e \) — Margin of error (decimal between 0 and 1)

Explanation: The formula balances confidence level (Z), variability (p), and precision (e) to determine the minimum number of participants needed.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures studies have adequate power to detect effects while avoiding unnecessary resource expenditure on excessive sampling.

4. Using the Calculator

Tips: Select confidence level (or enter custom Z-score), enter expected proportion (use 0.5 for maximum variability if unsure), and desired margin of error (typically 0.05 for 5%).

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: 1.96 for 95% confidence (most common), 2.576 for 99% confidence, or 1.645 for 90% confidence.

Q2: What if I don't know the expected proportion?
A: Use 0.5 (50%) as this gives the most conservative (largest) sample size estimate.

Q3: What's a reasonable margin of error?
A: Typically 5% (0.05) or less. Smaller margins require larger samples.

Q4: Does this work for continuous variables?
A: This formula is for proportions. Different formulas exist for continuous variables.

Q5: How to adjust for population size?
A: For finite populations, use the finite population correction factor.