1. What is the Sample Size Formula?

The sample size formula calculates the minimum number of participants needed in a study to achieve a desired margin of error at a specific confidence level. It's fundamental for designing statistically valid surveys and experiments.

2. How Does the Calculator Work?

The calculator uses the sample size formula:

Where:

• \( z \) — Z-score (determined by confidence level)
• \( p \) — Estimated proportion (0.5 for maximum variability)
• \( MOE \) — Margin of error (acceptable error range)

Explanation: The formula accounts for the relationship between confidence level, expected proportion, and desired precision to determine the minimum sample size needed.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures study results are statistically significant, reliable, and representative of the population while avoiding unnecessary costs of oversampling.

4. Using the Calculator

Tips:

• For 95% confidence, use z = 1.96
• When unsure of proportion, use p = 0.5 (most conservative)
• MOE is typically between 0.01 (1%) and 0.1 (10%)

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). The z-score corresponds to your desired confidence level.

Q2: Why use p = 0.5?
A: p = 0.5 gives the maximum sample size needed, ensuring adequate power regardless of the actual proportion in your population.

Q3: How does margin of error affect sample size?
A: Smaller MOE requires dramatically larger samples (n increases with the square of MOE). Halving MOE quadruples required sample size.

Q4: What if my population is small?
A: For populations under 20,000, use the finite population correction: \( n_{adj} = \frac{n}{1 + \frac{(n - 1)}{N}} \) where N is population size.

Q5: Are there alternatives to this formula?
A: For continuous data or more complex designs, other formulas or power analysis may be needed. This formula is best for proportion estimation.