1. What is the Sample Size Formula?

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

2. How Does the Calculator Work?

The calculator uses the sample size formula:

Where:

• \( n \) — Required sample size
• \( z \) — Z-score (determined by confidence level)
• \( p \) — Estimated proportion (0.5 for maximum variability)
• \( MOE \) — Desired margin of error

Explanation: The formula accounts for the relationship between confidence level (z-score), expected variability (p), and desired precision (MOE) to determine how many observations are needed.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures study results are statistically significant and reliable. Too small a sample may miss important effects, while too large wastes resources.

4. Using the Calculator

Tips: Common z-scores: 1.645 (90% CI), 1.96 (95% CI), 2.576 (99% CI). Use p=0.5 for maximum sample size when unsure. MOE is typically between 0.01 (1%) and 0.1 (10%).

5. Frequently Asked Questions (FAQ)

Q1: What's the most common confidence level used?
A: 95% confidence (z=1.96) is most common, providing a good balance between precision and sample size requirements.

Q2: Why use p=0.5 when unsure?
A: p=0.5 gives the maximum variability (p*(1-p)=0.25), resulting in the largest sample size needed, ensuring adequate power even for worst-case scenarios.

Q3: How does margin of error affect sample size?
A: Smaller margins require dramatically larger samples (n ∝ 1/MOE²). Halving MOE quadruples required sample size.

Q4: When is this formula not appropriate?
A: For very small or large p values (<0.1 or >0.9), finite populations, or complex sampling designs, other formulas may be needed.

Q5: How to adjust for population size?
A: For finite populations (N), use the corrected formula: n' = n/(1+(n-1)/N).