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, given a specific confidence level and standard deviation. It's essential for designing statistically valid studies.

2. How Does the Calculator Work?

The calculator uses the sample size formula:

Where:

• \( n \) — Required sample size
• \( z \) — Z-score corresponding to desired confidence level
• \( SD \) — Standard deviation of the population
• \( MOE \) — Desired margin of error

Explanation: The formula accounts for the relationship between confidence level (z-score), variability (SD), and precision (MOE) to determine the minimum sample size needed.

3. Importance of Sample Size Calculation

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

4. Using the Calculator

Tips: Enter z-score (e.g., 1.96 for 95% CI), standard deviation estimate, and desired margin of error. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How do I choose the right z-score?
A: Common z-scores: 1.645 (90% CI), 1.96 (95% CI), 2.576 (99% CI). Use higher values for greater confidence.

Q2: What if I don't know the standard deviation?
A: Use estimates from pilot studies or similar research. For proportions (0-1 scale), SD = √[p(1-p)].

Q3: How does margin of error affect sample size?
A: Smaller MOE requires larger samples. Halving MOE quadruples required sample size.

Q4: When should I use finite population correction?
A: When sampling >5% of a finite population, multiply result by N/(N+n-1), where N = population size.

Q5: What about non-random sampling?
A: These calculations assume random sampling. Non-random methods may require larger samples or different approaches.