1. What is Minimum Sample Size Calculation?

Minimum sample size calculation determines the smallest number of participants needed in a study to detect a statistically significant effect. It ensures research has adequate power while optimizing resources and time.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula for proportions:

Where:

• \( n \) — Minimum sample size (count)
• \( Z \) — Z-score corresponding to confidence level (unitless)
• \( p \) — Estimated proportion (decimal)
• \( e \) — Margin of error (decimal)

Explanation: This formula calculates the minimum sample size needed for estimating a population proportion with specified confidence level and margin of error.

3. Importance of Sample Size Determination

Details: Proper sample size calculation prevents underpowered studies (missing true effects) and overpowered studies (wasting resources). It ensures statistical validity and reliability of research findings.

4. Using the Calculator

Tips: Enter Z-score (1.96 for 95% confidence), estimated proportion (0.5 for maximum variability), and desired margin of error. All values must be valid (Z > 0, 0 ≤ p ≤ 1, e > 0).

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Common Z-scores are 1.645 (90% confidence), 1.96 (95% confidence), and 2.576 (99% confidence).

Q2: Why use p = 0.5 as default?
A: p = 0.5 gives the maximum sample size, ensuring conservative estimates when the true proportion is unknown.

Q3: What is a reasonable margin of error?
A: Typically 0.05 (5%) or 0.03 (3%) for most surveys. Smaller margins require larger samples.

Q4: Does this work for finite populations?
A: This formula assumes infinite population. For finite populations, use the finite population correction factor.

Q5: When should I use this formula?
A: Use for estimating population proportions in surveys, prevalence studies, and categorical data analysis.