1. What is Sample Size Calculation?

The sample size calculation determines the number of participants needed in a study to detect an effect with a specified level of confidence. It helps ensure studies are adequately powered without wasting resources.

2. How Does the Calculator Work?

The calculator uses the sample size formula for proportions:

Where:

• \( n \) — Required sample size
• \( z \) — Z-score corresponding to desired confidence level
• \( p \) — Estimated proportion in the population
• \( e \) — Margin of error (precision)

Explanation: The formula calculates how many participants are needed to estimate a population proportion within a certain margin of error at a specified confidence level.

3. Importance of Sample Size

Details: Proper sample size ensures study validity. Too small samples may miss important effects (Type II error), while excessively large samples waste resources.

4. Using the Calculator

Tips:

• Common Z-scores: 1.96 (95% CI), 2.576 (99% CI)
• Use p=0.5 for maximum variability (most conservative estimate)
• Margin of error is typically between 0.01 (1%) and 0.1 (10%)

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: For 95% confidence level use 1.96, for 90% use 1.645, and for 99% use 2.576.

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

Q3: How does margin of error affect sample size?
A: Smaller margins require dramatically larger samples (halving the margin quadruples the required sample size).

Q4: Is this formula for continuous or binary data?
A: This version is for binary (proportion) data. Different formulas exist for continuous data.

Q5: What about population size?
A: This formula assumes large populations. For small populations (<10,000), use finite population correction.