1. What is a Sample Size Calculator with Effect?

Definition: This calculator determines the required sample size for a study considering the Z-score, expected proportion, design effect, and margin of error.

Purpose: It helps researchers and statisticians determine how many participants or observations are needed for statistically valid results.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score (standard score)
• \( p \) — Expected proportion (probability)
• \( DE \) — Design effect
• \( E \) — Margin of error

Explanation: The formula calculates the minimum number of samples needed to achieve a desired confidence level and precision, adjusted for study design.

3. Importance of Sample Size Calculation

Details: Proper sample size estimation ensures study validity, adequate power to detect effects, and efficient resource allocation.

4. Using the Calculator

Tips: Enter the Z-score (default 1.96 for 95% CI), expected proportion (default 0.5 for maximum variability), design effect (default 1.0 for simple random sampling), and margin of error (default 0.05 for ±5%).

5. Frequently Asked Questions (FAQ)

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

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

Q3: What is design effect?
A: A factor (≥1) accounting for sampling design inefficiency compared to simple random sampling (e.g., 1.5-2.0 for cluster sampling).

Q4: How do I choose margin of error?
A: Smaller values (e.g., 0.03) give more precise results but require larger samples. 0.05 is common.

Q5: Does this include non-response or attrition?
A: No, consider increasing your sample size by 10-20% to account for potential dropouts.