1. What is Margin of Error?

The margin of error (MOE) quantifies the amount of random sampling error in a survey's results. It represents the radius of the confidence interval for a given statistic (usually at 95% confidence level).

2. How Does the Calculator Work?

The calculator uses the margin of error formula:

Where:

• \( p \) — Sample proportion (between 0 and 1)
• \( n \) — Sample size
• 1.96 — Z-score for 95% confidence level

Explanation: The formula shows that margin of error decreases as sample size increases, and is maximized when p = 0.5.

3. Importance of Margin of Error

Details: Margin of error is crucial for understanding the precision of survey results and for determining appropriate sample sizes in research studies.

4. Using the Calculator

Tips: Enter proportion (between 0 and 1) and sample size (positive integer). The calculator will compute the margin of error at 95% confidence level.

5. Frequently Asked Questions (FAQ)

Q1: Why 1.96 in the formula?
A: 1.96 is the z-score that corresponds to 95% confidence level in a normal distribution.

Q2: What's a good margin of error?
A: Typically 5% or less is considered acceptable for most surveys, though this depends on the specific application.

Q3: How does sample size affect MOE?
A: MOE decreases with the square root of sample size - to halve the MOE, you need to quadruple the sample size.

Q4: What if I don't know the proportion?
A: Use p = 0.5 for the most conservative (largest possible) margin of error estimate.

Q5: Can I use this for non-binary outcomes?
A: This formula is for binary proportions. Different formulas are needed for continuous data or multinomial outcomes.