1. What is the Margin of Error?

The margin of error (ME) 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 a proportion) and indicates how much the sample results may differ from the true population value.

2. How Does the Calculator Work?

The calculator uses the SurveyMonkey margin of error formula:

Where:

• \( z \) — Z-score (determined by confidence level)
• \( p \) — Sample proportion (between 0 and 1)
• \( n \) — Sample size
• \( N \) — Population size

Explanation: The first part calculates the standard error, while the second part applies the finite population correction factor when the sample is a significant fraction of the population.

3. Importance of Margin of Error

Details: The margin of error helps determine the reliability of survey results. A smaller margin indicates greater confidence that the sample results reflect the true population values.

4. Using the Calculator

Tips:

• For maximum margin of error, use p = 0.5
• Common confidence levels are 90% (z=1.645), 95% (z=1.96), and 99% (z=2.576)
• For large populations, the finite correction factor becomes negligible

5. Frequently Asked Questions (FAQ)

Q1: What confidence level should I use?
A: 95% is standard for most surveys, but you may use 90% for quicker surveys or 99% when higher confidence is needed.

Q2: Why use 0.5 for sample proportion?
A: p=0.5 gives the maximum margin of error, providing a conservative estimate when the true proportion is unknown.

Q3: When is the finite population correction important?
A: When your sample size exceeds 5% of the population, this correction significantly reduces the margin of error.

Q4: How does sample size affect margin of error?
A: Margin of error decreases with the square root of sample size - to halve the margin, you need to quadruple the sample.

Q5: Can I use this for non-survey applications?
A: Yes, this formula applies to any binomial proportion confidence interval calculation.