What is Margin of Error?
Margin of error measures survey accuracy, indicating how much results may differ from the true population value. It helps determine reliability of survey data. Researchers use it to understand potential variance in results at a specific confidence level. A smaller margin indicates more precise estimates. It's crucial in political polls, market research, and scientific studies to interpret data accuracy and make informed decisions based on statistical confidence.
Margin of Error Calculator
Confidence Level:
Population Size (optional):
Margin of Error Formula
The margin of error formula: MOE = z * √(p(1-p)/n) * √((N-n)/(N-1))
Where:
z = z-score (1.645 for 90%, 1.96 for 95%, 2.576 for 99% confidence)
p = proportion (0.5 for maximum variability)
n = sample size
N = population size (optional for finite population correction)
How to Use This Calculator
1. Enter sample size (minimum 30)
2. Select confidence level (90%, 95%, or 99%)
3. Optional: Enter population size for precise calculation
4. Click Calculate to get margin of error percentage
5. Use Clear button to reset all fields
Frequently Asked Questions
What is a good margin of error?
A 5% margin of error at 95% confidence is generally acceptable for most surveys. Lower margins provide more accuracy but require larger samples. The acceptable margin depends on research goals and industry standards. Political polls often use 3-5%, while scientific studies may demand smaller margins.
Does population size affect margin of error?
Population size mainly matters when it's relatively small compared to sample size. For large populations (>20,000), the effect becomes negligible. The finite population correction factor adjusts calculations for smaller populations, reducing margin of error when sample size exceeds 5% of population.
Why use 0.5 for proportion in calculations?
Using 0.5 (50%) produces maximum variability, giving the worst-case margin of error. This conservative approach ensures calculations account for maximum possible error. If prior knowledge suggests different proportions, specialists might adjust this value for more precise calculations.
How does confidence level affect results?
Higher confidence levels increase margin of error. A 99% confidence level widens the margin compared to 95% or 90%, as it requires more certainty that the true value lies within the range. Choose confidence level based on required certainty versus acceptable error tolerance.
What's the relationship between sample size and margin of error?
Sample size inversely affects margin of error - larger samples reduce margin. However, diminishing returns occur: doubling sample size only improves accuracy by √2. Balance desired precision with data collection costs when determining sample size.
When is finite population correction needed?
Use finite population correction when sample exceeds 5% of total population. This adjustment accounts for reduced variability when sampling significant population portions. For large populations (over 20,000), correction has minimal impact and can often be omitted.
Can margin of error predict exact survey results?
No, margin of error shows potential variation range, not exact outcomes. It indicates that true population value likely falls within the calculated range X% of the time (based on confidence level). It doesn't guarantee results or account for other errors like measurement bias.
Why different z-scores for confidence levels?
Z-scores correspond to standard deviations covering specific percentages of normal distribution. 1.96 covers 95% of data points in a normal curve, 1.645 covers 90%, and 2.576 covers 99%. These values derive from standard normal distribution tables used in statistical analysis.
How accurate are online margin of error calculators?
Quality calculators using proper formulas and assumptions provide mathematically accurate results. Accuracy depends on correct input values and understanding limitations. They don't account for sampling method errors or response bias, only statistical sampling error.
What's the difference between margin of error and confidence interval?
Margin of error is half the confidence interval width. A 95% confidence interval shows the range (estimate ± margin of error). While related, confidence interval expresses the range itself, while margin of error specifies the radius of that range.