1. What Is Sampling Error?

Sampling error refers to the difference between a sample statistic and the actual population parameter it estimates. It occurs because we observe a sample rather than the entire population.

2. How Does the Calculator Work?

The calculator uses the standard error formula for proportions:

Where:

• \( SE \) — Standard error (sampling error)
• \( p \) — Sample proportion (between 0 and 1)
• \( n \) — Sample size (number of observations)

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

3. Importance of Sampling Error

Details: Understanding sampling error is crucial for interpreting survey results, determining appropriate sample sizes, and constructing confidence intervals around estimates.

4. Using the Calculator

Tips: Enter the sample proportion (as a decimal between 0 and 1) and the sample size (must be ≥1). The calculator will compute the standard error of the proportion.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between sampling error and margin of error?
A: Sampling error is the standard error, while margin of error is typically 1.96 times the standard error (for 95% confidence).

Q2: How does sample size affect sampling error?
A: Sampling error decreases with the square root of sample size - to halve the error, you need to quadruple the sample size.

Q3: When is sampling error largest?
A: For proportions, sampling error is maximized when p = 0.5 (50%).

Q4: Can sampling error be eliminated?
A: No, but it can be reduced by increasing sample size or using more efficient sampling methods.

Q5: Is this formula appropriate for small samples?
A: For very small samples (n < 30) or extreme proportions (p near 0 or 1), more specialized methods may be needed.