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're measuring a sample rather than the entire population.

2. How Does the Calculator Work?

The calculator uses the sampling error formula:

Where:

• \( z \) — Z-score corresponding to the desired confidence level
• \( p \) — Sample proportion (between 0 and 1)
• \( n \) — Sample size

Explanation: The formula calculates the margin of error for a proportion at a given confidence level, showing how much the sample proportion might differ from the true population proportion.

3. Importance of Sampling Error Calculation

Details: Understanding sampling error helps researchers determine the reliability of their findings and is crucial for designing studies with appropriate sample sizes.

4. Using the Calculator

Tips: Enter the z-score for your desired confidence level (e.g., 1.96 for 95% confidence), the sample proportion (between 0 and 1), and the sample size. All values must be valid (n > 0, 0 ≤ p ≤ 1).

5. Frequently Asked Questions (FAQ)

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

Q2: What if I don't know the sample proportion?
A: Use p = 0.5 for maximum variability, which gives the most conservative (largest) error estimate.

Q3: How does sample size affect sampling error?
A: Error decreases as sample size increases, but the relationship is not linear - quadrupling the sample size only halves the error.

Q4: When is this formula appropriate?
A: For simple random sampling with replacement, or when sampling without replacement from a large population.

Q5: Can this be used for continuous data?
A: No, this formula is for proportions. For means, use: error = z × (σ/√n) where σ is the standard deviation.