1. What Are Statistical Limits?

Statistical limits (confidence limits) define the range within which a population parameter is estimated to lie with a certain degree of confidence. They are commonly used in statistical inference to quantify uncertainty.

2. How Does the Calculator Work?

The calculator uses the limits formula:

Where:

• Mean — The sample mean or point estimate
• Z — The Z-score corresponding to the desired confidence level
• Standard Error — The standard error of the estimate

Explanation: The formula creates a symmetric interval around the mean estimate, with the width determined by the standard error and the desired confidence level (through the Z-score).

3. Importance of Limits Calculation

Details: Calculating limits is essential for understanding the precision of estimates, comparing groups, and making inferences about populations from sample data.

4. Using the Calculator

Tips: Enter the mean value, appropriate Z-score for your confidence level (e.g., 1.96 for 95% CI), and the standard error of your estimate.

5. Frequently Asked Questions (FAQ)

Q1: What are common Z-score values?
A: Common values are 1.645 (90% CI), 1.96 (95% CI), and 2.576 (99% CI).

Q2: How is standard error calculated?
A: Typically as standard deviation divided by the square root of sample size (SE = σ/√n).

Q3: When should I use t-scores instead?
A: For small samples (typically n < 30) or when population standard deviation is unknown, use t-scores from the t-distribution.

Q4: What's the difference between confidence limits and prediction limits?
A: Confidence limits estimate where the population mean lies, while prediction limits estimate where individual observations would fall.

Q5: Can I use this for proportions?
A: Yes, but for proportions there are alternative methods (like Wilson score interval) that may perform better with extreme proportions.