1. What is Standard Error?

The Standard Error (SE) is a measure of the statistical accuracy of an estimate. It represents the standard deviation of the sampling distribution of a statistic, most commonly the mean.

2. How Does the Calculator Work?

The calculator uses the Standard Error formula:

Where:

• \( s \) — Standard deviation of the sample
• \( n \) — Sample size

Explanation: The standard error decreases as sample size increases, reflecting more precise estimates with larger samples.

3. Importance of Standard Error

Details: Standard error is crucial for constructing confidence intervals and conducting hypothesis tests. It helps quantify the uncertainty in sample estimates.

4. Using the Calculator

Tips: Enter the sample standard deviation and sample size. Both values must be positive numbers (sample size must be at least 1).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between standard deviation and standard error?
A: Standard deviation measures variability in data, while standard error measures the precision of sample statistics.

Q2: How does sample size affect standard error?
A: Standard error decreases with larger sample sizes (inverse square root relationship).

Q3: When should I use standard error?
A: When you want to assess the precision of sample estimates or construct confidence intervals.

Q4: Can standard error be zero?
A: Only if there's no variability in the population (standard deviation = 0) or sample size is infinite.

Q5: How is standard error related to confidence intervals?
A: 95% CI = mean ± 1.96 × SE (for normal distributions with large samples).