1. What is Standard Error?

The Standard Error (SE) measures the accuracy with which a sample represents a population. It indicates how far the sample mean is likely to be from the true population mean.

2. How Does the Calculator Work?

The calculator uses the Standard Error formula:

Where:

• \( s \) — Sample standard deviation
• \( n \) — Sample size

Explanation: The formula shows that standard error decreases as sample size increases, and increases with greater variability in the data.

3. Importance of Standard Error

Details: Standard error is crucial for constructing confidence intervals and conducting hypothesis tests. It helps determine the precision of sample estimates.

4. Using the Calculator

Tips: Enter the sample standard deviation and sample size. Both values must be positive (sample size must be greater than 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 precision of the sample mean estimate.

Q2: Why does standard error decrease with larger sample sizes?
A: Larger samples better approximate the population, reducing sampling error (law of large numbers).

Q3: When should I use standard error?
A: Use SE when estimating population parameters from sample data, especially for confidence intervals and significance testing.

Q4: Can standard error be zero?
A: Only if there's no variability in the data (all values identical) or sample size is infinite - both unrealistic scenarios.

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