1. What is Standard Error?

The Standard Error (SE) measures the precision of the sample mean as an estimate of the population mean. It quantifies how much the sample mean would vary across different samples from the same population.

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 how reliable the sample mean is as an estimate of the population mean.

4. Using the Calculator

Tips: Enter the sample standard deviation (must be ≥0) and sample size (must be ≥1). The standard deviation should be in the same units as your original measurements.

5. Frequently Asked Questions (FAQ)

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

Q2: Why does standard error decrease with larger sample sizes?
A: Larger samples provide more precise estimates of the population mean, reflected in a smaller standard error.

Q3: When should I use standard error vs standard deviation?
A: Use standard deviation when describing data variability, and standard error when discussing the precision of the mean estimate.

Q4: Can standard error be zero?
A: Only if the standard deviation is zero (all values identical) or sample size is infinite (impossible in practice).

Q5: How is standard error related to confidence intervals?
A: A 95% confidence interval is typically constructed as mean ± 1.96 × SE.