1. What is Standard Error?

The Standard Error (SE) measures the precision of a sample mean as an estimate of the population mean. It quantifies how much the sample mean would vary if you repeated the study multiple times.

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 researchers understand the precision of their sample estimates.

4. Using the Calculator

Tips: Enter the sample standard deviation (must be > 0) and sample size (must be ≥ 1). The calculator will compute the standard error of the mean.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between SD and SE?
A: Standard Deviation measures variability in data, while Standard Error measures precision of the sample mean.

Q2: Why does SE decrease with larger n?
A: Larger samples provide more precise estimates of the population mean, reflected in smaller SE.

Q3: When should I use SE vs SD?
A: Use SD to describe data variability, SE when discussing precision of mean estimates.

Q4: Can SE be zero?
A: Only if SD is zero (all values identical) or sample size is infinite (impossible in practice).

Q5: How is SE related to confidence intervals?
A: 95% CI = mean ± 1.96×SE (assuming normal distribution).