Home
Back
Standard Error Formula:
| From: | To: |
Standard Error (SE) is a statistical measure that quantifies the accuracy with which a sample represents a population. It estimates the variability of a sample statistic (like the mean) from the true population parameter.
The calculator uses the standard error formula:
Where:
Explanation: The formula shows that standard error decreases as sample size increases, indicating that larger samples provide more precise estimates of population parameters.
Details: Standard error is crucial in inferential statistics for constructing confidence intervals and conducting hypothesis tests. It helps researchers determine the precision of their estimates and the reliability of their conclusions.
Tips: Enter the standard deviation in appropriate units and the sample size as a whole number. Both values must be valid (SD > 0, n > 1).
Q1: What's the difference between standard deviation and standard error?
A: Standard deviation measures variability within a sample, while standard error measures the precision of a sample statistic as an estimate of the population parameter.
Q2: When should I use standard error?
A: Use standard error when constructing confidence intervals or conducting hypothesis tests about population parameters based on sample statistics.
Q3: Why does standard error decrease with larger sample sizes?
A: Larger samples provide more information about the population, resulting in more precise estimates and smaller standard errors.
Q4: Can standard error be zero?
A: Standard error approaches zero as sample size approaches infinity, but in practice, it's never exactly zero with finite samples.
Q5: How is standard error related to confidence intervals?
A: Confidence intervals are typically constructed as the sample statistic ± (critical value × standard error).