Standard Error
An estimate of the precision of a sample statistic, representing its variability across multiple hypothetical theoretical samples.
What is Standard Error?
The standard error measures the precision with which a sample statistic estimates a population parameter. It is calculated by dividing the sample standard deviation by the square root of the sample size. It represents the standard deviation of the sampling distribution.
Why Standard Error Matters
Standard error is crucial for inferential statistics; it is used to calculate confidence intervals and p-values, helping researchers determine how much their sample estimates might bounce around purely due to sampling noise.
Example
A pollster surveys 1,000 people and finds average approval is 50%. The standard error tells them how much that 50% estimate might vary if they surveyed a different random sample of 1,000 people.
Common Mistakes
- Confusing standard error with standard deviation; standard deviation describes the spread of individual data points, while standard error describes the precision of a sample mean.
- Assuming that increasing the sample size will shrink the standard deviation, rather than realizing it shrinks the standard error.