Standard Error (SE)
Definition
The standard deviation of the sampling distribution of an estimator. For the sample mean, SE equals the population standard deviation divided by the square root of n. A smaller SE means the estimate is more precise.
- Definition
- Standard deviation of the sampling distribution of an estimator
- Formula for mean
- Population SD divided by square root of n
- Relationship to sample size
- Larger n produces smaller SE
- Meaning
- Smaller SE indicates a more precise estimate
Common questions
How is standard error different from standard deviation?+
Standard deviation describes spread within a single sample of data. Standard error describes how much the sample mean itself would vary if the study were repeated many times, and it shrinks as sample size grows while standard deviation does not.
Why does increasing sample size reduce the standard error?+
Because SE equals the population standard deviation divided by the square root of n, larger samples average out random fluctuation more effectively, pulling the sample mean closer to the true population mean across repeated sampling.
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