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📘 How to interpret a standard error

Standard error summarizes how a statistic wobbles across repeated samples — not how individual observations scatter around a mean.

3
lessons
~15 min
to learn
Adults
level
Start the course →

What you’ll learn

  1. Name spread versus precisionDistinguish standard deviation of data from standard error of an estimate.Standard deviation describes observations; standard error describes sampling variability of a statistic.
  2. How sample size shapes SECalculate the estimated SE of a mean and explain how repeated samples and sample size change precision.Estimated SE is s divided by square root of n; quadrupling n roughly halves the mean's SE when variability is stable.
  3. Read and check SEInterpret SE in original units, connect it to confidence intervals, and check design assumptions.An SE summarizes estimator precision, not individual spread; a small SE is not proof of validity.

Questions this course answers

What does a standard error describe?

A standard error is the standard deviation of a statistic's sampling distribution.

For a sample mean, what happens to estimated SE when n is multiplied by four and s stays similar?

The sample mean's estimated SE is s divided by square root of n.

An SE of 1.5 minutes for a mean waiting time is measured in what units?

The standard error has the same units as the statistic it describes.

What should you check before trusting a small SE?

A simple SE can be too small when the design or dependence is not handled correctly.

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