Standard Error

Learn estimated standard error, sample size and precision.

Lesson 3 of 32 parts Practice Flashcards

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Estimated Standard Error

Objective: Explain estimated standard error, apply the stated method, and check its conditions.

For independent observations under the usual mean model, estimated SE of x̄ is s/√n. It describes sampling variability of an estimator, whereas s describes variability of individual observations. Dependence, complex sampling, or clustering requires an appropriate alternative calculation. SD of observations and SE of an estimate are not interchangeable.

Formulas

Estimated SE(x̄)=s/√n

Worked examples

Try itAn independent sample has s=42 and n=49. Find estimated SE of the sample mean.Show answer

Step 1: Estimate SE with s/√n. Step 2: Use (42)/√(49). Step 3: SE=6; it describes estimator variability, not raw-data spread.

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Estimated Standard Error

Objective: Explain estimated standard error, apply the stated method, and check its conditions.

Formulas

Estimated SE(x̄)=s/√n

Worked examples

Try itAn independent sample has s=42 and n=49. Find estimated SE of the sample mean.Show answer

Step 1: Estimate SE with s/√n. Step 2: Use (42)/√(49). Step 3: SE=6; it describes estimator variability, not raw-data spread.

Sample Size and Precision

Objective: Explain sample size and precision, apply the stated method, and check its conditions.

Under independent sampling with unchanged population SD, a mean’s SE scales as 1/√n. Quadrupling n halves SE; doubling n does not halve it. Precision gains do not eliminate bias, undercoverage, or measurement problems. Larger n improves this precision measure, not every aspect of study quality.

Formulas

$SE₂/SE₁=√(n₁/n₂)$

Worked examples

Try itA study increases independent sample size from 49 to 196, with the same population SD. Find old SE divided by new SE.Show answer

Step 1: SE is proportional to 1/√n. Step 2: The new sample size is four times the old size, so new SE is half the old. Step 3: The ratio old/new is 2.

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