Statistics for Researchers › Module 2: Samples and uncertainty

Standard error, simply

Lesson 2 of 3 · 2 min

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If you took a different random sample, you would get a slightly different average. The standard error (SE) measures how much the average would jump around from sample to sample.

SD versus SE

  • Standard deviation (SD): how much individual values vary.
  • Standard error (SE): how much the average would vary across repeated samples.

For a mean, SE = SD ÷ √n, where n is the sample size.

What the formula tells you

  • More data → smaller SE. The average becomes more stable.
  • But it shrinks with the square root. To halve the SE you need four times as much data.

ExampleStudents' test scores have an SD of 20 points. With 25 students, SE = 20 ÷ 5 = 4 points. With 100 students, SE = 20 ÷ 10 = 2 points. Four times the students, half the uncertainty.

Why it matters when reading

Error bars in papers are often SE bars. They look small because they describe the average, not the individuals. A tiny SE does not mean everyone behaved the same, only that the average is well estimated.

RememberSD describes the people; SE describes the average. Four times the data halves the standard error.