📏Standard error

The standard deviation of an estimate, not of the data. If I took the same size of sample again and again and worked out the mean each time, the standard error is how much those means would scatter.

• Standard deviation: how much individual values vary.
• Standard error: how much my summary of them would vary from sample to sample.

They are not the same thing, however often I say one for the other. The second shrinks as the sample grows, with the square root of n; the first does not shrink at all.

From 🎓 Lecture 5 - Sampling distributions, the idea that took me two attempts. It only became a thing I could see while doing 📌 Statistics I - Problem set 2 - Sampling distributions by simulation on the tram. The version for percentages is 📐 Standard error of a proportion.

Origin: error is from Latin errare, to wander, with no blame attached. The term is usually traced to the statistician Udny Yule in 1897, a few years after Karl Pearson named the standard deviation.

An example from my work. If 50 of 100 sampled dispatchers say they open the inbox first thing, the standard error of that 50 percent is the square root of 0.5 × 0.5 ÷ 100, which is 0.05: five points.

So the honest slide says about 50 percent, give or take ten, and the dishonest one says half of all dispatchers. Quadrupling the sample to 400 only halves the error.