Sampling distribution and standard error
A sampling distribution shows how a statistic, such as the sample mean, varies from sample to sample. Its standard deviation is the standard error: SE = sigma / square root of n.
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Analogy
If many people each tasted a different spoonful, their verdicts would vary. The standard error measures that variation.
Example
sigma = 12n = 36: SE = 12 / 6 = 2n = 144: SE = 12 / 12 = 14 times the sample halves the SE
In practice
A bigger sample gives a smaller standard error, so the estimate is more precise.
Practice
Flashcards
- Formula for standard error of the mean?sigma / square root of n.
Interview questions
- Explain the central limit theorem and why it justifies using normal methods for sample means.
- Sample means become approximately normal for large n
- Holds for non-normal populations
- Mean is mu, SD is sigma / square root of n
- Does not change the shape of the raw data
Questions people ask
What is the difference between standard deviation and standard error?
Standard deviation measures how spread out individual values are. Standard error measures how spread out a statistic, such as a sample mean, is across repeated samples. The standard error is smaller, equal to the standard deviation divided by the square root of n.
Why do I need four times the data to halve the error?
Standard error shrinks with the square root of n, not with n itself. To halve it you must make the square root twice as big, which means multiplying n by four. Precision gets expensive: each extra bit of accuracy costs more data.