Standard Error Statistics Example 2

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Example 2

medium
How does the standard error change when you quadruple the sample size from n=25n = 25 to n=100n = 100? Assume ฯƒ=30\sigma = 30.

Solution

  1. 1
    Step 1: With n=25n = 25: SE1=3025=305=6SE_1 = \frac{30}{\sqrt{25}} = \frac{30}{5} = 6.
  2. 2
    Step 2: With n=100n = 100: SE2=30100=3010=3SE_2 = \frac{30}{\sqrt{100}} = \frac{30}{10} = 3.
  3. 3
    Step 3: Quadrupling the sample size halved the SE (from 6 to 3). In general, multiplying sample size by kk divides SE by k\sqrt{k}, so 4=2\sqrt{4} = 2 means SE is halved.

Answer

Quadrupling sample size from 25 to 100 halves the SE from 6 to 3. SE decreases by a factor of k\sqrt{k} when sample size is multiplied by kk.
The standard error decreases with the square root of the sample size, not linearly. This means diminishing returns โ€” to halve the SE, you must quadruple the sample size. Understanding this relationship helps in planning studies with appropriate sample sizes.

About Standard Error

The standard error (SE) is the standard deviation of a sampling distribution, measuring how much a sample statistic (like the sample mean) typically varies from the true population parameter across repeated samples. It decreases as sample size increases.

Learn more about Standard Error โ†’

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