Pooled Sample Standard Error: How to Calculate it

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Pooled Sample Standard Error: Overview

pooled sample standard error
A standard error tells you how spread out your data is from a central point (the mean).

The standard error of a sample is another name for the standard deviation of a sample (this is also one of the AP Statistics formulas).

There’s a slight difference between standard deviation and pooled sample standard error:

  • When we are talking about a population, we talk about standard deviations.
  • When we talk about a sample we call it a standard error.

For calculations, you don’t have to worry about that difference: Both are calculated using the same formulas.
A pooled standard error accounts for two sample variances and assumes that both of the variances from the two samples are equal. It’s called a “pooled” standard error because you’re pooling the data from both samples into one. The formula for the pooled sample standard error is:

SEpooled = Sp √ (1/n1 + 1/n2)

Pooled Sample Standard Error: Steps

Sample problem: Calculate the pooled sample standard error for the following data from two samples:
Sample1 :n=25, s = 6.
Sample2 :n=25, s = 6.

Step 1: Insert your numbers into the formula. Use your variance (s) for sp (you can do this because both variances are the same:
SEp = 6 √ (1/25 + 1/25)

Step 2: Solve:
6 √ (1/25 + 1/25) ≈ 1.697.
The pooled sample standard error is about 1.697.

That’s it!

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