Comprehensive Calculator Guide
This calculator combines two groups’ standard deviations into one pooled SD, weighting each variance by its degrees of freedom, as used in the two-sample t-test and effect sizes. Groups of 30 and 20 with SDs 10 and 12 give a pooled SD of 10.84 on 48 degrees of freedom.
Pooling
Pooled variance = ((n₁ − 1)s₁² + (n₂ − 1)s₂²) ÷ (n₁ + n₂ − 2). It assumes similar variances; if one is over about four times the other, use Welch’s test.
How to Use
- Enter group 1’s SD and size.
- Enter group 2’s.
- Press “Calculate” to see the pooled SD, variance and df.
Formula Used
s_p = √(((n₁ − 1)s₁² + (n₂ − 1)s₂²) ÷ (n₁ + n₂ − 2))
Practical Examples
- Example 1
- 30 and 20: 10.84.
- Example 2
- Equal groups: 6.08.
Important Tips
- Check the variances are similar.
- Use sample SDs.
- Report df.
Common Mistakes to Avoid
- Averaging the SDs.
- Pooling unequal variances.
- Dividing by n₁ + n₂.
Frequently Asked Questions
- What is it?
- A shared SD estimate.
- Why not average SDs?
- Variances are pooled.
- Where used?
- t-tests and Cohen’s d.