Pooled Standard Deviation Calculator
Calculate pooled standard deviation for combining multiple datasets
Calculate Pooled Standard Deviation
Enter numbers separated by commas, spaces, or line breaks
Enter numbers separated by commas, spaces, or line breaks
Example Calculation
Two Study Groups Example
Dataset A: [5, 7, 9, 11, 13] (n₁ = 5)
Dataset B: [4, 6, 8, 10, 12] (n₂ = 5)
Mean A: 9, Mean B: 8
Variance A: 10, Variance B: 10
Calculation Steps
1. s²pooled = [(n₁-1)×s₁² + (n₂-1)×s₂²] / (n₁+n₂-2)
2. s²pooled = [(5-1)×10 + (5-1)×10] / (5+5-2)
3. s²pooled = [40 + 40] / 8 = 80/8 = 10
4. spooled = √10 = 3.1623
Key Concepts
Pooled Variance
Weighted average of individual variances
Sample Size
Each dataset contributes based on its size
Degrees of Freedom
Total samples minus number of groups
When to Use
Comparing multiple groups with similar variances
Clinical trials with multiple treatment groups
t-tests comparing two or more groups
ANOVA and experimental design analysis
Understanding Pooled Standard Deviation
What is Pooled Standard Deviation?
Pooled standard deviation is a weighted average of standard deviations from multiple groups or datasets. It provides a single measure of variability when combining data from different sources, assuming all groups have similar (homogeneous) variances.
Key Assumptions
- •Groups have similar variances (homoscedasticity)
- •Data from each group follows normal distribution
- •Independent random samples from each group
- •Each group has at least 2 observations
Formula Breakdown
spooled = √[Σ((ni - 1) × si²) / Σ(ni - 1)]
- spooled: Pooled standard deviation
- ni: Sample size of group i
- si²: Sample variance of group i
- (ni - 1): Degrees of freedom for group i
Note: The pooled standard deviation gives more weight to groups with larger sample sizes, making it a more robust estimate than simple averaging.
Applications
Two-Sample t-Tests
Used to estimate the common standard deviation when comparing means of two independent groups.
ANOVA Analysis
Foundation for calculating within-group variation in analysis of variance tests.
Clinical Research
Combining results from multiple treatment groups or study sites with similar variability.