What is the Pooled Variance Calculator?
A Pooled Variance Calculator is a tool used in statistics to calculate the combined variance of two independent groups. It is useful when comparing the variability of two data sets. The pooled variance is calculated using the formula: Sp² = ((n1-1)s1² + (n2-1)s2²) / (n1 + n2 - 2), where n represents the sample size and s² represents the sample variance. This calculator is particularly helpful in t-tests and other analyses where homogeneity of variance is assumed.
How to Use the Pooled Variance Calculator
To use this calculator, enter the sample sizes and variances for two groups. Input the sample size (n1 and n2) and variance (s1² and s2²) for each group. Click the "Calculate" button to see the pooled variance result. The clear button can reset the inputs for new calculations. This calculator applies the pooled variance formula to give a quick and accurate result for statistical analysis.
Calculate Pooled Variance
FAQs
What is pooled variance?
Pooled variance is a statistical measure that combines the variances of two or more groups. It is often used in t-tests to assess the consistency of data dispersion between groups, assuming homogeneity of variance.
How is pooled variance calculated?
Pooled variance is calculated by taking a weighted average of the variances of each group. The formula is Sp² = ((n1-1)s1² + (n2-1)s2²) / (n1 + n2 - 2).
When to use pooled variance?
Pooled variance is used when comparing the variances of two groups with equal or similar sample sizes, particularly in t-tests where equal variance is assumed.
What is the difference between pooled variance and sample variance?
Sample variance measures the spread within a single group, while pooled variance combines variances from multiple groups for comparisons.
What are the assumptions for pooled variance?
Pooled variance assumes homogeneity of variance, meaning the groups being compared should have similar variances for accurate analysis.
Can pooled variance be negative?
No, variance measures dispersion, which is always non-negative. If the calculated value is negative, it indicates an error in input values.
Is pooled variance used in ANOVA?
Yes, pooled variance is commonly used in ANOVA and other analyses involving multiple groups to compare the variances.
What fields use pooled variance?
Pooled variance is used in fields like psychology, sociology, and biology, especially when comparing treatment effects across groups.
Why use pooled variance over separate variances?
Pooled variance is preferred when assuming equal variances across groups, as it provides a more stable estimate in such cases.
Does pooled variance apply to non-normal distributions?
While pooled variance is generally used for normally distributed data, it may be adapted for other distributions if variance assumptions hold.