1. What is Pooled Variance?

Pooled variance is a method for estimating the combined variance of two or more samples when they are assumed to have the same variance. It is commonly used in statistical tests like the two-sample t-test.

2. How Does the Calculator Work?

The calculator uses the pooled variance formula:

Where:

• \( n_1 \) — Sample size of group 1
• \( s_1^2 \) — Variance of group 1
• \( n_2 \) — Sample size of group 2
• \( s_2^2 \) — Variance of group 2

Explanation: The formula weights each sample variance by its degrees of freedom (n-1), providing a combined estimate of population variance.

3. Importance of Pooled Variance

Details: Pooled variance is essential in hypothesis testing when comparing means of two groups, particularly in independent samples t-tests where equal variances are assumed.

4. Using the Calculator

Tips: Enter sample sizes (must be ≥2) and variances (must be ≥0) for both groups. All values must be valid numbers.

5. Frequently Asked Questions (FAQ)

Q1: When should pooled variance be used?
A: Use pooled variance when conducting independent samples t-tests and you can assume that both groups have equal population variances.

Q2: What if variances are significantly different?
A: If variances are unequal, consider using Welch's t-test instead, which doesn't assume equal variances.

Q3: Can pooled variance be used for more than two groups?
A: Yes, the concept can be extended to multiple groups, though the formula becomes more complex.

Q4: What are the assumptions for using pooled variance?
A: The main assumptions are that the populations are normally distributed and have equal variances.

Q5: How is pooled variance different from regular variance?
A: Pooled variance combines information from multiple samples to estimate a common population variance, while regular variance describes variability within a single sample.