1. What is Pooled Variance?

Pooled variance is a method for estimating the combined variance of two different samples, assuming they have equal variances. It's 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:

• \( n1 \) — Sample size of first group
• \( Var1 \) — Variance of first group
• \( n2 \) — Sample size of second group
• \( Var2 \) — Variance of second group

Explanation: The formula weights each sample variance by its degrees of freedom (n-1), then divides by the total degrees of freedom from both samples.

3. Importance of Pooled Variance

Details: Pooled variance provides a better estimate of the common population variance when comparing two groups, particularly in hypothesis testing and confidence interval calculations for the difference between means.

4. Using the Calculator

Tips: Enter sample sizes (must be ≥2) and variances (must be ≥0) for both groups. The calculator will compute the pooled variance.

5. Frequently Asked Questions (FAQ)

Q1: When should I use pooled variance?
A: Use pooled variance when conducting a two-sample t-test and you can assume equal variances between the two populations.

Q2: What if my sample sizes are very different?
A: The pooled variance approach works best when sample sizes are similar. For very different sample sizes, consider Welch's t-test instead.

Q3: Can I use this for more than two samples?
A: This formula is specifically for two samples. For more samples, different methods like ANOVA should be used.

Q4: What are the assumptions for using pooled variance?
A: The main assumptions are that both samples come from normally distributed populations with equal variances.

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