1. What is the Pooled Variance T Statistic?

The pooled variance t-statistic is used in hypothesis testing to compare the means of two independent groups when the population variances are assumed to be equal. It's a fundamental tool in statistical analysis for determining if there's a significant difference between two group means.

2. How Does the Calculator Work?

The calculator uses the pooled variance t-statistic formula:

Where:

• \( \bar{X}_1 \) — Mean of group 1
• \( \bar{X}_2 \) — Mean of group 2
• \( s_p^2 \) — Pooled variance
• \( n_1 \) — Sample size of group 1
• \( n_2 \) — Sample size of group 2

Explanation: The formula calculates how many standard errors the difference between means is from zero, helping determine statistical significance.

3. Importance of T Statistic Calculation

Details: The t-statistic is crucial for conducting independent samples t-tests, which are widely used in research to compare means between two groups and determine if observed differences are statistically significant or due to random chance.

4. Using the Calculator

Tips: Enter the means of both groups, the pooled variance, and the sample sizes for both groups. All values must be valid (variance > 0, sample sizes > 0).

5. Frequently Asked Questions (FAQ)

Q1: When should I use pooled variance t-test?
A: Use when comparing means of two independent groups and you can assume equal population variances (homogeneity of variance).

Q2: How is pooled variance calculated?
A: \( s_p^2 = \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1 + n_2 - 2} \), where s₁² and s₂² are sample variances.

Q3: What is a significant t-value?
A: Significance depends on degrees of freedom and chosen alpha level (typically 0.05). Compare calculated t to critical t-value from t-distribution table.

Q4: What if variances are not equal?
A: Use Welch's t-test instead, which doesn't assume equal variances.

Q5: What are degrees of freedom for this test?
A: Degrees of freedom = n₁ + n₂ - 2 for the pooled variance t-test.