1. What is the 2 Sample T-Test?

The two-sample t-test (independent samples t-test) is a statistical method used to determine whether the means of two independent samples are significantly different from each other. It's commonly used in research to compare two groups.

2. How Does the Calculator Work?

The calculator uses the two-sample t-test formula:

Where:

• \( \bar{x}_1, \bar{x}_2 \) — Sample means
• \( s_1^2, s_2^2 \) — Sample variances
• \( n_1, n_2 \) — Sample sizes
• \( t \) — Calculated t-statistic

Explanation: The formula compares the difference between sample means relative to the variability in the data and the sample sizes.

3. When to Use This Test

Details: Use this test when you want to compare the means of two independent groups with continuous data. Assumptions include normally distributed data, equal variances (for standard t-test), and independent observations.

4. Using the Calculator

Tips: Enter the mean, variance, and sample size for both groups. Sample sizes must be ≥2 and variances must be ≥0. The result is the t-statistic which you can compare to critical values from t-distribution tables.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between paired and unpaired t-tests?
A: Paired tests compare the same subjects under two conditions, while unpaired (this calculator) compares two independent groups.

Q2: What if my variances are unequal?
A: Consider using Welch's t-test which doesn't assume equal variances.

Q3: How do I interpret the t-statistic?
A: Compare it to critical values from the t-distribution with appropriate degrees of freedom. Larger absolute values indicate stronger evidence against the null hypothesis.

Q4: What sample size do I need?
A: Generally, larger samples increase test power. 30+ per group is often recommended.

Q5: Can I use this for non-normal data?
A: For non-normal data, consider non-parametric alternatives like the Mann-Whitney U test.