1. What is Student's t-test?

The Student's t-test is a statistical hypothesis test used to determine if there is a significant difference between the means of two groups. The t-value measures the size of the difference relative to the variation in your sample data.

2. How Does the Calculator Work?

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

Where:

• \( \bar{x_1}, \bar{x_2} \) — Sample means of group 1 and group 2
• \( s_1, s_2 \) — Sample standard deviations
• \( n_1, n_2 \) — Sample sizes

Explanation: The numerator measures the difference between group means, while the denominator estimates the standard error of that difference.

3. Interpretation of t-value

Details: A larger absolute t-value indicates a greater difference between groups relative to the variability within groups. The significance depends on degrees of freedom and chosen alpha level (typically 0.05).

4. Using the Calculator

Tips: Enter the means, standard deviations, and sample sizes for both groups. Standard deviations must be ≥0 and sample sizes must be positive integers.

5. Frequently Asked Questions (FAQ)

Q1: When should I use this t-test?
A: Use when comparing means of two independent groups with normally distributed data and approximately equal variances (for standard t-test).

Q2: What's a "large" t-value?
A: The critical value depends on degrees of freedom. Typically, |t| > 2 suggests statistical significance for moderate sample sizes.

Q3: What if my variances are unequal?
A: Consider using Welch's t-test which doesn't assume equal variances.

Q4: What are degrees of freedom for this test?
A: For standard t-test: df = n₁ + n₂ - 2. For Welch's t-test: more complex calculation.

Q5: How is this different from paired t-test?
A: Paired t-test is for dependent samples (e.g., before/after measurements on same subjects).