1. What is the t-test?

The t-test is a statistical test used to determine if there is a significant difference between the means of two groups. It compares the means while accounting for the variability in the data through the standard deviations and sample sizes.

2. How Does the Calculator Work?

The calculator uses the independent samples t-test formula:

Where:

• \( \bar{x}_1 \) — Mean of group 1
• \( \bar{x}_2 \) — Mean of group 2
• \( s_1 \) — Standard deviation of group 1
• \( s_2 \) — Standard deviation of group 2
• \( n_1 \) — Sample size of group 1
• \( n_2 \) — Sample size of group 2

Explanation: The numerator measures the difference between group means, while the denominator (standard error) accounts for the variability and sample sizes of both groups.

3. Interpretation of Results

Details: A larger absolute t-value indicates a greater difference between groups relative to the variability in the data. To determine statistical significance, compare the t-value to critical values from the t-distribution with appropriate degrees of freedom.

4. Using the Calculator

Tips: Enter 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 this independent samples t-test when comparing means from two separate groups with normally distributed data.

Q2: What's a good sample size for t-tests?
A: Generally, n ≥ 30 per group is good, but smaller samples can work if data are normally distributed.

Q3: How do I determine significance?
A: Compare your t-statistic to critical values from the t-distribution table using (n₁ + n₂ - 2) degrees of freedom.

Q4: What if my standard deviation is 0?
A: SD=0 means all values are identical, making the t-test undefined as there's no variability to assess.

Q5: Can I use this for paired data?
A: No, for paired/matched data (e.g., before-after measurements), use a paired t-test instead.