1. What is a Paired Sample T-Test?

Definition: A statistical test that compares the means of two related groups to determine if their population means differ significantly.

Purpose: Used when comparing measurements from the same subjects under different conditions (e.g., before/after treatment).

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( t \) — T-statistic (dimensionless)
• \( M_d \) — Mean difference between paired measurements
• \( s_d \) — Standard deviation of the differences
• \( n \) — Sample size (number of pairs)

Explanation: The mean difference is divided by the standard error of the difference (standard deviation divided by square root of sample size).

3. Importance of Paired T-Test

Details: This test accounts for individual variability by comparing measurements within the same subjects, making it more powerful than independent samples t-test for paired data.

4. Using the Calculator

Tips: Enter the mean difference, standard deviation of differences, and sample size (must be ≥ 2). The calculator will compute the t-statistic.

5. Frequently Asked Questions (FAQ)

Q1: What does the t-statistic tell me?
A: The t-statistic measures how many standard errors the mean difference is from zero. Larger absolute values indicate stronger evidence against the null hypothesis.

Q2: How do I interpret the t-statistic?
A: Compare your t-statistic to critical values from the t-distribution table with n-1 degrees of freedom to determine statistical significance.

Q3: What's a typical sample size for this test?
A: While it can work with small samples (n ≥ 2), larger samples (n ≥ 30) provide more reliable results.

Q4: When should I use a paired t-test vs independent t-test?
A: Use paired when comparing the same subjects under different conditions; use independent when comparing different groups.

Q5: What if my standard deviation is zero?
A: A zero standard deviation means all differences are identical, which would make the t-statistic undefined (division by zero).