1. What is a Paired Difference Test?

Definition: A statistical test that compares the means of two related groups to determine if their difference is statistically significant.

Purpose: Used when measurements are taken from the same subjects before and after a treatment, or when comparing matched pairs.

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 Difference Test

Details: This test accounts for individual variability by focusing on differences within pairs, making it more powerful than independent samples tests 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: When should I use a paired t-test?
A: When you have two measurements from the same subjects (before/after) or matched pairs, and want to test if their means differ significantly.

Q2: What does the t-statistic tell me?
A: A larger absolute t-value indicates stronger evidence against the null hypothesis (no difference). Compare it to critical values from t-distribution.

Q3: What's a good sample size for this test?
A: Generally ≥ 30 pairs for reliable results, but can work with smaller samples if differences are normally distributed.

Q4: How do I interpret negative t-values?
A: The sign indicates direction of difference. The absolute value determines significance.

Q5: What if my standard deviation is zero?
A: This means all differences are identical, which is extremely unlikely with real data. Check your calculations.