1. What is a Paired Difference Test Calculator?

Definition: This calculator computes the t-statistic for paired (dependent) samples, comparing measurements taken on the same subjects under different conditions.

Purpose: It helps researchers determine if there's a statistically significant difference between paired measurements.

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 mean difference (standard deviation divided by square root of sample size).

3. Importance of Paired Difference Test

Details: This test is crucial for before-after studies, matched pairs, or any situation where measurements are naturally paired.

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: It measures how many standard errors the mean difference is from zero. Higher absolute values indicate stronger evidence against the null hypothesis.

Q2: What's a typical sample size for this test?
A: While it works with small samples (n ≥ 2), larger samples (n ≥ 30) provide more reliable results.

Q3: How do I interpret negative t-values?
A: The sign indicates direction of difference. The absolute value determines significance.

Q4: What's the relationship between this and p-value?
A: The t-statistic is used with degrees of freedom (n-1) to determine the p-value from t-distribution tables.

Q5: When should I use paired vs unpaired t-test?
A: Use paired when measurements are related (same subjects, matched pairs), unpaired for independent groups.