1. What is the Dependent T Test?

The dependent t-test (also known as the paired t-test) is a statistical procedure used to determine whether the mean difference between two sets of observations is zero. It is commonly used when measurements are taken from the same subjects under different conditions.

2. How Does the Calculator Work?

The calculator uses the dependent t-test formula:

Where:

• \( \text{mean\_diff} \) — Mean of differences between paired observations
• \( \text{sd\_diff} \) — Standard deviation of the differences
• \( n \) — Number of paired observations

Explanation: The formula calculates how many standard errors the mean difference is from zero, providing a t-statistic that can be compared to critical values from the t-distribution.

3. Importance of T-Statistic Calculation

Details: The t-statistic is crucial for determining statistical significance in paired experiments. It helps researchers determine if observed differences are likely due to the experimental intervention or simply random chance.

4. Using the Calculator

Tips: Enter the mean of differences, standard deviation of differences, and number of pairs. All values must be valid (sd_diff > 0, n ≥ 2).

5. Frequently Asked Questions (FAQ)

Q1: When should I use a dependent t-test?
A: Use a dependent t-test when you have paired or matched samples, such as pre-test/post-test measurements, or when subjects are measured under two different conditions.

Q2: What assumptions does the dependent t-test make?
A: The test assumes that the differences between pairs are approximately normally distributed and that the observations are randomly sampled from the population.

Q3: How do I interpret the t-value?
A: A larger absolute t-value indicates a greater difference between the paired observations. Compare the calculated t-value to critical values from the t-distribution with n-1 degrees of freedom to determine statistical significance.

Q4: What is the difference between dependent and independent t-tests?
A: Dependent t-tests are for paired data, while independent t-tests are for comparing means between two different groups of subjects.

Q5: Can I use this test for small sample sizes?
A: Yes, the t-test is specifically designed for small sample sizes (typically n < 30), though the data should reasonably meet the normality assumption.