1. What is the Dependent T Test?

The dependent t-test (also known as paired t-test) is used to compare the means of two related groups or measurements. It determines whether there is a statistically significant difference between the means of paired observations.

2. How Does the Calculator Work?

The calculator uses the dependent t-test formula:

Where:

• \( \text{mean\_diff} \) — Mean of the differences between paired observations (unit of data)
• \( \text{sd\_diff} \) — Standard deviation of the differences (unit of data)
• \( n \) — Number of pairs (unitless)
• \( t \) — T-statistic value (unitless)

Explanation: The formula calculates how many standard errors the mean difference is from zero, indicating whether the observed difference is statistically significant.

3. Importance of Dependent T Test

Details: The dependent t-test is crucial for analyzing before-after studies, matched pairs, and repeated measures designs where observations are not independent but come from the same subjects under different conditions.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: When should I use a dependent t-test?
A: Use it when you have paired or matched observations, such as pre-test/post-test measurements, or when subjects serve as their own control.

Q2: What assumptions does the dependent t-test make?
A: The test assumes that the differences are normally distributed and that the observations are paired and dependent.

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

Q4: What's the difference between dependent and independent t-tests?
A: Dependent t-test compares means from the same group at different times, while independent t-test compares means from two different groups.

Q5: What if my data violates the normality assumption?
A: For non-normally distributed differences, consider using non-parametric alternatives like the Wilcoxon signed-rank test.