Paired T-Test Calculator
Easily calculate Paired T-Test online to compare means of two related samples. Input data, significance level, and get test statistic, p-value. Visualize results and copy output.
Data for the first group. Each value should correspond to a paired value in Data Set 2.
Data for the second group, paired with Data Set 1.
The probability of rejecting the null hypothesis when it is true. Common values are 0.05, 0.01.
Results
T-Distribution Visualization
Understanding the Paired T-Test
The Paired T-Test is a statistical test used to determine if there is a significant difference between the average values of two measurements taken on the same subjects or related subjects. This test is appropriate when you have paired observations (e.g., before and after measurements).
Key Concepts:
- Null Hypothesis (H₀): There is no significant difference between the means of the two related groups.
- Alternative Hypothesis (H₁): There is a significant difference between the means of the two related groups.
- Test Statistic (t): A value calculated from your sample data, used to determine the p-value.
- P-value: The probability of observing a test statistic as extreme as, or more extreme than, the statistic obtained from your sample if the null hypothesis is true.
- Significance Level (α): A threshold chosen by the researcher to decide whether to reject the null hypothesis. Commonly set at 0.05.
Formula:
The test statistic for a paired t-test is calculated as:
$$ t = \frac{\overline{d}}{s_d / \sqrt{n}} $$Where:
- \( \overline{d} \) is the mean of the differences between the paired observations.
- \( s_d \) is the standard deviation of the differences.
- \( n \) is the number of pairs.
Interpretation:
If the p-value is less than or equal to the significance level (p ≤ α), we reject the null hypothesis and conclude there is a statistically significant difference between the means of the two related groups. Otherwise, we fail to reject the null hypothesis.
For more detailed information, you can refer to statistical textbooks or online resources on paired t-tests.