Paired T-Test Calculator

This calculator helps you perform a paired t-test, which is used to determine if there is a statistically significant difference between the means of two related groups. Enter your paired sample data and significance level to calculate the test statistic and p-value.

The paired t-test is based on the assumption that the differences between the paired observations are normally distributed.

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

Test Statistic (t):
Degrees of Freedom (df):
P-value:
Significance Level (α):
Hypothesis Test:

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.