Calculate Paired T-Test by Hand
The paired t-test is a statistical test used to compare the means of the same group under two different conditions. Calculating it by hand is crucial for understanding the underlying assumptions and methodology. This calculator guides you through the process, ensuring accurate results.
- Enter the number of pairs (n).
- Enter the mean of pair 1 (X̄).
- Enter the mean of pair 2 (X̄₂).
- Enter the standard deviation (s).
- Click ‘Calculate’.
The formula for the paired t-test is:
t = (X̄₁ – X̄₂) / (s / √n)
Where:
- X̄₁ is the mean of pair 1.
- X̄₂ is the mean of pair 2.
- s is the standard deviation.
- n is the number of pairs.
Examples
Suppose we have 10 pairs of data (n=10), with means X̄₁ = 15 and X̄₂ = 18, and standard deviation s = 3.
t = (15 – 18) / (3 / √10) = -2.887
Comparison of Means
| Pair | Mean |
|---|---|
| 1 | 15 |
| 2 | 18 |
T-Test Results
| T-Value | Degrees of Freedom | P-Value |
|---|---|---|
| -2.887 | 9 | 0.014 |
Tips
- Ensure your data meets the assumptions of the paired t-test.
- Use a significance level (alpha) of 0.05 for most tests.
- Consider using a different test if the assumptions are not met.
What are the assumptions of the paired t-test?
The assumptions are: independence of observations, random sampling, normality, and equal variances.
For more information, see the paired t-test guide from Statistics How To.