1. What is a P-value in T-test?

The P-value in a T-test measures the probability of observing the test results (or more extreme results) assuming the null hypothesis is true. It helps determine the statistical significance of your findings.

2. How is P-value Calculated?

The calculator uses the following formula:

Where:

• \( t \) — Calculated t-statistic from your data
• \( \text{df} \) — Degrees of freedom (n-1 for one-sample test)
• \( \text{CDF} \) — Cumulative distribution function of the t-distribution

Explanation: For a two-tailed test, we calculate the probability in both tails beyond the observed t-value. For one-tailed tests, we only consider one tail.

3. Interpretation of P-value

Details:

• P-value < 0.05: Typically considered statistically significant (reject null hypothesis)
• P-value ≥ 0.05: Not statistically significant (fail to reject null hypothesis)
• Smaller p-values indicate stronger evidence against the null hypothesis

4. Using the Calculator

Tips:

• Enter the t-statistic calculated from your data (can be positive or negative)
• Enter the appropriate degrees of freedom
• Select whether you're conducting a one-tailed or two-tailed test
• The calculator will compute the exact p-value

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between one-tailed and two-tailed tests?
A: One-tailed tests look for an effect in one direction only, while two-tailed tests consider both directions. Two-tailed is more conservative and generally preferred.

Q2: What if my p-value is exactly 0.05?
A: This is at the conventional threshold for significance. Interpretation depends on your field's standards and the consequences of Type I/II errors.

Q3: How do I calculate degrees of freedom?
A: For one-sample t-test: df = n-1. For two-sample t-test: df = n1 + n2 - 2 (assuming equal variances).

Q4: Can p-value be zero?
A: No, it can be very small (e.g., < 0.0001) but never exactly zero. It represents a probability.

Q5: What are common significance levels?
A: α = 0.05 is most common, but 0.01 and 0.10 are also used depending on the field and study context.