1. What is a P-value from T Score?

The P-value from a T score is the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. It helps determine statistical significance in t-tests.

2. How the Calculator Works

The calculator uses the Student's t-distribution to compute the two-tailed P-value:

Where:

• \( t \) — Calculated t-score from your data
• \( df \) — Degrees of freedom (sample size - 1 for one-sample t-test)
• t.cdf — Cumulative distribution function of the t-distribution

Explanation: The formula calculates the area under both tails of the t-distribution beyond the observed t-score.

3. Interpretation of Results

Details: A small P-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, while a large P-value suggests weak or no evidence against it.

4. Using the Calculator

Tips: Enter your calculated t-score and degrees of freedom. The calculator will provide the two-tailed P-value. For one-tailed tests, divide the result by 2.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between one-tailed and two-tailed P-values?
A: Two-tailed tests for any difference (greater or smaller) while one-tailed tests for a difference in a specific direction.

Q2: How do I find degrees of freedom?
A: For one-sample t-test: n-1. For independent two-sample t-test: n1 + n2 - 2. For paired t-test: number of pairs - 1.

Q3: What if my P-value is exactly 0.05?
A: This is at the conventional threshold for significance. Consider the context and possibly report the exact P-value.

Q4: Can I use this for very large degrees of freedom?
A: Yes, but as df increases, the t-distribution approaches the normal distribution.

Q5: Why is my P-value different from statistical software?
A: Small differences may occur due to different approximation methods or rounding.