1. What is P-value from T-ratio?

The p-value represents the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. In this case, we calculate it from the t-distribution.

2. How Does the Calculator Work?

The calculator uses the t-distribution formula:

Where:

• \( P \) — Probability (p-value) as percentage
• \( t \) — T-ratio (unitless test statistic)
• \( df \) — Degrees of freedom (integer)
• \( CDF_t \) — Cumulative distribution function for t-distribution

Explanation: The calculator computes the area under the t-distribution curve beyond the observed t-ratio, converted to percentage.

3. Importance of P-value Calculation

Details: P-values are fundamental in hypothesis testing, helping determine statistical significance. They quantify how incompatible the data are with the null hypothesis.

4. Using the Calculator

Tips: Enter the t-ratio value (can be positive or negative) and degrees of freedom (must be positive integer). The calculator returns two-tailed p-value by default.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between one-tailed and two-tailed p-values?
A: One-tailed tests directionality (greater or less than), while two-tailed tests any difference. This calculator provides two-tailed results.

Q2: How do degrees of freedom affect the p-value?
A: Higher degrees of freedom make the t-distribution approach normal. With small df, tails are heavier, affecting extreme p-values.

Q3: What is considered a statistically significant p-value?
A: Typically p < 0.05 (5%) is considered significant, but this threshold depends on your field and specific study.

Q4: Can I calculate critical t-values from p-values?
A: Yes, but this calculator only goes from t to p. You'd need the inverse CDF for the reverse calculation.

Q5: Why does my p-value show as 0.0000%?
A: This means the p-value is extremely small (< 0.00005), essentially zero for practical purposes.