Calculate P-Value from T-Score

T-Score to P-Value Conversion:

\[ P = 2 \times (1 - \text{CDF}(|T|, df)) \]

P-Value:

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

The P-value from a T-score represents 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 Does the Calculator Work?

The calculator uses the T-distribution:

\[ P = 2 \times (1 - \text{CDF}(|T|, df)) \]

Where:

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

Explanation: The formula calculates the area under the t-distribution curve beyond the observed t-score, multiplied by 2 for two-tailed tests.

3. Importance of P-Value Calculation

Details: P-values help determine whether to reject the null hypothesis in statistical tests. A small p-value (typically < 0.05) suggests strong evidence against the null hypothesis.

4. Using the Calculator

Tips: Enter your calculated t-score, degrees of freedom, and select whether you need a one-tailed or two-tailed p-value. Degrees of freedom must be positive.

5. Frequently Asked Questions (FAQ)

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

Q2: How do I determine degrees of freedom?
A: For a one-sample t-test, df = n-1. For independent two-sample t-test, df = n1 + n2 - 2. For paired t-test, df = 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, effect size, and whether multiple comparisons were made.

Q4: Can I get exact p-values for very small/large t-scores?
A: Extremely small p-values may be limited by numerical precision. For very small p-values, consider reporting "p < 0.0001" instead.

Q5: When should I use a t-test vs z-test?
A: Use t-tests when population standard deviation is unknown (most common). Use z-tests when population standard deviation is known and sample size is large.