1. What is the Critical T Statistic?

The critical t statistic (t_crit) is the cutoff value that determines the rejection region in a t-test. It depends on the significance level (α) and degrees of freedom (df), and is used to make decisions in hypothesis testing.

2. How Does the Calculator Work?

The calculator uses the inverse t-distribution function:

Where:

• \( \alpha \) — Significance level (0 to 1)
• \( df \) — Degrees of freedom (≥1)

Explanation: The function returns the t-value that corresponds to the specified significance level and degrees of freedom in a t-distribution.

3. Importance of Critical T Values

Details: Critical t values are essential for determining statistical significance in t-tests, constructing confidence intervals, and making inferences about population means.

4. Using the Calculator

Tips: Enter the significance level (typically 0.05 for 5% significance) and degrees of freedom (usually n-1 for sample size n). Both values must be valid (0 < α < 1, df ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between one-tailed and two-tailed critical values?
A: One-tailed tests use α directly, while two-tailed tests use α/2. This calculator assumes two-tailed tests by default.

Q2: How does degrees of freedom affect the critical value?
A: As df increases, the t-distribution approaches the normal distribution, and critical values decrease toward z-scores.

Q3: What are typical critical values for α = 0.05?
A: For df=10, t_crit≈2.228; for df=30, t_crit≈2.042; for df>120, approaches 1.96 (normal distribution).

Q4: When should I use t-critical values vs z-scores?
A: Use t-values when population standard deviation is unknown and sample size is small (<30). For large samples, they converge.

Q5: Can I use this for non-parametric tests?
A: No, critical t values are specific to t-tests which assume normally distributed data with unknown variance.