1. What is Critical T Value?

The critical t value is a threshold value from the t-distribution that defines the boundary for statistical significance in hypothesis testing. It's used to determine whether to reject the null hypothesis in t-tests.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \alpha \) — Significance level (0 to 1)
• \( df \) — Degrees of freedom
• \( t.inv \) — Inverse t-distribution function

Explanation: The critical t value represents the cutoff point beyond which we reject the null hypothesis in a two-tailed test.

3. Importance of Critical T Value

Details: Critical t values are essential for determining statistical significance in t-tests, confidence intervals, and various statistical analyses involving small sample sizes or unknown population variances.

4. Using the Calculator

Tips: Enter the significance level α (typically 0.05, 0.01, or 0.001) and degrees of freedom. The calculator will return the critical t value for a two-tailed test.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between one-tailed and two-tailed critical values?
A: One-tailed tests use α while two-tailed tests use α/2. This calculator provides values for two-tailed tests.

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

Q3: When should I use t-distribution instead of normal distribution?
A: Use t-distribution when sample size is small (typically n < 30) and population variance is unknown.

Q4: What are typical significance levels used?
A: Common significance levels are 0.05 (95% confidence), 0.01 (99% confidence), and 0.001 (99.9% confidence).

Q5: Can I use this for one-tailed tests?
A: For one-tailed tests, use α instead of α/2 in the calculation.