Calculate T Critical Value

T-Distribution Inverse:

\[ t_{\text{crit}} = t^{-1}(df, \alpha) \]

T Critical Value (t_crit):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is T Critical Value?

The t critical value (t_crit) is the cutoff point on the t-distribution that defines the rejection region for hypothesis testing. It depends on the degrees of freedom and the chosen significance level (α).

2. How Does the Calculator Work?

The calculator uses the inverse t-distribution function:

\[ t_{\text{crit}} = t^{-1}(df, \alpha) \]

Where:

\( df \) — Degrees of freedom
\( \alpha \) — Significance level (probability in the tail)

Explanation: The function returns the t-value where the cumulative probability equals 1-α for the given degrees of freedom.

3. Importance of T Critical Value

Details: T critical values are essential for constructing confidence intervals and conducting t-tests in statistics. They help determine whether to reject the null hypothesis.

4. Using the Calculator

Tips: Enter positive integer degrees of freedom and a significance level between 0 and 1 (typically 0.05 for 95% confidence).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between one-tailed and two-tailed tests?
A: For two-tailed tests, use α/2 as your significance level input (e.g., 0.025 for α=0.05 two-tailed).

Q2: How does degrees of freedom affect t_crit?
A: As df increases, t_crit approaches the z-value. With small df, t_crit is larger to account for uncertainty.

Q3: When should I use t-distribution instead of normal?
A: Use t-distribution when sample sizes are small (<30) and population standard deviation is unknown.

Q4: What if my df isn't in the table?
A: This calculator provides exact values for any df, unlike traditional tables.

Q5: Can I use this for non-integer df?
A: While possible mathematically, df is typically an integer representing sample size minus constraints.