Critical T Score Calculator

α (Significance Level)

A value between 0 and 1, e.g. 0.05 for a 5% significance level.

Choose one

n (Sample Size)

About This Test

What Is a Critical T-Score?

The critical t-score is the cutoff on the t-distribution that separates "likely due to chance" from "statistically significant." The t-distribution is similar to the normal distribution but with heavier tails, which accounts for the extra uncertainty in smaller samples.

When to Use It

Hypothesis tests and confidence intervals for a mean, when the population standard deviation is unknown
Comparing two group means with a t-test
Any small-to-moderate sample where you're estimating variability from the data itself

The Concept

\[ P(T > t_{\alpha,\,df}) = \alpha \]

Worked Example

For a sample size of 25 (df = 24) at α = 0.05, what's the critical t-value?

\( \alpha = 0.05, \ df = n - 1 = 24 \)
Two-tailed critical value: \( t_{0.025,\,24} \approx \pm 2.064 \)
If your calculated t-statistic falls outside ±2.064, you reject the null hypothesis at the 5% significance level.

Your Results

Shaded regions show the two-tailed rejection zone. Dashed lines mark the one-tailed (left and right) critical values.

Need Help with Stats?

Contact us

Related Resources:

Perfect for students, researchers, and professionals looking to build real statistical skills.

[Get Started Today!]