Critical Values Degrees of Freedom Calculator

Critical values are essential in statistical hypothesis testing. They help determine whether your sample data provides enough evidence to reject the null hypothesis. This calculator helps you find critical values for t-distribution and chi-square distribution based on degrees of freedom and significance level.

What Are Critical Values?

Critical values are thresholds used in statistical hypothesis testing to determine whether to reject the null hypothesis. They are derived from probability distributions and depend on:

The type of distribution (t-distribution, chi-square, etc.)
Degrees of freedom (df)
Significance level (α)
Tail type (one-tailed or two-tailed test)

For example, in a t-test, if your calculated t-value exceeds the critical value, you reject the null hypothesis.

How to Use This Calculator

Select the distribution type (t-distribution or chi-square)
Enter the degrees of freedom (df)
Select the significance level (α)
Choose the tail type (one-tailed or two-tailed)
Click "Calculate" to get the critical value

The calculator will display the critical value and show it on a chart for visualization.

T-Distribution Critical Values

The t-distribution is used when working with small sample sizes. Critical values for t-distribution depend on:

Degrees of freedom (df)
Significance level (α)
Tail type

For one-tailed tests, the critical value is the t-value that leaves α% of the area in one tail. For two-tailed tests, it's the t-value that leaves α/2% in each tail.

Chi-Square Critical Values

The chi-square distribution is used in goodness-of-fit tests and tests of independence. Critical values for chi-square depend on:

Degrees of freedom (df)
Significance level (α)

Chi-square tests are always right-tailed, so there's no distinction between one-tailed and two-tailed tests.

FAQ

What is the difference between one-tailed and two-tailed tests?

In a one-tailed test, you're only interested in one direction of the effect (e.g., only higher values). In a two-tailed test, you're interested in both directions (e.g., both higher and lower values). This affects how the significance level is divided between tails.

How do I determine the degrees of freedom?

Degrees of freedom depend on the specific statistical test. For a one-sample t-test, df = n-1 where n is the sample size. For a chi-square test, df depends on the number of categories and constraints.

What if my degrees of freedom aren't listed in the calculator?

For degrees of freedom not in the calculator's tables, you can use linear interpolation between the closest available values or consult more comprehensive statistical tables.