Critical Value Calculator Given Degrees of Freedom

What is a Critical Value?

A critical value is a threshold value from a statistical distribution that is used to determine whether results are statistically significant. In hypothesis testing, you compare your test statistic to the critical value to decide whether to reject the null hypothesis.

For the t-distribution, critical values depend on:

• The degrees of freedom (df)
• The significance level (α)
• Whether you're testing a one-tailed or two-tailed hypothesis

How to Use This Calculator

1. Enter the degrees of freedom (df) for your sample
2. Select your significance level (α)
3. Choose whether you're testing a one-tailed or two-tailed hypothesis
4. Click "Calculate" to get the critical value

The calculator will display the critical value and show it on a chart for visualization. You can also reset the form to start over.

Understanding the t-Distribution

The t-distribution is a probability distribution that is used when the sample size is small and the population standard deviation is unknown. It's similar to the normal distribution but has heavier tails, especially for small sample sizes.

The shape of the t-distribution depends on the degrees of freedom (df), which is calculated as n-1 where n is the sample size. As df increases, the t-distribution approaches the normal distribution.

Worked Example

Suppose you have a sample size of 15 (so df = 14) and you want to test a hypothesis at α = 0.05 with a two-tailed test.

1. Enter df = 14
2. Select α = 0.05
3. Choose "Two-tailed" test
4. Click "Calculate"

The calculator will display the critical value of approximately ±2.145. This means that if your test statistic is more extreme than ±2.145, you would reject the null hypothesis at the 0.05 significance level.