F Critical Value Calculator

This F Critical Value Calculator helps you quickly find the cutoff value from the F distribution for hypothesis testing. You simply need to enter the significance level (α), numerator degrees of freedom (df1), and denominator degrees of freedom (df2). The calculator instantly returns the F critical value used in ANOVA, variance comparison tests, and regression model evaluations.

How to Use the Calculator

Using the F Critical Value Calculator is quick and easy. In just a few steps, you can find the critical value for your F-test without looking through long F-distribution tables or doing manual calculations.

Here’s how the calculator works:

• Step 1: Enter the Significance Level (α). This is the probability threshold for your test, commonly set at 0.05 for 95% confidence level, or 0.01 for 99% confidence level.
• Step 2: Enter the Numerator Degrees of Freedom (df₁). This value comes from the number of groups minus one in your test.
• Step 3: Enter the Denominator Degrees of Freedom (df₂). This usually comes from the total sample size minus the number of groups.
• Step 4: Click “Calculate” button. The calculator will return the F critical value similar to one you get when using F distribution table.

What is an F Critical Value?

The F critical value is a threshold taken from the F distribution. It is used in statistical tests to determine whether the difference between group variances or model effects is significant. When you perform an F-test, such as ANOVA or regression analysis, you calculate an F statistic from your data. To make decisions regarding your proposed hypotheses, you compare the F statistic with the F-critical to make valid decisions. Specifically, if the computed F statistic is larger than the critical F-value, you reject the null hypothesis. Otherwise, you fail to reject the null hypothesis.

Therefore, F-critical value is useful in hypothesis testing because it helps you decide whether the observed variation is unlikely to have occurred by chance. The value depends on your chosen significance level (α) and the degrees of freedom for the numerator and denominator.

F-Critical Value Formula

The F critical value formula is: $F_{\alpha, df_1, df_2}$

Where:

• α is the significance level
• df1​ is the numerator degrees of freedom
• df2​ is the denominator degrees of freedom.

Therefore, having the above parameters allows you to easily find the F-critical value, either using the calculator or from the F-distribution table.

Want to learn more about critical F-values? check out our comprehensive guide on how to find F-critical values using F-tables.

Finding F-Critical Value Using the Calculator

You can easily find F critical value for any F-test using our calculator. Follow these examples to learn how to obtain the critical values using the calculator.

Example 1: A teacher wants to know if the average scores of three different classes are significantly different. The significance level is 0.05, the numerator degrees of freedom is 2, and the denominator degrees of freedom is 27. Find the corresponding F-critical value.

Solution

To find the F critical value:

1. Enter 0.05 as the significance level.
2. Enter 2 for df₁ and 27 for df₂.
3. Click “Calculate” to get the F critical value. The resulting critical value is 3.3541 (See Figure 1).

Example 2: A factory manager wants to check if three machines produce parts with different variances. The significance level is 0.01, df₁ is 2, and df₂ is 47. Find the corresponding F-critical value.

Solution

To find the F critical value:

1. Enter 0.01 as the significance level.
2. Enter 2 for df₁ and 47 for df₂.
3. Click “Calculate” to see the F critical value. The calculator gives a critical value of 5.0874 (See Figure 2).

Frequently Asked Questions