# Find an F Critical Value

Find an F Critical Value##
Minitab^{®}
– Procedure

You may need to find an *F* critical value if you are using the critical value approach to conduct a hypothesis test that uses an *F*-statistic.

- Select
**Calc**>>**Probability Distributions**>>**F**... - Click the button labeled
**Inverse cumulative probability**. (Ignore the box labeled**Noncentrality parameter**. That is, leave the default value of 0.0 as is.) - Type in the number of numerator degrees of freedom in the box labeled
**Numerator degrees of freedom**. - Type in the number of denominator degrees of freedom in the box labeled
**Denominator degrees of freedom**. - Click the button labeled
**Input Constant**. In the box, type the cumulative probability for which you want to find the associated*F*-value. - Select
**OK**. The*F-*value will appear in the session window.

##
Example

Some researchers at UCLA conducted a study on cyanotic heart disease in children. They measured the age at which the child spoke his or her first word (*x*, in months) and the Gesell adaptive score (*y*) on a sample of 21 children.

Is there evidence of a relationship between age at first word and Gesell adaptive score? That is, should we reject the null hypothesis *H*0: *β*1 = 0 against the alternative hypothesis *H*A: *β*1 ≠ 0 at the 0.05 level? The resulting data (adaptive.txt) yield an ANOVA *F*-statistic of 13.20.

## Minitab Dialog Box

Because the *F*-test is large regardless of whether the population slope is positive or negative, the *F*-test is always a one-sided test. Therefore, because we want to conduct the hypothesis test at the 0.05 level, the appropriate **cumulative probability** to enter is 0.95. The number of **numerator degrees of freedom** is always 1 for a simple linear regression model with one predictor. Because there are 21 measurements in the sample, the appropriate number of **denominator degrees of freedom** is 19. Therefore, your Minitab dialog box should look like:

### Sample Minitab Output

In this case, Minitab tells us that the *F*-critical value is:

### Inverse Cumulative Distribution Function

F distribution with 1 DF in numerator and 19 DF in denominator

P ( X ≤ x) | x |
---|---|

0.95 | 4.38075 |