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# How to Find the F Critical Value in R

When you conduct an F test, you will get an F statistic as a result. To determine if the results of the F test are statistically significant, you can compare the F statistic to anÂ F critical value. If the F statistic is greater than the F critical value, then the results of the test are statistically significant.

The F critical value can be found by using anÂ F distribution tableÂ or by using statistical software.

To find the F critical value, you need:

• A significance level (common choices are 0.01, 0.05, and 0.10)
• Numerator degrees of freedom
• Denominator degrees of freedom

Using these three values, you can determine the F critical value to be compared with the F statistic.

### How to Find the F Critical Value in R

To find the F critical value in R, you can use theÂ qf()Â function, which uses the following syntax:

qf(p, df1, df2. lower.tail=TRUE)

where:

• p:Â The significance level to use
• df1: The numerator degrees of freedom
• df2: The denominator degrees of freedom
• lower.tail:Â IfÂ TRUE, the probability to the left ofÂ pÂ in the F distribution is returned. If FALSE, the probability to the right isÂ returned. Default is TRUE.

This function returns the critical value from the F distribution based on the significance level, numerator degrees of freedom, and denominator degrees of freedom provided.

For example, suppose we would like to find the F critical value for a significance level of 0.05, numerator degrees of freedom = 6, and denominator degrees of freedom = 8.Â

```#find F critical value
qf(p=.05, df1=6, df2=8, lower.tail=FALSE)

[1] 3.58058```

The F critical value for a significance level of 0.05, numerator degrees of freedom = 6, and denominator degrees of freedom = 8 isÂ 3.58058.

Thus, if weâ€™re conducting some type of F test then we can compare the F test statistic toÂ 3.58058.Â If the F statistic is greater than 3.58058, then the results of the test are statistically significant.

Note that smaller values of alpha will lead to larger F critical values. For example, consider the F critical value forÂ a significance level of 0.01, numerator degrees of freedom = 6, and denominator degrees of freedom = 8.Â

```#find F critical value
qf(p=.01, df1=6, df2=8, lower.tail=FALSE)

[1] 6.370681```

And consider the F critical value with the exact same degrees of freedom for the numerator and denominator, but with a significance level ofÂ 0.005:

```#find F critical value
qf(p=.005, df1=6, df2=8, lower.tail=FALSE)

[1] 7.951992```

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