*70*

The **F distribution tableÂ **is a table that shows the critical values of the F distribution. To use the F distribution table, you only need three values:

- The numerator degrees of freedom
- The denominator degrees of freedom
- The alpha level

The F distribution is used most commonly in an Analysis of Variance, or *ANOVA* for short. For example, here is what the output table for an ANOVA might look like:

Source | SS | df | MS | F | P |
---|---|---|---|---|---|

Treatment | 58.8 | 2 | 29.4 | 1.74 | 0.217 |

Error | 202.8 | 12 | 16.9 | ||

Total | 261.6 | 14 |

In this example, the numerator degrees of freedom for the F statistic is **2**,Â the denominator degrees of freedom for the F statistic is **12**, and the F statistic itself is **1.74**. Suppose the alpha level we are using is 0.10. In the table above, we see that the p-value for this F statistic is 0.217. Since 0.217 is greater than the alpha level, we would conclude that this F statistic is not statistically significant.

If we instead wanted to use the F Distribution Table, we would use the F Distribution Table for alpha = 0.10. We would locate the critical value in the table that corresponds to a numerator degrees of freedom of 2 (DF1 = 2 in the table) and a denominator degrees of freedom of 12 (DF2 = 12 in the table) and find that this value is **2.8068**.

Since our F statistic of **1.74** from the ANOVA table is not greater than the F critical value of **2.8068** from the F Distribution table, we would conclude that the F statistic is not significant at the alpha level of 0.10.

**The F Distribution Table Provides Critical Values, Not P-Values**

Notice in the example above that the F Distribution Table simply gives us an F critical value to compare our F statistic to. The F Distribution Table does not directly give us a p-value.

**If you have an F statistic with a numerator degrees of freedom and denominator degrees of freedom and you would like to find the p-value for it, then you would need to use an F Distribution Calculator.**

For example, suppose we knew that our F statistic was 1.74, the numerator degrees of freedom was 2, and theÂ denominator degrees of freedom was 12 and we wanted to find the p-value for this F statistic. In this case, we would enter the following numbers into the F Distribution Calculator:

*Note: Leave the last box blank. The calculator will automatically find this value for you.*

This tells us that the cumulative probability is 0.78300. This is the area to the left of the F statistic in the F distribution. Typically weâ€™re interested in the area to the right of the F statistic, so in this case the p-value would be 1 â€“ 0.78300 = 0.217.

**When to Use the F Distribution Table**

If you are interested in finding the F critical value for a given numerator degrees of freedom, denominator degrees of freedom, and alpha level, then you should use the F distribution table.

Instead, if you have a given F statistic (from an ANOVA or some other statistical test) with a given numerator degrees of freedom and denominator degrees of freedom and you simply want to know the p-value of that F statistic, then you would need to use an F Distribution Calculator to do so.