F distribution table 0.
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The F distribution table 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, 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 the 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 we’re interested in the area to the right of the F statistic, so in this case the p-value would be 1 – 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. This table contains the upper critical values of the F distribution.
This table is used for one-sided F tests at the α = 0.05, 0.10, and 0.01 levels. More specifically, a test statistic is computed with ν1 and ν2 degrees of freedom, and the result is compared to this table. For a one-sided test, the null hypothesis is rejected when the test statistic is greater than the tabled value. This is demonstrated with the graph of an F
distribution with ν1 = 10 and ν2 = 10.
The shaded area of the graph indicates the rejection region at the α significance level. Since this is a one-sided test, we have α probability in the upper tail of exceeding the critical value and zero in the lower tail. Because the F distribution is asymmetric, a two-sided test requires a set of of tables (not included here) that contain the rejection regions
for both the lower and upper tails.
