The F Distribution Table, also known as the Ftable, plays a crucial role in statistical analysis for conducting Ftests. These tests help compare variances between two or more groups, making them valuable tools in various fields like research and engineering. Here’s an explanation of the table and its usage:
What it shows:
The Ftable lists critical values for the Fstatistic, which is calculated based on the variances in your data. It has two main sections:
 Onetailed: Used for onesided tests, where we are interested in the probability of a value falling in one tail of the distribution (e.g., higher than a certain value).
 Twotailed: Used for twosided tests, where we consider both tails of the distribution (e.g., significantly different between groups).
Within each section, you’ll find:
 Numerator degrees of freedom (df1): Represents the number of groups minus 1 in the numerator of the Fstatistic.
 Denominator degrees of freedom (df2): Represents the total number of observations minus the number of groups in the denominator of the Fstatistic.
 Significance level (α): Represents the probability of rejecting the null hypothesis (H0) when it’s actually true, typically 0.05 (5%) or 0.01 (1%).
 Critical values: These are specific thresholds for your calculated Fstatistic based on df1, df2, and α.
How to use it:

Calculate your Fstatistic: This involves using your sample data and the formula for the Fstatistic based on the specific Ftest you’re conducting (e.g., oneway ANOVA, twoway ANOVA).

Identify the appropriate section: Onetailed for onesided tests, twotailed for twosided tests.

Locate the row with your numerator degrees of freedom (df1).

Find the column with your denominator degrees of freedom (df2).

Compare your calculated Fstatistic to the critical value:
 Reject H0 if your Fstatistic is greater than or equal to the critical value. This indicates a statistically significant difference in variances between the groups.
 Fail to reject H0 if your Fstatistic falls below the critical value. This suggests insufficient evidence for a significant difference in variances.
F Table for α = 0.05
F Table for α = 0.025
F Table for α = 0.01