The F-distribution table

The F-distribution table - how to use

What is the F-distribution table?

The F-distribution table lists the point on the x-axis of the F-distribution beyond which 5% of the surface area of the curve lie. We use it every time we run Analysis of Variance (ANOVA)

What is the F-distribution?

The F-distribution is a curve like the normal curve or the t-curve. It is actually a modified t-curve that takes into account how many groups and how many subjects we have in our experiment. .

How to use the F-table

The first, left column is the df (degrees of freedom) of the denominator of the F ratio, (also called the error term).
The first, top line is the degrees of freedom of the numerator of the F ratio.

Example

In an experiment with 3 groups, of 10 subjects each, we have df between 2, and df within 27.
Suppose that we analyzed our data using ANOVA and we found an F=12.54. We call this "the computed F".

Step-by-step guide

Step 1. Enter the F table. Place your finger on the first left column at 27, then draw your finger to the third column which has the heading 2. You read the value 3.354 We call this "the required F" also called ."critical value".
Step 2. Now you compare your computed F which was F=12.54 to the required F of this table which is 3.354 Your computed F is bigger, so the finding of your experiment is significant, "p<0.05".

In scientific reports, we always report this p value. Example: "The difference between the mean of the group that received the drug and the group that received no drug was significant (p<0.05>".

What does "p<0.05" mean?
It means that the probability that your finding is due to chance (and not to what you did to the subjects of your experiment) is less tan 5%, 5 in a hundred.

What does "p<0.01" mean?
It means that the probability that your finding is due to chance (and not to what you did to the subjects of your experiment) is less tan 1%, 1 in a hundred.

What does "p<0.001" mean? It means that the probability that your finding is due to chance (and not to what you did to the subjects of your experiment) is less tan 1 in a thousand.