F Distribution Probability Calculator

Degrees of freedom can be described as the number of scores that are free to vary. For example, suppose your friend tossed three dice, and the total score added up to 12. If your friend told you that he rolled a 3 on the first die and a 5 on the second, then you know that the third die must be a 4 (otherwise, the total would not add up to 12). In this example, 2 die are free to vary while the third is not. Therefore, there are 2 degrees of freedom.

In many situations, the degrees of freedom are equal to the number of observations minus one. Thus, if the sample size were 20, there would be 20 observations; and the degrees of freedom would be 20 minus 1 or 19.

You can use the following equation to compute an f statistic:

f = [ s₁²/σ₁² ] / [ s₂²/σ₂² ]

where σ₁ is the standard deviation of population 1, s₁ is the standard deviation of the sample drawn from population 1, σ₂ is the standard deviation of population 2, and s₁ is the standard deviation of the sample drawn from population 2.

The degrees of freedom (v₁) refers to the degrees of freedom associated with the sample standard deviation s₁ in the numerator; and the degrees of freedom (v₂) refers to the degrees of freedom associated with the sample standard deviation s₂ in the denominator.

A cumulative probability is a sum of probabilities. The F distribution calculator computes two cumulative probabilities:

• Probability (F≤f). This is the cumulative probability that an F statistic is less than or equal to the value f.
• Probability (F≥f). This is the cumulative probability that an F statistic is greater than or equal to the value f.

An f statistic (also known as an f value) is a random variable that has an F distribution. Here are the steps required to compute an f statistic:

• Select a random sample of size n₁ from a normal population, having a standard deviation equal to σ₁.
• Select an independent random sample of size n₂ from a normal population, having a standard deviation equal to σ₂.
• The f statistic is the ratio of s₁²/σ₁² and s₂²/σ₂². Thus, f = [ s₁²/σ₁² ] / [ s₂²/σ₂²]

A probability is a number expressing the chances that a specific event will occur. This number can take on any value from 0 to 1. A probability of 0 means that there is zero chance that the event will occur; a probability of 1 means that the event is certain to occur. Numbers between 0 and 1 quantify the uncertainty associated with the event.

For example, the probability of a coin flip resulting in Heads (rather than Tails) would be 0.50. Fifty percent of the time, the coin flip would result in Heads; and fifty percent of the time, it would result in Tails.