# Chi-Squared help

#### Zell49

##### New Member
Can anyone help me? I've been trying to connect all the elements need below, but I just cant!

Can anyone tell me how chi-squared and the F-distribution are related?

Also, what is the mathematical relationship (how they are equal)?

#### BioStatMatt

##### TS Contributor
Ok, lets define some random variables, say x1 and x2. Further let each of these variables have chi-square distributions with degrees of freedom r1 and r2 respectively. Then the random variable z, defined by:

z = (x1/r1) / (x2/r2)

has an F distribution with degrees of freedom (r1,r2).

Note here that a chi-square distribution has one parameter, its degrees of freedom (i.e. r1 or r2). An F distribution has two parameters, the numerator degrees of freedom and the denominator degrees of freedom (i.e. r1 and r2).

You can look up the actual pdf of an F random variable in a mathematical statistics book (or derive it youself). However, the important relationship between chi-square random variables and an F random variable is that given above.

Let me know if this helps. Also, this is a good question to ask a statistician if you have the chance.

~Matt