# structuring a proof

#### the42up

##### New Member
I am working on a problem to show that the non central f distribution is a generalization of the f distribution. I understand this conceptually but actually structuring it in a precise manner eludes me. Particularly also showing the noncentrality parameter in terms of expected mean squares.

#### Dason

What are you given? I would assume that setting the non-centrality parameter to 0 in the pdf of the non-central F and then noticing that what you're left with is the pdf of the central F should be enough of a proof?

#### the42up

##### New Member
sure is, the problem is, I need to structure the proof in such a way as to demonstrate the relationship between expected mean squares and the f test.

I think I am tripped up on the trivial nature of the proof. I want to show that as expected mean square treatment approaches expected mean square error, then the non central f distribution approaches the more familiar f distribution. How to precisely structure the proof is where I am having a bit of the issue.

#### Dason

Is that your exact prompt? If not can you provide the exact problem you're given?

#### the42up

##### New Member
given -F=MS1/MS2
lambda=(E(MS1)-E(MS2))*a-1/E(MS2).

show
noncentral f distribution is a generalization of f using lamdba.

#### the42up

##### New Member
it seems trivial to show that as Expected of the treatment approaches the error, then lambda will equal zero and give you an f distribution. Thus showing the relationship in terms of expected mean squares. Its just writing this in a precise manner that eludes me.

I suppose my question is whether it is necessary to demonstrate this in the context of PDFs.

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