# What F value stands for in ANOVA analysis?

#### statser

##### New Member
Hi everyone,

When I do ANOVA test, I notice in the output many values among them P, F values.
Could somebody please tell me what F value in ANOVA test stands for ?
Should one rely on too for the significance ?

Thank you for help

#### WeeG

##### TS Contributor
I guess you mean the value of the F statistic.

In order to determine if your test if significant, you need to have some test statistic. in the Anova case, we use the F statistic ( like in Regression - try to find the connection between the two ).

If you want your model to be significant, you need a P value of equal or smaller than 0.05 ( for 95% ).

#### statser

##### New Member
I guess you mean the value of the F statistic.

In order to determine if your test if significant, you need to have some test statistic. in the Anova case, we use the F statistic ( like in Regression - try to find the connection between the two ).

If you want your model to be significant, you need a P value of equal or smaller than 0.05 ( for 95% ).
Yes, actually I mean F statistic but I don't understand what does it mean ? I kno P value but not F ! what the difference between P and F values ?

#### WeeG

##### TS Contributor
well, like I said, F is the test statistic and is equal to:

F=variance of the group means / mean of the within group variances

the p-value on the other hand, is the probability of obtaining a result at least as extreme as the one that was actually observed, given that the null hypothesis is true.

p value is a probability, F is a value of a test...2 different things.

#### statser

##### New Member
well, like I said, F is the test statistic and is equal to:

F=variance of the group means / mean of the within group variances

the p-value on the other hand, is the probability of obtaining a result at least as extreme as the one that was actually observed, given that the null hypothesis is true.

p value is a probability, F is a value of a test...2 different things.
Thank you WeeG.

#### way2abhi994

##### New Member
Is there is range for this f value in regression analysis. if so what is the range and how it can be interpreted?

#### Dason

It must be positive. It can be interpreted as the ratio of the between groups variance and the within groups variance as mentioned above.

##### New Member
So how does the F statistic show the significance of a test? Does it have to be of a certain value? Or does the significance just depend on the p value?
Also is the F statistic the same as F observed?
Thanks

#### CurlPopper

##### New Member
The data in ANOVA can be divided by "This is the part where we can explain why the values vary" (MSM) and "This is stuff we have no idea why it does vary" (MSE)

- We want the explained variance (MSM) to be as high as possible, because we want to explain stuff.
- We want the "Stuff where we have no Idea about"(MSE) to be as small as possible.

Now you always get some value of MSM, is it significant?

The F statistic in ANOVA is answering the Question "Is the part of explained variance significant?" by comparing "the variance you can explain" with the "variance you can not explain"
By calculating "explained Variance/ unexplained variance"
If my "explained variance" is way higher than the "unexplained variance" I will get a large F statistic.

MSM = 100.000
MSE = 20

F= 5000 (nice)

If my "unexplained variance" is way higher than my "explained variance" I will get a small F (never smaller than 1).

MSM = 25
MSM = 20
F = 1,25 (meh...)

We want large "explanations of variance". Thus, we want large F values in ANOVA. But how large is large enough? Similar to the t statistic, there is a P value corresponding to the F statistic you obtained. You have to look that up in a table. Based on the P value that corresponds to your F statistic, you have to decide whether you will assume that a significant amount of variance is explained or not.

#### penQ

##### New Member
Dude or Dudette - thankyou! this is the best explanation of F value and now I understand. That is sooo cool!
!

The data in ANOVA can be divided by "This is the part where we can explain why the values vary" (MSM) and "This is stuff we have no idea why it does vary" (MSE)

- We want the explained variance (MSM) to be as high as possible, because we want to explain stuff.
- We want the "Stuff where we have no Idea about"(MSE) to be as small as possible.

Now you always get some value of MSM, is it significant?

The F statistic in ANOVA is answering the Question "Is the part of explained variance significant?" by comparing "the variance you can explain" with the "variance you can not explain"
By calculating "explained Variance/ unexplained variance"
If my "explained variance" is way higher than the "unexplained variance" I will get a large F statistic.

MSM = 100.000
MSE = 20

F= 5000 (nice)

If my "unexplained variance" is way higher than my "explained variance" I will get a small F (never smaller than 1).

MSM = 25
MSM = 20
F = 1,25 (meh...)

We want large "explanations of variance". Thus, we want large F values in ANOVA. But how large is large enough? Similar to the t statistic, there is a P value corresponding to the F statistic you obtained. You have to look that up in a table. Based on the P value that corresponds to your F statistic, you have to decide whether you will assume that a significant amount of variance is explained or not.

#### Karabiner

##### TS Contributor
Dude or Dudette - thankyou! this is the best explanation of F value and now I understand. That is sooo cool!
!
Well, the meaning of an F-value is explained nicely, but unfortunately,
degrees of freedom were not mentioned.

It isn't simply the case that, say, "F=12.2" translates into "p=0.0134".
Which "p-value" belongs to a certain F-value depends on the degrees
of freedom. Degrees of freedom are based on a) how many groups were
compared, and b) how many subjects were included. The same
F-value can be clearly significant or clearly non-significant, depending
on how many groups and how many subjects were included into the
analysis.

As proposed by staassis, www.en.wikipedia.org/wiki/F-test should