# compare F statistics vs P-values

#### szm

##### Member
Hi
I have a question about comparing F statistics among effects.
I have the following anova table

HTML:
Parameter     Estimate               Standard Error         t Value       Pr > |t|
Factor1        12088.62915           2249.053598           5.37        <.0001
Factor2        -28.62915               2249.053598          -8.7          <.0001
Factor3        88.62915                2249.053598           6.3         <.0001
Factor4       -62915                    2249.053598          -2.99        <.0001
Factor5       -1208291                2249.053598           3.73        <.0001
Factor6       2088.62915             2249.053598         -7.33         <.0001
Since all the pvalues are equal, is it valid if I say F = (t)*2 and conclude that Factor2 has the greatest impact on my response variable?

#### spunky

##### Doesn't actually exist
is it valid if I say F = (t)*2 and conclude that Factor2 has the greatest impact on my response variable?
nope...

i'm pretty sure your p-values are not equal. they're just so small (i can see all your t-statistics are on the larger range) that the computer doesn't bother printing the whole collection of decimal points.

besides, t-statistics/p-values tend to be really lousy measures of variable importance. things are not "more significant' than others just because they have a larger test statistic/smaller p-value. they're either significant or not.

#### szm

##### Member
Thank you for the reply spunky!

I probably misunderstood what I read a while ago.

I should mention that this output comes from PROC GLM using the solution option. So basically it is the output of regression.
I read that in regression, the independent variable with the largest F statistic (t^2) has the greatest impact on the response variable.
Maybe I misunderstood, I read it a while ago..

#### Englund

##### TS Contributor
I read that in regression, the independent variable with the largest F statistic (t^2) has the greatest impact on the response variable.
A p-value is not a measure of effect size nor of practical significance!

#### spunky

##### Doesn't actually exist
I read that in regression, the independent variable with the largest F statistic (t^2) has the greatest impact on the response variable.
Maybe I misunderstood, I read it a while ago.
i could see why some people believe that is the case. about a year ago i was really into this idea of "relative variable importance" which is basically trying to order variables in terms of how "important" they are and contribute to the prediction power of your model. now i don't think any of those things work but if you're keen on looking around you can google stuff like the Budescu & Azen's Dominance Analysis, Thomas, Hughes and Zumbo's Pratt Index, Johnson and Lebreton's Relative Weights or the good ol' squared semi-partial correlations.

there are as many measures of importance as definitions of importance are, and most of them are some way of chopping up the R^2 and attributing part of the shared variance to each variable. there're plenty of SPSS/SAS macros to calculate them and some (like the Pratt Index) is just the product of the standardized beta coefficient with its correlation and stuff like that.

#### szm

##### Member
Thanks again,

I am trying to figure out which of my 5 independent variables has the greatest impact on the response so I will try to read more!

Thank you

#### spunky

##### Doesn't actually exist
which of my 5 independent variables has the greatest impact on the response
how do you define "impact"? how do you measure it? most variance explained? change on the depdent variable/response? the way in which you measure "impact" should tell you which method or statistic to use and not all definitions of "impact" imply the other ones.