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Suppose two ANOVA models, #1 and #2.
In #1 the F value is 500.
In #2 the F value is 50.
Same degrees of freedom.
Both, of course, are highly significant -- p<.0001.
Can we say anything about the 500 vs 50?
Is model #1 in some way better than #2?
Thanks!
Nicholas Kormanik
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@NKormanik wrote:
Suppose two ANOVA models, #1 and #2.
In #1 the F value is 500.
In #2 the F value is 50.
Same degrees of freedom.
Both, of course, are highly significant -- p<.0001.
Can we say anything about the 500 vs 50?
It is true that if you have more data points (i.e. more degrees of freedom), you will have a better chance to achieve statistical significance with the same level of error.
Is model #1 in some way better than #2?
Define "better".
Paige Miller
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model versus the other.
On which model would you place your bet?
Both models are significant, as said above.
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I don't gamble, first. So I decline to answer.
Second, I have no idea what these models are or what they predict, I don't have your data, and you haven't provided the measures of goodness-of-fit, so I decline to answer for that reason as well.
Paige Miller
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I think so.
model #1 in some way better than #2
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@Ksharp wrote:
I think so.
model #1 in some way better than #2
Ok, I'll have to disagree with this, unless you are using a different meaning of "better" than I am. I want to see goodness of fit statistics, and not F-test, to determine which model fits better. Without goodness of fit measures, I can't say which model is better. If we're not talking about how well the model fits, then what definition of "better" are you using?
Paige Miller
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Same true of t-values?
Say, two t-values are significant, but one is 10X larger than another.
Could we say that the variable with the much larger t-value is in some way more significant?
Does seem reasonable.
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What I've asked here seems like an entirely reasonable question:
Comparing hugely different F-values (and, t-values).
What can one (a very experienced expert statistician) say regarding such differences.
In researching, however, I came across a series of articles that seem to question the foundations, and pop the balloon:
https://www.tandfonline.com/toc/utas20/current
One example:
Good grief.
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Goodness of fit measures tell you how well a model fits; not F-tests, not t-tests.
Paige Miller
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Yeah. I think so.
t-value and F-value in some way are the same thing, they all measure the deviation under H0 is true .
So bigger is more significant .
But You should listen to Paige's advice . Also Check Goodness of Fitness test .
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Would the following be reasonable candidates for "Goodness of Fit"? I see they are provided through Proc Mixed, which I was using.
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Yes. That is right way to compare two model .