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Re: statistical comparison of parameters from two applications of NonlinearModelFit

• To: mathgroup at smc.vnet.net
• Subject: [mg116231] Re: statistical comparison of parameters from two applications of NonlinearModelFit
• From: dantimatter <google at dantimatter.com>
• Date: Tue, 8 Feb 2011 05:03:31 -0500 (EST)
• References: <ii8s8s$2o1$1@smc.vnet.net> <iibdvk$nq3$1@smc.vnet.net>

Hi All,
Thanks for the great responses.  :)

> Now we're ready to talk about detecting a difference between b1 and
> b2. The formal test of the hypothesis that there is no difference
> is a student t: (b1 - b2)/Sqrt[ASE[b1]^2 + ASE[b2]^2] = -.170 .
> The degrees of freedom are data dependent, but in your case the t
> is so small that it will never be significant, no matter what the
> degrees of freedom are.
>
> To achieve significance, the t would have to be at least 12 times
> its current value, which means you would need 144 times as many
> sample points as you currently have. (Note: I've cut a lot of
> corners here. A proper analysis would be much messier but would
> lead to the same conclusion -- you need a whole lot more data,
> on the order of 200 times as much as you have shown us.)

Instead of increasing the number of data points (which I can't really
do at this point), couldn't I just say that in order for t to be "at
least 12 times its current value", b2 needs to be less than or equal
to some cutoff b2*?

Also, I've read somewhere that there are tests other than Student's T,
but I don't know if those are more or less appropriate for this
particular scenario.


> Finally, here's some code that should reproduce some of the
> NonlinearModelFit output:

Is there a reason why I shouldn't use NonlinearModelFit?

Thanks!