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Re: comparison between two value in a sample, please help...
Posted:
Nov 18, 2012 10:02 AM


Thank you very much for your kindly help, and sorry for no feedback for such long time. I have some questions about this problem. If possible, please give me help. Thanks in advance.
In the following, I will do the calculation according to your comments. Please tell me whether I am wrong or not.
On 20120818 9:39, Rich Ulrich wrote: > On Fri, 17 Aug 2012 01:49:39 0400, Rich Ulrich > <rich.ulrich@comcast.net> wrote: > > [snip, a bunch] >> >> I *think* what follows is a safe, conservative procedure  >> The minimum, proper fitted equation will show no less error >> than the measurement error. For that, the pooled SD is > > Keep in mind that the MSresidual is an estimate of the variance > (which is the square of the standard deviation) of the residual. > > When I was learning to use regression, it helped me when > I realized that fact. Then I started making a point of noticing that > variance, and taking the square root ... just to make sure that > I was still analyzing the same set that I thought I was, and that > nothing was going strange. > > >> about 42, or the "Meansquareresidual" is the square of >> 42, with 10 d.f. Take the Mean square for Regression from >> the 5point regression and divide it by *this* residual, >> instead of the computed residual, to get the safe Ftest. > > Oops! slligh correction  For the 5 point regression, each > point is the average of three measures. The SD of the *3* > taken separately is 42; the SD of the average is, naturally, > the raw SD divided by the square root of N, or sqrt(3). > Or  the MS is not 42squared, but is 42squared, divided > by 3. >
Pooled SD:
sqrt(sum((33.69357 27.84428 33.20421 57.29368 51.11501)^2)*2/10) = 42.20993
i.e., Meansquareresidual = 42.20993^2/3 = 593.8927
The Analysis of Variance Table for the 5point regression is:
Response: y Df Sum Sq Mean Sq F value Pr(>F) x 1 39777 39777 15.48 0.02924 * Residuals 3 7709 2570
So, the Mean square for Regression is 39777. Then the safe Ftest is:
F_value = 39777/593.8927 = 66.97675 on 1 and 3 DF.
The corresponding P value is 0.003816985.
My question is what's the meaning of this P value? Does it mean that the regression is significant? If so, does it mean that the value of N in 1952 differs with that in 1998?
If the P value large that 0.05 (and alpha is set to 0.05), then how to interpret the result?
What I hope to know is whether the value of N in two different year is significant.
>> >> The ratio of the two socalled Residual terms can be used as >> a test of whether the regression is "over fitted". >>
Would you like to tell me how to form the ratio? 2570/593.827 on 3 and 3 DF?
> Still useful, but you do use the corrected value. >
Thanks again for your kindly help.
Regards, Jinsong



