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Topic: comparison between two value in a sample, please help...
Replies: 3   Last Post: Nov 18, 2012 10:02 AM

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Jinsong Zhao

Posts: 22
Registered: 11/27/10
Re: comparison between two value in a sample, please help...
Posted: Nov 18, 2012 10:02 AM
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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 2012-08-18 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 MS-residual 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 "Mean-square-residual" is the square of
>> 42, with 10 d.f. Take the Mean square for Regression from
>> the 5-point regression and divide it by *this* residual,
>> instead of the computed residual, to get the safe F-test.

>
> 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 42-squared, but is 42-squared, divided
> by 3.
>


Pooled SD:

sqrt(sum((33.69357 27.84428 33.20421 57.29368 51.11501)^2)*2/10) = 42.20993

i.e., Mean-square-residual = 42.20993^2/3 = 593.8927

The Analysis of Variance Table for the 5-point 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 F-test 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 so-called 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



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