On Fri, 9 Mar 2001, Wei Xiao wrote:
> Suppose I went to 10 lakes. I want to measure the relation with water
> temperature (WT) and air temperature (AT). So I can do a regression
> with these 10 points like this:
> | *
> | * AT
> | *
> |__*__________________
> WT
>
> However, to be sure, I took 3 AT's and 3 WT's at each lake. Now any
> particular AT is not correlated with WT.
How can that be? Did you not take each AT and WT at the same time and
in the same place? (Not necessarily at the same time, or in the same
place, as the other pairs of (WT,AT); in fact, preferably the
measurements should have been made at different (time, place) if what
you were trying to do was to get a measure of the variability in WT
and AT at each lake.)
If you claim they're not correlated because all six values were taken
more or less simultaneously at the same place, and they were not taken
in (WT,AT) pairs, then the three WT values are not independent
observations, nor are the three AT values, but within each of THESE
triplets the values are correlated in an unknown, and possibly
unknowable, way. Then all you can do is take the easy way out:
take the average of the three WT values as the WT for that lake,
and similarly for the three AT values.
> Instead, they are kind of have error in both X and Y axis.
This remark is not helpful. If you only had one value of (WT,AT) at
each lake, those values would surely have measurement error in both
measurements.
> Can somebody show me a better way to analyze this?
> I prefer talking in SAS or SAS macro.
Sorry, not one of my languages.
> Here is hypotheticall data sheet.
> Lake, WT, AT
> Lake1 10 15
> Lake1 11 14
> Lake1 12 13
> ...
>
> Notice there is no relation between WT and AT reading.
> I can record this way too:
> Lake, WT, AT
> Lake1 10 13
> Lake1 11 14
> Lake1 12 15
> ...
It is not at all clear why you can legitimately shuffle these values
around with respect to each other: unless either (a) all 6 values are
recorded simultaneously in the same place; or (b) you took all 6
values at 6 different times and places, so that there really is no
empirical connection between any particular AT and any particular WT.
Either case would seem to me to represent faulty experimental
procedure... to put it politely.
-- DFB.
----------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 (603) 535-2597
184 Nashua Road, Bedford, NH 03110 (603) 471-7128
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