Rich Ulrich wrote:
> - Since you don't see the grievous problem with that, I will try to
> point to it, and recommend that you need more advice than you are apt
> to receive over the Net.
>
> When you approach a limit, such as 100%, it is wise to consider what
> you have as the DIFFERENCE, or 100%-X. "Consider" it. Sometimes it
> may not be important; a lot of times, it is. And when it is in terms
> of VARIANCE, it is always important.
>
> For 99%, the Error variance amounts to 1%; for 94%, the Error is 6
> times as large at 6%. When you have an F-test, the numerator has
> R-squared and DF, the denominator has (1-Rsquared) and its DF. The 1%
> or 6% is Denominator -- so for this 5 points, the F-test is 6 times as
> big.
>
...
>
> But you cannot legitimately compare a correlation
> "with Y" to another correlation "with square-root(Y)".
>
>
Rich,
Somehow I think your sticking on the wrong point in my question. My analysis IS
NOT INTENDED to compare the correlation with and without the square root transform.
Originally, everything was done with the transform. However, some people in my
field think that any transformation is just a "trick" to make the results seem more
important than they really are. I did it both ways to dispel the criticism that the
square root transform somehow biased my results. My point is that although in the
raw data I get X% of the variance explained and in the square root transformed data
I get (X +/- 5%), the CONCLUSION remained the same.
Here's the actual percentages from my study:
Amount of variance explained
Regression parameter Raw SQRT
A 55.0
% 51.5 %
B 20.4
% 23.5 %
C 24.6
% 25.0 %
Now it seems to me that this "trick" of the square root transform has not
artifically biased the variance in parameters A, B, or C such that my CONCLUSION
would be any different (that A contributes more than B or C). The original
complaint was that perhaps the 51.5 % was really too high of a value and was being
biased (or artifically inflated) by the transform. That is what I was disputing.
-Tony
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