🚀 go-pugleaf

A Climate modeller colleague asked the following:
I am planning to remove trend from some GCM results (CO2 levels).
I suspect this affects degrees of freedom for t-tests, F-tests, etc.
Can  anyone help please?
I plan to remove the trend without changing the mean.
I suspect not changing mean implies that only one df is lost.

So if original data are 
y[1], y[2], ... , y[i], ... , y[N]
where i represents year, so data are equally spaced in time.

Detrended value for year i is:
y[i] - r(y,i) * ( sd(y) / sd(i) ) * ( i - mean(i) )

where r(y,i) is correlation between y & i
r(y,i) = ( sum(i*y[i]) - mean(i) * mean(y) ) / ( sd(i) * sd(y) )

Since i is simply 1, 2, ... , N
by algebra:
mean(i) = ( N + 1 ) / 2
sd(i) = sqrt( ( N * N - 1 ) / 12 )

In my case N = 20 for both control (normal CO2) & double CO2 samples.
I plan to detrend both samples before comparing 
(1) means using t-test 
(2) variances using F-test.

What is the effect of this detrending on degrees of freedom for these tests?
Are these tests meaningful?

Len.Makin@mel.dit.csiro.au               | Senior Computer Scientist    |
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