On Thu, 13 Jul 2006, Michael Tobis wrote:
> I believe your calculations presume independent samples.
>
> On 7/13/06, Roger Coppock <[EMAIL PROTECTED]> wrote:
> > I do know that the probability
> > that the Earth's global mean surface temperature
> > is slowly rising is roughly 20 nines, or
> > 99.999999999999999999%. That is well above
> > 1%, and that clearly should be a policy concern.
OK, this has come up before, and Roger has resisted my argument about
autocorrelation affecting the sig levels. So, here is a simple example. First
the results: this is generating a random (and hence, "really" no trend) series
200 times, with a given level of autocorrelation "a", and finding out how many
of the series are assessed to have a stat sig trend. If all the stats are
working properly, then 10% should be ("falsely") judged to have a trend (since
I'm using 90% sig level). So:
a=0
wmc> .run indep
13.0000% were judged significant
wmc> .run indep
9.50000% were judged significant
wmc> .run indep
11.0000% were judged significant
a=0.5
wmc> .run indep
34.0000% were judged significant
wmc> .run indep
35.5000% were judged significant
wmc> .run indep
36.0000% were judged significant
a=0.75
wmc> .run indep
54.5000% were judged significant
wmc> .run indep
54.0000% were judged significant
wmc> .run indep
50.5000% were judged significant
(AR1 means that x_i+1 = x_i * a + e_i; e_i being random noise).
So: a=0 gets you 10% (close enough...); and we see that as a increases more and
more series are "falsely" judged to be sig. I'm sure this can be done
analytically too (james? michael?).
Code below:
;
; Pro to demonstrate how autocorrelation skews statistics of trend
;
n=200 ; Number of realisations
l=100 ; Length of each realisation
a=0.750 ; Autocorrelation
c=0
p=0.10 ; 0.10 = 90% (two-tailed) sig test
for i=0,n-1 do begin
; Generate an AR1 series - ie, autocorrelation of "a"
s=ar1(a,l)
; Regress the series, and decide if the trend is sig (1) or not (0)
r=reg_explain(/quiet,pp_regress(s,/arr),prob=p)
; Count those that are sig
c=c+r
endfor
; How many are judged sig? Should be 10% if all has gone well
print,c/float(n)*100,'% were judged significant'
end
William M Connolley | [EMAIL PROTECTED] | http://www.antarctica.ac.uk/met/wmc/
Climate Modeller, British Antarctic Survey | (01223) 221479
If I haven't seen further, it's because giants were standing on my shoulders
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