At 19:05 31/03/05 +0100, Ted Harding wrote (in part):
> > Maybe someone can help me understand all this?
>I think you already do, John! Clearly, the results for
>a whole population are simply a statement of fact, with
>no sampling to inject the randomness required to underlie
>probabilistic statements of uncertainty, just as you state
>in you para 1 above.
Ah, I'm glad I'm not alone!
>Again, you're right in para 4 about the theoretical possibility
>of using Time Series methods if you have observed the whole
>population at several time points. But these can only work
>if there is a structural model for the time series with
>respect to which deviations, to be assigned to "random noise",
>can be derived. The thorny question then is: on what basis
>can any specific generic model (e.g. trend + autoregressive)
>be assumed? Where is the evidence for it?
Having now looked at the data, I'm relatively surprised by how 'smooth' the
curve is, at least until fairly recent times, and I imagine that a standard
empirical stochastic model would probably fit pretty well. Unless it is
just a 'quirk' which will subsequently be reversed, the apparent flattening
of the curve in recent years might not fit such a model so well. I would
suspect that any attempt at 'deterministic' modelling would be all but
impossible, because of the existence of so many, varied and usually
unquantifiable (perhaps even undetectable) factors that will be at
work. Maybe the multitude of factors is actually the saving grace, with
their overall effect being to 'even outt' what would otherwise be anything
but a 'smooth curve'!
>Reading over this, I seem to be saying the same as you!
Yes, I think that is largely true.
>Since Alison says there is a confidence interval of (0.5,0.9)
>for the 0.7, this must have been calculated according to
>some procedure for which assumptions can be identified,
>so maybe I should now go and read up what is said about this
>(if anything) in Alison's reference for the bulletin in her
>first mail.
I've now looked, and the Bulletin itself appears to do nothing other than
present the actual figures and discuss them - with no attempt at any
estimation or inference that I've noticed. As she has now explained, it
seems that it was Alison herself who calculated the confidence interval. I
thought from what she wrote that I understood what she was describing, but
the fact that I arrived at the same answer by using what I thought was a
'more appropriate' (albeit very simplistic) approach does make me wonder -
maybe Alison had done the same as me!
Just to be clear about the two 'methods' ..... I described in a recent post
what 'my' approach was (trying to get a handle on year-to-year random
variation). What I had assumed Alison was describing was simply to
determine the standard error of a comparison between SAMPLES which had
proportions of CSs of 22.0% (N approx 394,560) and 22.7% (N approx 431,925)
(those N's being 72% of the total number of deliveries in the two years),
which by my reckoning gives a SE for the difference of 0.092%, hence a 95%
CI of approx. +/-0.18 ... i.e. (0.52,0.88) for the 0.7% difference. If
that is, indeed, what she did, then it is obviously a pure co-incidence
that she got virtually the same answer as me. Had it transpired that
year-to-year variability was very much greater than it actually is, then
'my' (I would say 'more appropriate') CI would have become very much wider,
whereas Alison's would have obviously remained unaltered, since her
calculation (if she did as I've described) is obviously oblivious to
year-to-year variation.
Kind Regards,
John
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