Rock Thickness & Confidence Intervals

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Charles is going to have to straighten me (and perhaps others) out on the
expression of confidence intervals "in terms of rock thickness."  The only
way this makes any sense to me is if rock thickness within a species'
observed range bears some sort of quantifiable relationship to rock
thickness outside of that observed range.  For example, if a hiatus or a
condensed interval is present within the observed species's range (or just
above its last occurrence or below its first occurrence), then a centimeter
gap between fossil occurrences doesn't mean the same thing throughout the
interval in which you are interested.  Unless we can demonstrate that we
are looking at the same things in the gap size distribution and the
interval of sediment accumulation above the last appearance (and/or below
the first appearance) I don't see why we should expect that the gap size
distribution would tell us anything about what might be true outside the
universe of our measurements.  We know that time is, for our purposes,
linear and so if we recast our stratigraphic distances as temporal
intervals we have a solid foundation upon which to build our inferences.
But knowing what we know about sequence stratigraphy and expected levels of
continuity in different depositional settings, it seems to me that assuming
1 cm of sediment accumulation is an equivalent quantity throughout any
stratigraphic sequence passes way beyond the limit of what I would call
justifiable.

Are statistical constructs based on unrealistic assumptions better than
nothing?  I'm not so sure.  I'm one of those apparently odd individuals who
finds no dishonor in saying "I don't know" when that is in fact the truth.
To some extent it does depend on the way you cast your null hypothesis.
Certainly a critical commentator would have little trouble dismissing any
interpretations based on confidence intervals that make unrealistic
assumptions about the data from which they are derived.  At the very least
you should admit to the assumptions you are making and leave it to the
reader to determine whether or not interpretations derived from your
calculations are reasonable.  My concern is that such discussions are not
being required and that the exercise of quantification will take precedence
over the qualifications imposed on that exercise by the nature of the data.
If we allow that situation to develop we will only be making our jobs more
difficult than they already are.  To be perfectly candid, though I should
also admit that I am more than willing to promote any argument that will
emphasize the need for detailed stratigraphic analyses.  Stratigraphy has
been in trouble for quite some time within the science of geology and as
paleontologists I think we should take advantage of every opportunity to
stress its importance as well as its complexity.

Norm MacLeod


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Norman MacLeod
Senior Research Fellow
N.MacLeod@nhm.ac.uk (Internet)
N.MacLeod@uk.ac.nhm (Janet)

Address: Dept. of Palaeontology, The Natural History Museum,
                     Cromwell Road, London, SW7 5BD

Office Phone: 071-938-9006
Dept. FAX:  071-938-9277
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