When to apply confidence intervals (RE Norm MacLeod)

[marshall@xxxxxx (Charles Marshall)]

Applying Strauss and Sadler (1989) and Marshall (1994) type confidence
intervals to core, or other "discretely" collected stratigraphic data.

In my 1994 paper (following Springer and Lilje, 1988) I state that
confidence intervals can be safely applied in any situation (including core
data) where the mean gap size and standard deviation in gap size are
essentially equal.  Obviously if a section were sampled every 20 cm, and if
a taxon were found in every sample, the standard deviation in the gap size
would be zero, and the Strauss and Sadler and/or Marshall (1994) approach
should not be applied.  This test is crude, but it will at least give you
an idea of where you stand.

There is a simpler rule of thumb for when to apply these confidence
intervals:  let us suppose you have sampled your stratigraphic range at
some regular interval.  The question you have to ask yourself is:  if you
were to re-sample at a smaller interval (say, at half the original
interval) would the number of fossil horizons recorded go up appreciably.
If the answer is NO, then go ahead and apply the Strauss and Sadler or
Marshall confidence intervals.  If the answer is YES, then you should NOT
apply the confidence intervals, or if you do, you should recognize that
they will be much too big (which may be fine if you have set up you null
hypothesis in such a way that you do not increase the chance of rejecting
it if the confidence intervals are too big).  Norm may be quite right that
many stratigraphic ranges based on core data may meet this test.  Note
though, that for a taxon with a "gappy" record, if the number of fossil
horizons goes up with a finer sampling interval, then the confidence
intervals should not be applied, despite the fact that the range is
"gappy".   You should not use as you rule-of-thumb that any range with gaps
in it is analyzable with the Strauss and Sadler or Marshall approaches
(Caveat:  it may be that you can, but this must be demonstrated - I am
currently working a method that does this).

With regards the difficulties in converting rock thicknesses to time, this
is an important problem.  However, the Marshall (1994) approach does NOT
make the assumption that sedimentation rates are constant or uniform
(unlike Strauss and Sadler), as long as one is willing to have one's
confidence intervals expressed in terms of rock thickness and not time
(which is better than nothing, but not ideal ...).  BUT the Marshall
approach (along with Strauss and Sadler) does make the assumption that
there is no secular trend in sedimentation rate etc. on the scale length of
the entire observed stratigraphic range.

Charles Marshall
Earth and Space Sciences
UCLA