Precision and Significant Figures
  May 04, 2006 10:07 PDT 
I thought this would be a good time to bring up precision and significant figures. I am looking at the number of significant figures being reported for the heights in some of the recent posts and wondering if that level of precision can really be justified (i.e. two decimal places). My understanding is that the resulting measurement should be reported to the level of precision of the least precise instrument and that the last digit is always assumed to be an estimation. The laser may report to the nearest 0.5 feet (digital) but most clinometers have an analog face graded into whole degrees. This means that we can report the angle to the nearest 0.1 (since we estimate the tenth position) and therefore the tree heights should be reported to the nearest 0.1 (one digit in doubt).
This is a website that nicely summarizes significant figures, precision. Accuracy, and rounding.

In any event, we should probably standardize the level of precision we should report our measurements to. I'd like to see what other ENTS have to say.
RE: Precision and Significant Figures
  May 04, 2006 10:43 PDT 
Hi Gary,

yes, I've been meaning to bring this up for a long time too. I haven't really examined it much yet, but I highly suspect that
the number of sig figs is way overdone with many of the Ents measurements. I've been meaning to get around to making
a spreadsheet where you enter your estimate for uncertainty in reading clinometer and laser finder uncertainty table and all
and then have plug everything into the total error propagation formula for the tree height formula.

Re: Precision and Significant Figures   Edward Frank
  May 04, 2006 15:00 PDT 

Gary is right. Clearly reporting our measurements of heights to the nearest 1/100th of a foot is overkill. It does not represent a reasonable assessment of the accuracy of the measurement. What the correct number of significant figure would be depends on the assumptions made when stating the problem. I think Gary's outline is a reasonable one. The tree height can be measured to within a foot when using care and is enhanced taking multiple shots of the top from different points. Using the 1/10 digits as significant figures should be correct.

If someone wants to perform a more rigorous analysis of the question and report it to the group, I would be interested in seeing the results. Of course the assumptions about the measurement accuracy and precision made in the analysis would also need to be presented and discussed. I think a general model needs to be defined that could be applied to all of the height measurements being reported. A detailed stat analysis could be made of every measurement, but that would be so time consuming as to be counter productive.

Ed Frank
RE: Precision and Significant Figures   John Eichholz
  May 04, 2006 18:09 PDT 


You sure are right that the experimental evidence does not support 0.01
foot precision. I often have readings that vary by a few tenths of a
foot when I remeasure the same tip from spots a few feet apart. Similar
experience if I return to the same spot on a different day. The fewer
the readings, the greater the uncertainty is how it works, I believe.

A much more significant factor is whether we measure the same top. Tips
can vary by several feet even though they are visually adjacent.      
Because of this, my first measurement of a tree is hardly ever the
tallest. After taking readings at several points, though, the certainty
of the result being the tallest spot improves.

It is very similar to measuring several trees in a grove to find the
tallest. The more trees you measure, the more sure you can be to have
found the tallest.

In the end, it is my opinion that careful ENTS height measurements can
be reported with a precision of +/- 0.1 foot, with the assumption that
the accuracy is limited to +/-0.5 feet or so, and that the height could
be revised (usually upward) upon remeasurement.

John Eichholz

Re: Precision and Significant Figures   Don Bertolette
  May 04, 2006 20:49 PDT 

Gary/John/Bob/et al-
I've said it before without much response, but for another reason I agree
with John/Gary ---- I would suggest that a mature growing, living, respiring
deciduous tree, could vary as much as an inch to a half foot (0.1 foot to
0.5 foot) in response to temperature and relative humidity extremes. This
isn't to say that everyone shouldn't be honing their dendromorphological
RE: Precision and Significant Figures   Robert Leverett
  May 05, 2006 05:33 PDT 

Ed, Larry, Gary,

   You all are absolutely correct. Reporting measurements to the nearest
1/100th of a foot is, indeed, misleading. With the state of our
instruments, measurement accuracy is to +/- 0.5 feet on good days and
+/- 1.0 to +/- 1.5 feet on not so good days. On first time cracks, we
can easily be off +/- 3.0 feet. We only gain the higher level of
accuracy through repeated measurement and from different locations and
in different lighting conditions. The patterns we obtain for a tree can
be analyzed with formal statistics or we can apply just plain common
sense. I actually prefer the latter because there is no reason to
average in suspect readings just to have an average based on more
readings. Highly questionable readings can usually be identified and
rejected to boil the readings down to a set of equally probables. It is
a process. Always a process. Can you imagine trying to explain that to
American Forests?

   Our interpretation should always be that the 10ths place is always of
questionable accuracy. I quit reporting Rucker indices to hundredths
long ago because I realized that others would not understand that I well
knew the hundredths place was not significant. I'm certain Dale, Tom,
Will, undertand that every bit as much as I do. It has been fun to make
a game out of upping the Rucker index and reflecting it in our postings
to hundredths, but to communicate what we are doing better, you all are
correct. We should agree to express our height measurements to the
nearest tenth of a foot.     


RE: Precision and Significant Figures   Robert Leverett
  May 05, 2006 05:41 PDT 


Indeed you have made that suggestion. It was a potentially good
discussion thread. I, myself, didn't respond though because I didn't
have either confirming or refuting evidence, but I do believe you to be

Now, John Eichholz and I just have to figure out when each champion
tree in Mohawk exhales and take our measurements then.