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Just as a footnote to the interesting topic that Ruth has raised here, one source of observer error that technology has all but eliminated is inter-observer bias in reading the vernier scale on calipers.  Back in the mists of time, I did a little informal investigation, based on the premise that in a sufficiently large dataset of measurements taken to 0.1mm, the integers 0 through 9 after the decimal point ought to occur with equal frequency.  But they don't.  Some colleagues show a high frequency of 0 with a low frequency of 9 and 1, whilst others show a high frequency of 5, but low 4 and 6.  Still others showed the inverse of one or other of those distributions.  In other words, different individuals were more or less likely to coax borderline vernier readings towards whole or half-millimetres.  Two datasets that I had recorded about 10 years apart showed the same bias: clearly hard-wired behaviour! 
 
Terry O'Connor
-----Original Message-----
From: Analysis of animal remains from archaeological sites [mailto:[log in to unmask]] On Behalf Of Ruth F. Carden, Zoology
Sent: 28 July 2003 17:29
To: [log in to unmask]
Subject: [ZOOARCH] re measurement error advice - thanks

Dear all

First off I wish to thank those who replied to my plea. Have found the references interesting.

Secondly, interestingly enough even though this topic of measurement error (precision and accuracy of measurements) is very topical in the world of anthropology, it largely is either ignored or presumed to be low in the area of systematic zoology and morphometrics in general. This I found most suprising as the degree of measurement error has such influence on subsequent univariate and multivariate analyses. Such that the resulting intra or inter- variation obtained in morphometrics may in fact be due to the spurious effect of measurement error rather than the actual difference or natural variation.

In most cases, the error is persumed to be low, but nevertheless it should be checked, even if the measurer is experienced in taking the measurements. In my own case, I decided on the following method after much trawling through the literature, perhaps it will be of use for others.....? Obviously it is not the only way do calculate the measurement error, rather just one thrown into the soup of morphometrics for us to digest!

I have been measuring various postcranial cervid bones for the last 5 years, and had to check if my measurement values were accurate and precise on repeated measures.
Following Lynch, J. M. and O'Sullivan, W. M. (1993), method of checking for measurement error - they used the following equation (it uses the within-specimen cofficients of variation calculated for each measurement, afterwhich these coefficients are corrected for small sample size (Haldane, J.B.S. 1955 cited in Lynch & O'Sullivan 1993):

ME% = 100 [(1+1/4n)SD/mean)]
where n  is the sample size (of replicates)
SD is the standard deviation
mean is the mean of the replicates per individual. 

Lynch, J. M. and O'Sullivan, W. M. (1993). Cranial form and sexual dimorphism in the Irish otter Lutra lutra L.  Biology and Environment: Proceedings of the Royal Irish Academy 93B: 97-105.

Haldane, J.B.S. (1955). The measurement of variation. Evolution 9:484.


Thanks again to those who responded to my earlier plea, much appreciated.

Hope this email finds ye all well
Kind regards & Slainte
Ruth



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Ruth F. Carden B.Sc.
Mammal Research Group
Zoology Department
National University of Ireland, Dublin
Belfield, Dublin 4
Ireland
e-mail: [log in to unmask]
Tel: (+)353-1-7162261 (note new number)
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