Archaeological Laboratory

Measurement Errors and Parameter Estimates


See Correction on Question 8 (sorry, it says "3", but it's 8. See FAQ)

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 Date Labwork: 20 September 2006
  Due date: 11 October 2006

Note the Correction Below!

 Introduction and Purpose In this lab, you will make some simple measurements on lithic flakes and rim sherds, and use the data you and the other students collect to assess the measurement errors. The purpose is to familiarize you with most of the basic measuring devices we use in the course, to practice drawing graphs, and also to get you thinking about sources of error in measurement. You will be using real artifacts, so make sure you handle them properly. Note that this is the lab that students in ARH 312 should be doing, not the more generic one elsewhere on the web site.
Directions for the Lab Activity  

There will be a series of stations arranged around the lab. At each station, there will be an artifact (lithic, sherd, etc.) and you will take the measurements requested with the instrument provided, and record your measurements on the recording form. In each case, think about any sources of error that you would expect to affect your measurement. Try to estimate the likely magnitude of these errors (put this estimate on the form too), and pay attention to your measurement units.

Try to do at least one of the stations in each group of stations.

 Equipment     You will use:
  • Rulers
  • Calipers
  • Goniometers
  • Electronic balance
  • Diameter charts
  • Measuring box
  • Measuring grid
  • Munsell Colour Chart
  • Gloves and table pad
  • Data Recording Form
 Stations 1-9    (pick one or two of these stations, including, if possible, 1, 2, or 3)

For all the sherds at one station (or two if you can), measure the maximum length in mm and the maximum width perpendicular to length, also in mm, using calipers. Keep in mind what difficulties you have doing this. Think about how you decided what constituted the "length" and "width" and how they might differ from those in the measuring box (station 20).

For the rim sherds only, measure the a) rim diameter (cm), and b) preserved circumference (%), of each potsherd, using a diameter chart.

First, you should learn how to stance a rim sherd. To do this, hold a sherd upside-down with its lip touching a hard surface, such as a table top. Gently rock the sherd forward and backward along the direction of its thickness. Note that when you rock it one way, the rim makes something like an arch, with the lip touching the table only in two places, at either end. When you rock it the other way, the lip touches the table at only one point, in the middle. Only when the sherd is ìat stanceî does the lip touch the table pretty much all along its length.

Now, stance each sherd on the diameter chart in such a way that one end of the rim touches the %-line, or y-axis, and the curvature of the rim follows one of the concentric arcs on the chart. When you get a good match to one of these arcs, you can read the diameter of the pot from which the rim sherd came on either the x-axis or y-axis. Note that your certainty about which arc makes the best fit varies from sherd to sherd. This is the error, or precision, of your measurement. Estimate the size of this error. For example, if all three of the arcs for 18, 19 and 20 cm seem to fit pretty well, pick the middle value of 19 as your best fit but show an error estimate of ± 1 cm. If on the other hand you are sure the diameter is not 18 or 20 cm, but very close to 19 cm, then show your error estimate as ± 0.5 cm.

Next, notice the radiating lines on the chart. These are marked in such a way as to allow you to estimate the proportion of the rim's circumference that each sherd represents. Making sure that your sherd is still at stance, lined up properly with the arc that most closely fits its curvature, and with one end of the lip touching the y-axis, read off the value of the radial line that comes closest to the other end of the lip. Write down this value for each sherd on the recording form, as well as your estimate of the error on the measure (e.g., one sherd might measure 7.5 ± 2 % of the circumference, or a proportion of 0.075 ± 0.02).

  Stations 1-3    Here ALSO remeasure the 10 sherds' maximum length and maximum perpendicular width in mm, but this time using a ruler instead of calipers. Note differences in both precision and the practical difficulty of making measurements.
   Station 10, 11, 12, or 13   At this station, you will measure the a) length, and b) width perpendicular to length of each blade or flake with a pair of calipers. Think about how you decided what constituted the "length" and "width."
 Station 14    At this station, you will measure the edge angle of a retouched flake with a goniometer, a kind of protractor. By edge angle, we mean measuring it perpendicular to the edge (in other words, we want to know if the edge is sharp and acute, or obtuse). Think about difficulties you had making this measurement consistently. How did you select a location along the edge to take the measurement?  How would you expect edge angle measurements to differ both between different observers and with one observer measuring it repeatedly?
Station 15    Calibrate the electronic balance using the 300 g weight provided. Measure the mass (in grams) of the pottery sherd with the balance.
Station 16   Calibrate the electronic balance using the 300 g weight provided. Measure the mass (in grams) of the flake with the balance.
 Stations 17-19   At one of these stations, you will measure the colour of the surface of a potsherd using a Munsell Soil Colour Chart.  Record the Hue, Value, and Chroma on your data sheet.  Estimate the range of error you think you might make on each of these three attributes separately.
 Station 20   Here you will measure a) the vertical height of two potsherds at stance (i.e., perpendicular to the rim line), and b) the max. width of the sherds perpendicular to vertical height with a measuring box ( in millimetres). Think about how this width measurement differs from both the % perserved circumference and the maximum width perpendicular to maximum length of sherds (stations 2-14).
 Station 21   Count the number of incised lines over a 50mm length of the rim sherd.
 Station 22   Measure the height of the "collar" on the rim sherd in mm, using calipers. Note that the "collar" is the thickened section close to the lip of the pot.
 Station 23   Measure the interior diameter of the tabocco pipe's bowl using the calipers (note that for interior measures you use the opposite side of the calipers), in mm.

The point of this lab will be to assess what kinds of measurements, or what kinds of measuring tools, were most prone to error, and why, and to see just how much intra- and inter-observer error there can be even for simple measurements. Your lab report should be brief and to the point (max. 3 pages plus graphs).  This report should be in the form of a proper lab; briefly explain the problem, your results, and how you arrived at them. Then give your conclusions (generally by answering our questions).

After we are able to compile your measurements, we will post all the students' measurements for certain stations on the web site here. You will use this information plus your own observations to answer the following questions in the lab.

Note that you will get a chance to practice doing the graphs in the lab session of 28 September, so you would be wise to be prepared by then to answer questions that involve graphing. We WILL take marks off for improperly drawn or labelled graphs.

Note: After you do the lab, I will post the data for comparing measurements. If you have a problem with overlapping text on the table, try resizing your window, selecting a smaller font size, or copy and paste the data into a word processor or excel table.


The following are questions you should address in the "conclusions" of your lab.

  1. Which measurements did you think were the least reliable (least precise, or with the most inter-observer error)?  Why do you think that is? (Answer in two or three sentences only). (2 points)
  2. For the terracotta sherds, which you measured twice, compare the two sets of measurements to test for reliability in measurement. Use an appropriate graph to do this (ignore sherds that only got measured once). Identify measurements that have suspicious results (what do you call these?) (3 points)
  3. Examine the edge angles (station 14), keeping in mind that these are all allegedlymeasurements of the same thing. Given the amount of variation in student measurements in the table, and keeping in mind the concept of uncertainty, pick two of the student's measurements from the table that you think have too many digits and round them off to an appropriate number of significant digits.  Say why you chose the number of significant digits you did and MAKE SURE that you tell us what the original measurement was as well as your rounded off version. Are the stated estimates of error (where there are any in the table), very realistic? (2 points)
  4. For the edge angles (station 14) how did you select a location along the edge to take the measurement?  Plot a histogram of the different measurements of the same edge angle. What does it show? How would you account for the differences in measurement that the graph portrays?  Draw another histogram showing the same data but with a smaller or larger interval.  how does changing the interval affect the shape of the histogram?  (6 points)
  5. For Stations 17-18, where you recorded the colour of sherds, assume that Hue, Value, and Chroma are on ordinal scales and propose the best estimates of each sherd's true colour.  What measure of central tendency is appropriate here?  How would you express uncertainty around this estimate? (2 points)

Tip: Pay attention to the amount of variability in the class's measurements and ask yourself how reliable the measures of the three colour dimensions were. Decide what is the most likely "true" measure of each and on what basis. Also decide how you would indicate your uncertainty about that measure. Are there any outliers among the data? If so, what should you do with them?

  1. For Stations 1-13, and 20, how do the definitions of "width" differ given the way you measured width in each case?  Also, how does "height" in station 20 differ from both width and length in the other cases? HINT: Use a diagram in your answer if you find it helpful. (2 points)
  2. Pay attention to the amount of variability in the class's measurements, and to how many significant digits some people claimed, and ask yourself how some of the outliers may have occurred. Suggest what the most likely height and width (in mm) is, to the correct number of significant digits (2 points). Note: It looks suspiciously as though some of you copied one another's measurements instead of making your own. What effect does this have on your statistics? What should you do about the repeated measurements? (Don't do this in future!). Also, many of you did not follow instructions properly. Many measured in cm when you were asked to measure in mm. I did the conversion when it was obvious. Others reversed the measurements for sherds 1 and 2, which I corrected, but note that this is an easy way to result in data-entry errors. BE CAREFUL.
  3. Using the data on 4 rim sherds, from stations 1-3, calculate the standard deviations on the diameter measurements (i.e., how consistent are the results among students - you will have ten standard deviations, one for each selected sherd) and average EVE for each sherd. Draw a scatterplot of average preserved circumference (EVE, x-axis) against the standard deviation in the measurements of diameter for all ten sherds (y-axis).  There will be 10 points on the scatterplot. Is there any relationship between the repeatability of the measurements of diameter and the preserved circumference?  If so, why might that be? (6 points)

Ginaden, D., and Holdaway, S., 2000. Understanding observer variation when recording stone artifacts. American Antiquity 65: 738-747. (This is a really good article for you to look at if you want to do a really serious job on your lab!).

Nance, J., 1987, Reliability, validity, and quantitative methods in archaeology. In Quantitative Research in Archaeology, Progress and Prospects, edited by M. S. Aldenderfer, pp. 244-93. Sage Publications: Newbury Park, CA.