Tools for Quantitative Archaeology
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Tools for Quantitative Archaeology |
C14: Graphical Analysis of C14 Samples
C14 provides a graphical way to analyze collections of radiocarbon dates. Consider a single carbon date. For any given time interval, e.g. 450 to 500 BP, the probability that the true date of a sample is within the interval can be calculated from a normal distribution. For example, the probability that the true date is between 1 and two standard deviations from the mean date is about 0.14.
For this reason, it makes sense to treat each radiocarbon date not as a single point in time but as a normally distributed probability with a mean and standard deviation given by the lab. To look at several dates from the same provenience, for each interval we simply sum the probabilities associated with the dates. Thus, in each interval, we get total probability for that interval. In a sense, then, this total probability represents the number of "complete" dates for that time period. Thus, a total probability of 2.4 in an interval may derive from 6 different actual dates. The total associated with the complete set of dates is equal to the number of dates in the sample. C14 calculates and graphs these numbers and expresses them as percentages and cumulative percentages. Given some reasonable assumptions, a unimodal graph may be indicative of a single continuous occupation, while distinctly multimodal distributions may indicate gaps in the occupation, or at least gaps in the production of dated material.
In a single run, C14 will analyze up to 500 proveniences with a total of up to 1000 dates. In addition to the analysis of the single proveniences, C14 in two ways lumps together all samples from all proveniences and tabulates and graphs the results. In the first aggregation, the dates are aggregated as they are for the individual proveniences; each date is a probability that sums to 1.0. In the second aggregation, the samples from each provenience are standardized to sum to 1.0, so in the aggregated results each provenience counts as a distribution that sums to one. In many cases these final aggregations will not be meaningful, in which case they can be ignored.
PROGRAM OPERATION
Input C14 Data File {.ADF} ?
Enter the file name (or path name) of the Antana Format file that contains the C14 data. The program first reads two values, the number of samples, and the number of variables. The number of variables must be either 3 or 2. For each sample, the program reads either a label, a mean date and a standard deviation or just a mean date, and standard deviation.
The labels are used to group the samples. The labels may be strings of any length, however, only the first 8 characters are used. Because the file is free format, the labels must not include embedded blanks, commas, #'s or returns. The row label file may also be used to assign label (group identifiers, usually a provenience label) to samples. If a label is included both in the original data file and in a row label file, the latter label takes precedence.
The samples may be entered in any order. All dates are interpreted as radiocarbon years B.P., and only uncorrected dates should be used as calibrated dates are not normally distributed. All these values must be separated by blanks a comma or carriage returns. Strings contained between #'s are read as comments and are ignored (e.g. individual lab numbers may be included in #..#). The mean and standard deviation can be given in any reasonable numeric format.
Provenience Label File (NUL if None) {NUL} ?
Name of a file with one line per sample, that provides a provenience label for each sample. The first label is associated with the first sample, the second with the second, etc. The program will separately analyze each set of samples that have the same provenience label. Thus, the label file can be used to specify different kinds of aggregation of samples in the original data set. The labels lines may include any characters, however only the first string (up to 32 characters), from the first non-blank character up to the next blank, is used by the program to label the sample. For example, in the line "Site1 Lab No. 12345" the label would be "Site1". Note that because a blank will break the label string, the line "Site 1 Lab No. 12345" the label would be only "Site". Each line should have at least one non-blank character that will serve as the label, otherwise the program will read the label from the next line.
Listing File {xxxxxxxx.LST} ?
Enter the file name (or path name) of the file in which the program output is placed. To send the output directly to the printer enter PRN. To see it on the screen enter CON.
nn Samples, nn Sites
C14 Date Range: nnnn to nnnn
2 S.D. Range: nnnn to nnnn
The program reports that it has read the data and gives the range of mean dates. It also gives the earliest and latest date that is five standard deviations from a mean date. (The program does its calculations over this interval.)
Earliest Date Interval to Plot {nnnn} ?
Latest Date Interval to Plot {nnnn} ?
Time Increment {nnn} ?
The program now asks how you want the information displayed. You can specify the starting and ending points and the interval width for the calculations and the histogram.
Percent of Distribution w/i Occupation Span {75} ?
The program will indicate the median of the date distributions and a percentile interval around the median. This prompt asks what fraction of all probabilistic dates should be included in the latter interval. This has no effect on the calculations, it affects the display only.
Print Individual Site Date Distributions {Y} ?
n: provenience label
The program asks if you want the individual provenience date distributions listed. Then, as it progresses through the proveniences it lists the sequential provenience number and the provenience label that it is processing in order to give you something to watch.
Print Unweighted Aggregate Data Distribution {Y} ?
Print Site-weighted Aggregate Date Distribution {Y} ?
The program then asks whether or not you want the aggregate distribution and the site-weighted aggregate distribution listed.
C14 Program End
Program End reports the normal end of the program. Note that the program does a fair amount of computation and may take a while to run.
SAMPLE RUN
Input C14 Data File {.DAT} ?
Read Data
Input Complete
Listing File {C14.LST} ?
24 Samples, 3 Sites
C14 Date Range: -1830 to -480
5 S.D. Range: -2215 to 1025
Earliest Date Interval to Plot {-2215} ?
Latest Date Interval to Plot {1025} ?
Time Increment {160} ?
Percent of Distribution w/i Occupation Span {75} ?
Print Individual Site Date Distributions {Y} ?
Print Unweighted Aggregate Data Distribution {Y} ?
Print Site-weighted Aggregate Date Distribution {Y} ?
C14 Program End
SAMPLE INPUT
94 #Samples# 3 #Variables# # Woodland Period C14 Data from:# # Braun, D.P. 1985 Absolute Seriation: A Time-series Approach. In C. Carr# # For Concordance in Archaeological Analysis. Westport Publishers# 1 1400 70 1 1530 70 2 1800 70 2 1810 70 2 1840 75 2 1880 70 2 1970 70 2 2000 70 2 2590 70 3 1240 70 3 1250 70 4 1050 75 4 1110 75 4 1630 80 4 1700 70 4 1780 75 4 1805 95 4 1830 50 ...
SAMPLE OUTPUT (PARTIAL)
In the output the percentages (not the counts) are plotted with *'s. For ease of interpretation, the date labels the middle of the interval plotted, the cumulative percentage is the cumulate percentage at the end of the interval. If all *'s will not fit on a standard page then an > is printed at the right margin. The Percent interval is denoted with >'s next to the histogram axis and the median date count is indicate by a - next to the histogram axis. Negative dates are in the future.
C14: Aggregation of C14 Samples - Keith W. Kintigh Earliest Date -2750 Latest Date -650 Time Increment 100 Percent 75.00 Aggregated Samples - All Sites - 94 Samples Middle Rel to Date Pct of Cum% of Date AD1950 Count Dates Dates 2700 -750 0.63 0.67 1.03 |* 2600 -650 1.42 1.52 2.54 |** 2500 -550 1.83 1.94 4.49 |** 2400 -450 1.33 1.42 5.90 |* 2300 -350 1.67 1.78 7.69 |** 2200 -250 3.24 3.45 11.14 |*** 2100 -150 5.43 5.77 16.91 >|****** 2000 -50 8.35 8.88 25.79 |********* 1900 50 10.86 11.56 37.35 |************ 1800 150 10.83 11.52 48.87 |************ 1700 250 8.04 8.55 57.42 -|********* 1600 350 5.79 6.15 63.57 |****** 1500 450 5.56 5.92 69.49 |****** 1400 550 6.15 6.54 76.03 |******* 1300 650 6.24 6.64 82.67 |******* 1200 750 6.49 6.91 89.58 >|******* 1100 850 5.68 6.04 95.62 |****** 1000 950 2.84 3.02 98.64 |*** 900 1050 0.83 0.88 99.52 |* 800 1150 0.27 0.29 99.81 | 700 1250 0.10 0.11 99.92 | C14 Program End
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Page Last Updated - 08-Dec-2007