Frank Bayham & Don Morris have made an interesting adaptational argument concerning the occupation, particularly the archaic occupation, of the Picacho area. Roughly speaking, they suggest that the area is only occupied during periods of thermal maxima, that is, relatively warm periods, as indicated by oxygen isotope analysis.
Bayham and Morris have C14 dates from about 7000BP to the present, and argue that the culturally associated C14 dates indicate that occupation of the area is restricted to the periods from 5000 to 3600BP, 2900 to 1700BP, 1400 to 750BP, and 600 to 400BP. These episodes are are argued to correspond reasonably well with the thermal maxima at (7000BP,) 4000BP, 2000BP, 1000BP, and 500BP. However, at the Southwest Symposium last year, Cynthia Irwin-Williams rejected their argument, suggesting that this was basically a fortuitous set of radiocarbon dates.
Your job, whether or not you choose to accept it, is to evaluate the validity of Cynthia Irwin-Williams claim. While I am open to other approaches, I have an idea of how to proceed that I believe is within your programming reach.
Generally, assess the likelihood that 19 radiocarbon dates chosen at random from the period 7000BP to the present would be restricted to Bayham and Morris' 4 episodes. Write a program that will select repeated sets of 19 dates with mean ages randomly distributed between 0 and 7000. Associate with each date in each set a standard deviation chosen (with replacement) from the 19 standard deviations that the investigators happened to obtain. Then, for each set of 19 dates count the number of dates that are inconsistent with the hypothesized periods of occupation using two criteria: dates that have a mean age during an episodes with no supposed occupation and the number of dates whose 1 standard deviation ranges overlap a supposed vacant period. (For now ignore the significant calibration problems and assume all ages are in radiocarbon years BP.)
Select a large number, say 1000, samples of 19 dates and tabulate the distribution of the results for the two criteria, i.e., the number of sets of 19 with no mean date errors versus the number with mean date errors, and the number of sets of dates that have 1, 2, 3 ... dates overlapping the vacant intervals. Do a similar test, restricting the interval to the period 5000BP to the present. Repeat the test for both intervals (7000 and 5000BP to the present) using against occupation periods defined solely on the basis of the midpoints between thermal maxima and minima: 4750 to 3500, 2500 to 1750, 1250 to 800, and 550 to 400. Compare the simulated results against the degree of fit of the actual dates to the intervals. Try to obtain a probabilitic assessment of the likelihood of a fortuitous outcome as good or better than Bayham and Morris' actual data.
You will want to make your program general enough that you can solve other problems of this type. Thus, you may wish to read in the set of (up to 50) standand deviations and (up to 50) occupation periods. You will definitely need to use arrays. Please turn in a floppy disk, labeled with your name, that has written on it your program. Identify on the label the program names (in case there is are additional programs on the disk).
Turn in a brief (2 p max) written statement presenting your interpretation of the analysis and your conclusions vis a vis Irwin-Williams' argument. Include a printed listing of the program and printed output for the 4 cases.
For reference:
Thermal maxima occurred at about: 7000BP, 4000BP, 2000BP, 1000BP, and 500BP.
Minima occurred at about: 5500BP, 3000BP, 1500Bp, 600BP, and 300BP.
C14 Dates (from Bayham et al 1986: Appendix 1)
Dates with cultural associations (mean std):
4850 100, 4570 90, 3920 290, 4300 310, 4290 330, 4000 220, 4880 85, 4350 90, 4110 90, 2630 220, 2220 110, 2040 150, 1840 150, 1260 90, 1050 100, 870 50, 830 50, 770 60, 430 60
Dates with no cultural association:
7000 100 nc, 4560 130 nc , 3330 140 nc, 2830 250 nc, 200 190 nc,
Bayham, Frank, Donald H. Morris, and Steven Shackley
1986 Prehistoric Hunter-gatherers of South Central Arizona: The Picacho Reservoir Archaic Project. Arizona State University Anthropological Field Studies 13.