DISPERSION DIAGRAMS: A NEW APPROACH TO THE DISPLAY OF CARBON-14 DATES

A statistical approach to the display of sets of ¹⁴C dates is suggested. All available dates of any particular culture are used to calculate the two quartiles and the median dates for it. The ‘dispersion’of the dates is then displayed as a bar showing the extreme dates, the quartiles and the median; thus neither individual dates nor their standard deviations are shown. This ‘dispersion diagram’saves much space when the dates of several cultures are to be displayed. The argument is developed that the inter-quartile range, which does not change very much when new dates become available and are added to the set, is a good index of the time span during which a culture flourished, and this range should normally be quoted rather than the mean, median or extreme dates of the culture. With samples of nine or more it can be shown by the Hypergeometric Distribution that there is a 97% chance of two cultures being different if their inter-quartile ranges just fail to overlap, so that this method of display is useful in assessing the overlap of cultures. The fact that the dispersion diagram contains within it a measure of the statistical uncertainties of the individual estimates and therefore can replace the standard deviation of each individual ¹⁴C date is discussed.