Dispersion Diagrams: A New Approach to the Display of Carbon‐14 Dates

Abstract

S 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.

Summarizing a Set of Radiocarbon Determinations: A Robust Approach

“…The techniques presented in this paper have several advantages over the comparable techniques proposed before (Ottaway, 1973;Ward and Wilson, 1978;Aitchison et al, 1991). One of these advantages is that the statistical model using a Bayesian framework is more consistent with the archaeological problem under study, resulting in coherent interpretations for the probability distributions of the parameters explained earlier.…”

“…Therefore there is a need to summarize sets of radiocarbon determinations which, as we shall see, can be formulated as a probtem of statistical inference. Some of the problems associated with summarizing a set of independent radiocarbon determinations have been studied before (Ottaway, 1973;Ward and Wilson, 1978;Aitchison et al, 1991) by different approaches. In this paper we take a Bayesian approach and demonstrate how the robustness of an analysis can be assessed.…”

The chronology and duration of the prehistoric ditched enclosures: the case of Marroquíes Bajos (Jaén)

“…Solo se han tenido en cuenta las dataciones cuya desviación estándar fuera igual o inferior a 80 años para, de esta forma, reducir el efecto negativo que las amplias desviaciones tienen en el intervalo temporal resultado de la suma de probabilidades. La muestra resultante son 9 yacimientos: 4 de la cuenca del Guadiana (Juromenha I, Porto Torraõ, Perdigões y Bela Vista 5: Valera 2013c), 3 de la Meseta (Camino de las Yeseras: 5 La suma de probabilidades es una herramienta ampliamente utilizada en la literatura arqueológica para medir la duración e intensidad de los fenómenos analizados (Ottaway 1973;Aitchison et al 1991). No obstante, presenta varias limitaciones que deben ser tenidas en cuenta en la valoración de los resultados.…”

Khirokitia and the Initial Settlement of Cyprus

“…For series of dates, the dispersion diagram technique (Ottaway 1973) maximizes the positive, redundant information provided by radiocarbon dates while retaining a good indication of their relative reliability. The individual character of each determination must of course be kept in mind when assessing the confidence to be placed either in series or in single dates.…”