# Several recent works have relied on the comparison of SPDs

#### Written by gcole on April 23, 2022

The null-hypothesis in this case is the equality of the SPDs: the sample dates are generated from identically shaped population curves. For example, Collard and colleagues have compared different site types, whilst Stevens and Fuller suggested a failing of Neolithic farming in Britain based on the observed divergence in the SPD obtained from hazelnut/wild plants and cereal/crops. We argue that these types of studies can benefit from a statistical test that can highlight statistically significant differences, as well as provide a global p-value.

## We also examined a uniform distribution as an alternative null that does not assume an exponential increase in the underlying population, but instead look for significant deviations from a simpler “flat” model

- 14 C samples of each site of each set are calibrated and aggregated (i.e. a pooled mean is computed) in bins based on prior archaeological knowledge (e.g. same context unit) or chronological proximity (e.g. by site-phase, as in , or ).
- Pooled mean probabilities obtained from bins are summed to generate an empirical SPD for each set.
- The assignment of each bin to a specific set is randomly permuted (so that the total number of bins associated to each set is identical to the observed), and an SPD is generated from each set.
- Step 3 is repeated n times, and a local Z-score computed to remove the effects of short term wiggles and the underlying trend of the null model for both observed and simulated data.
- A 95% upper and lower confidence interval is then computed from the simulated SPD. Observed SPDs above (or below) the envelope is identified as statistically significant local deviations, indicating divergences between the focal set and the aggregate of all sets.
- Following the same procedure detailed in , we generate a null distribution from the total area outside the confidence envelope for each simulated SPD. We then apply the same procedure for each observed set, and compare its value to this distribution. The proportion of the latter that is larger or equal than the observed provides an estimate of the p-value for each set. Notice that the comparison is based on the overall shape of the SPDs. In other words, such a global p-value might be high even in case significant local deviations are detected, especially when two sets exhibit similar shape for large portions of theirs SPDs.

The approach is robust to https://hookupdate.net/herpes-dating/ inter-regional differences in the research intensity (hence sample size), as the comparison is based on the “shape” of the SPDs (i.e. the relative change in summed probabilities within each region) and not on differences in their absolute magnitudes. As for other frequency-based proxies (e.g. site and house counts), without a quantifiable knowledge of research intensity it is virtually impossible to distinguish whether observed difference in density is due to the actual underlying populations or just a consequence of differences in the sampling fraction. By maintaining the observed number of bins for each region, and by comparing population trajectories rather than absolute differences in density, the proposed method bypasses this problem. Thus, it is worth noting that significant negative (or positive) deviations of the SPD in one region does not necessarily imply a lower (or higher) absolute population density, but that the drop in the proxy within the dynamics of that region was significantly stronger compared to rest of the data.

## Here we introduce a non-parametric extension of the hypothesis-testing approach that enables the statistical comparison of two or more sets of 14 C dates

We first assessed whether the SPD of 14 C dates for each area showed statistically relevant fluctuations when compared against the uniform and the exponential null models, following the procedure described in , using 10,000 Monte-Carlo simulations, and calibrating (via direct numerical integration) with the IntCal13 curve and scripts based on the Bchron package in R statistical computing language . The exponential distribution was used as a null model portraying both the temporally increasing taphonomic loss and the long-term population increase observed in prehistoric populations [36,55]. The choice of this second null model was partly dictated by a general impression of a rise-and-fall pattern that is distinct from other studies where a steady growing trend is evident (e.g. ). We compared the shape of the SPDs of three regions with the permutation test described above, using the same calibration procedure and same number of iterations (i.e. 10,000).