Counting sheep: sample size and statistical inference in stable isotope analysis and palaeodietary reconstruction created by Jessica Pearson and Matt Grove

The analysis of stable isotopes from biological remains has contributed greatly to archaeological knowledge in recent decades, with major contributions to areas such as prehistoric diet and mobility. The increasing importance of isotopic studies within archaeology has been paralleled by an increasing sophistication of laboratory techniques. At present, however, the relationship between sample size and the strength of the conclusions that can be drawn about the underlying population has received insufficient attention. In this paper we undertake to provide a series of statistical analyses that demonstrate the strength of inference in relation to sample size using a large corpus of carbon and nitrogen isotope measurements of bone collagen from a single species at one site (n = 174). We employ a sub-sampling approach to establish sample sizes at which estimated mean values asymptote, and derive confidence intervals accordingly. Our study quantifies the probability that means calculated from samples of various sizes would contain the estimated true value of the population mean with their 95 per cent confidence limits. Using these results, we suggest that large discrepancies should be expected where fewer than eight samples are used to estimate the population mean, but that sampling redundancy occurs with more than forty samples. We would encourage isotope specialists working with other types of material to undertake similar studies in order to better understand the strengths and limitations of stable isotope data.