• A simple procedure for investigating differences in sexual dimorphism between populations

      Lewis, Stephen J.; Chester College of Higher Education (Oxbow Books (for The Osteoarchaeological Research Group), 1997-12-01)
      Although sexual dimorphism has a strong genetic component in many animals, external factors may alter its expression - enhancing or diminishing it depending on the parameter measured and the type of influence experienced. A measure of sexual dimorphism may be used, therefore, to characterise a whole population and the factors acting upon it. Differences between populations for such factors may then be investigated by comparing sexual dimorphisms and may be more informative than merely comparing population means. A quick and relatively simple technique which provides a coefficient of the relationship between a continuous variable and another which is dichotomous, such as sex, is the point biserial correlation. This is a less frequently described extension of the commonly used Pearson product-moment correlation. The point-biserial correlation coefficients can be calculated for a given parameter and compared to determine whether the same sexual dimorphism is evident in different samples. If it is not, some factor influencing one or other population, as a whole, may require further investigation. The full procedure, which can be performed without the need for statistical tables, and the necessary formulae are described. This method, in its generalised form, may also be applied to the study of bilateral asymmetry.
    • A tabular method for performing Fourier analysis of complex biological shape

      Lewis, Stephen J.; Chester College of Higher Education (Oxbow Books (for The Osteoarchaeological Research Group), 1997-12-01)
      Whilst linear dimensions are easily measured and analysed numerically, curvilinear forms are difficult both to define and to compare and are frequently left unexplored. A method of describing curved or non-uniform shapes, which has become popular among a number of biological workers, is Fourier analysis — a numerical analytical technique with an established mathematical background. Of the three stages followed when using this technique to describe biological shape - the construction of a wave-like curve from the shape being studied, the numerical (Fourier) analysis and the use of the Fourier coefficients to perform statistical analyses - that of how the Fourier analysis is performed is largely unreported. This leaves many unclear about how to perform a technique which they may otherwise find useful. A tabular method, which allows the computational steps of Fourier analysis to be monitored throughout, is described. This procedure can be readily performed, using a computer spreadsheet or on paper. The original curve may also be reconstructed from the Fourier coefficients, allowing one to check the success and accuracy of the method and to determine the number of coefficients necessary to define the shape to the required precision.
    • Visualizing multivariate analysis - An intuitive approach to high dimensional statistical extractions

      Lewis, Stephen J.; Chester College of Higher Education (Oxbow Books (for The Osteoarchaeological Research Group), 1997-12-01)
      The numerical output of multivariate statistical analyses may extend to a greater number of dimensions than can be comprehended and so may appear abstract and divorced from the original data. A need arises, therefore, for the provision of a more intuitive understanding of the results of such techniques - perhaps of a graphical nature. A simple method is to plot, what have come to be known as, Andrews' curves. A tabular procedure, using a standard computer spreadsheet, is described whereby the coefficients produced by various multivariate statistical techniques can be substituted into a simple equation to produce a smooth, wave-like curve characterising the source data. Importantly, this technique also provides a means whereby groups of curves may be compared visually to identify clusters and curves of similar or dissimilar overall shape. Similarly, "outliers" may also be spotted.