Speaker: Dr. Hugh McCague, York University
Institute for Social Research

Title: Directional Statistics and Hunting Quanta 

Abstract: Directional statistics, circular data analysis and spherical data analysis involve the analysis of angular data. Directional statistics adapts and extends the methods for analysing linear non-angular data particularly through the use of vector operations and trigonometry. Some variables that are not angles but that are cyclical in nature, such as some time measurements and measurements arising from multiples of fundamental units (quanta), may be best analysed by being transformed into angles. In some cases, linear non-angular methods may be suitable for analysing angular data, but in other cases the methods of directional statistics are required. Response and explanatory variables may be both angular and non-angular in nature. Data for directional statistics arises in wide ranging fields and disciplines such as psychology, medicine, biology, kinesiology, engineering, physics, astronomy, meteorology, oceanography, geography, geology, and archaeology. The angular and cyclic nature of this form of data has wide-ranging repercussions for the plotting of data, hypothesis testing, and model fitting and diagnostics. I will illustrate briefly some of the methods of directional statistics, and consider an example of hypothesis testing involving metrological units, “hunting quanta.”

Suggested Readings:

Textbooks
        Fisher, N. I. (1993). Statistical Analysis of Circular Data. Cambridge and New York: Cambridge University Press.
        Mardia, K. V., & Jupp, P. E. (2002). Directional Statistics. Chichester, UK: Wiley.
        Pewsey, A., Neuhäuser, M. & Ruxton, G.D. (2013). Circular Statistics in R. Oxford: Oxford University Press, 2013.

Specific Applications
        Guterman, P., Allison, R & McCague, H. (2009). The application of circular statistics to psychophysical research. Proceedings of Fechner Day, 25, 185-190.
        Lanos, P., & Jumel, G. (1992). La Methode du Quantogramme dans la Recherche d'Unites de Mesure Inconnues: Application à la recherche de métriques anciennes dans la paysages. Revue d'Archéometrie 16, 121-144.
        McCague, H. (2001). The Mathematics of Building and Analysing a Medieval Cathedral. Proceedings of the Canadian Society for History and Philosophy of Mathematics, 13, 167-176.