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CASE STUDIES


Fishy business Statistica


A


udrey Geffen, from the University of Bergen, with her two co-authors, argues that the complexity of Atlantic herring populations is at odds with the discrete


block methods used for their management and assessment. Furthermore, this disjunction throws into question ecological and biodiversity hypotheses. Using Statsoft’s Statistica, they analyse otolith


microchemistry data as a method of establishing more sophisticated mapping by age, origin, and other characteristics. Square-root-transformed concentrations of barium, copper, lithium, manganese, magnesium, sodium and strontium are analysed as an underpinning classifier system, the core otolith signatures of populations from different areas being identified by linear discriminant analysis and evaluated for reliability of assignment using statistical reference measures. ANOVA and cross- validated canonical analysis identify and assign spawning fish by origin, and an impressive array of checking methods were used to maximise the quality of sampling and conclusions. Those conclusions suggest that, although herring


off British shores appear to be a single population (albeit with multiple origins), much greater attention to location and pattern of recruitment is required if management is to be based on reliable information.


Sources Geffen, A.J., et al., ‘Characterization of herring populations west of the British Isles: an investigation of mixing based on otolith microchemistry.’ ICES Journal of Marine Science, 2011. 68(7): pp.1447-1458.


Statistica: www.statsoft.com


a) LDA model of juvenile herring based on chemical composition of otolith cores, with fish sampled in 2004 used to determine the model, and ellipses showing 95 per cent confidence intervals around group centroids. b) Distribution of juveniles sampled in 2003 according to the 2004 model, with 2004 group ellipses shown for comparison


Wears the diamonds? SPSS


B


ecause of their hardness, fragmentary diamonds are used in many industrial tools for cutting, drilling or machining of resistant materials. Even they are not, of course, infinitely hard, so they do wear away in use. In the cutting of stone, whether at the quarry or later in the


distribution chain, diamond fragments are bonded to steel beads on continuous loops of wire pulled rapidly over the block which, in effect, form a water-cooled band saw. Within the industry, it is well recognised that a range of factors interact to affect the wear rate, and therefore the useful life, of these wires. Using SPSS to perform the necessary multiple linear regressions, Yilmaz


Ozcelik of Hacettepe University, Ankara, investigated the interrelation between variables in search of a reliable predictor for wire life in marble and sandstone cutting. Uncontrollable influences include characteristics of the rock, while those which are, to some extent, controllable include aspects of the tools, machinery to which they are attached, and operating environment. Ozcelik compiled a list of 26 variables, from texture coefficient to cutting rate, then analysed field and laboratory data to isolate significant stepwise linear regression models. Wear rate models were obtained, and their adequacy checked by ANOVA. He found that rise in rate of wear is strongly linked to fall in cutting rate, and to high levels of quartz and opaque mineral content, but not to texture coefficient. SPSS delivered several useful wear rate model equations with a good fit to experimental and observed data, allowing good wear predictions to be incorporated into planning.


Sources Ozcelik, Y., ‘Estimation of wear rate on diamond beads during cutting with diamond wire by using multiple linear regression techniques.’ Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2011. 225(7): pp.1537-1549.


SPSS: www-01.ibm.com/software/analytics/spss/products/statistics/


Learning from past mistakes Mathematica


‘A


’, who politely declined to use her real name, is a graduate from a Russell Group university and holder of a Master’s degree in business statistics. She now works for one of those vaguely civil service organisations with websites and mission statements curiously devoid of information.


About her work, however, she is very specific and precise. She analyses history.


Not recent history, nor any particular history: all of history or, at least, huge swathes of it. Her interest is not in past events themselves, but in the patterns which can be extracted and used to build predictive models upon which future policy might be based. A’s chosen working environment is Wolfram Mathematica. She prefers, she says, the abstract control and uncommitted nature of building from a purely symbolic mathematical language, even though she is working with purely statistical concepts, to the prefigured purpose built assumptions of a data analysis product. Her present focus of attention is analysis of social, economic, demographic,


military and political patterns across Eurasia during the decline and fall of the Han and Roman empires. She has large systems of Mathematica analyses, banks of variable declarations linked to external databases, and outputs to existing databases containing previous results. She has recently completed similar examinations of the collapsing Nri, Oyo and Benin empires. Her employers hope to find echoes from some of these fragments in the post-Soviet world and a hypothesised future collapse of present geopolitical power structures.


Sources Mathematica: www.wolfram.co.uk/mathematica/


26 Statistics special


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