Abstract
Multivariate analysis is used in the search for one or more types of structure. The statistical zap applies a single method to determine one preselected type of structure. Several zaps suffice to ascertain several types of structure. The statistical shotgun represents an alternative approach. Here, a series of methods is applied to the data with the intent of ascertaining all possible types of structure that may exist. If strong structure is present, an appropriate zap will probably reveal it, and a variety of techniques will determine the same general structure. If only the main structure is required, the zap is adequate. In this situation, the shotgun will display a basic consistency which is at least reassuring. However, zaps may fail to detect a more subtle secondary structure of geological interest which will be displayed by the shotgun. For weakly structured data, a zap will only determine one type of structure but the shotgun reveals all. Study of the ontogeny of Parastylonurus myops(Clarke), a Lower Silurian eurypterid from New York (USA) shows the virtues of the statistical shotgun.
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Andrews, H. E., Brower, J. C., Gould, S. J., and Reyment, R. A., 1974, Growth and variation inEurypterus remipes DeKay: Geol. Inst. Univ. Uppsala Bull., n.s., v. 4, no. 6, p. 81–114.
Blackith, R. E., and Reyment, R. A., 1971, Multivariate morphometrics: Academic Press, London and New York, 412 p.
Brower, J. C., 1973, Ontogeny of a Miocene pelecypod: Jour. Math. Geology, v. 5, no. 1, p. 73–90.
Clarke, J. M., 1907, TheEurypterus Shales of the Shawangunk Mountains in eastern New York: New York State Mus. Bull. 107, p. 295–310.
Clarke, J. M., and Ruedemann, R., 1912, The Eurypterida of New York: New York State Mus. Mem. 14, 628 p.
Davis, J. C., 1973, Statistics and data analysis in geology: John Wiley & Sons, Inc., New York, 550 p.
Dixon, W. J., ed., 1970a, BMD Biomedical computer programs: Univ. Calif. Publ. in Automatic Computation, No. 2 (2nd ed.), 600 p.
Dixon, W. J., ed., 1970b, BMD Biomedical computer programs, X-series supplement: Univ. Calif. Publ. in Automatic Computation, No. 3, 260 p.
Gould, S. J., 1967, Evolutionary patterns in pelycosaurian reptiles: a factor-analytic study: Evolution, v. 21, no. 2, p. 385–401.
Gould, S. J., and Littlejohn, J., 1973, Factor analysis of caseid pelycosaurs: Jour. Paleontology, v. 47, no. 5, p. 886–891.
Harman, H. H., 1967, Modern factor analysis (2nd ed.): Univ. Chicago Press, Chicago and London, 474 p.
Hunt, A. S., 1967, Growth, variation and instar development of an agnostid trilobite: Jour. Paleontology, v. 41, no. 1, p. 203–208.
Kesling, R. V., 1951, The morphology of ostracod molt stages: Illinois Biol. Mon., v. 21, no. 1–3, 324 p.
Kesling, R. V., 1952, Doubling in size of ostracod carapaces in each molt stage: Jour. Paleontology, v. 26, no. 5, p. 772–780.
Kesling, R. V., 1953, A slide rule for the determination of instars in ostracod species: Contr. Mus. Paleontology, Univ. Michigan, v. 11, no. 5, p. 97–109.
Morrison, D. F., 1967, Multivariate statistical methods: McGraw-Hill Book Co., New York, 338 p.
Ondrick, C. W., and Srivastava, G. S., 1970, CORFAN-FORTRAN IV computer program for correlation, factor analysis (R- and Q-mode) and varimax rotation: Kansas Geol. Survey Computer Contr. 42, 92 p.
Parks, J. M., 1970, FORTRAN IV program for Q-mode cluster analysis on distance function with printed dendrogram: Kansas Geol. Survey Computer Contr. 46, 32 p.
Palmer, A. R., 1957, Ontogenetic development of two olenellid trilobites: Jour. Paleontology, v. 31, no. 1, p. 105–128.
Palmer, A. R., 1962, Comparative ontogeny of some opisthoparian, gonatoparian and proparian Upper Cambrian trilobites: Jour. Paleontology, v. 36, no. 1, p. 87–96.
Passano, L. M., 1960, Molting and its control,in The physiology of Crustacea, v. I, Metabolism and growth: Academic Press, New York, p. 473–536.
Przibram, H., 1931, Connecting laws of animal morphology: Four lectures held at the University of London, March, 1929: London Univ. Press, London, 62 p.
Reyment, R. A., 1960, Studies on Upper Cretaceous and Lower Tertiary Ostracoda: Part I, Senonian and Maestrichtian Ostracoda: Stockholm Contr. Geol. 7, 238 p.
Reyment, R. A., 1963, Studies on Nigerian Upper Cretaceous and Lower Tertiary Ostracoda: Part II, Danian, Paleocene and Eocene Ostracoda: Stockholm Contr. Geol. 10, 286 p.
Reyment, R. A., 1972, Application of multivariate morphometrics in paleontology: Intern. Geol. Cong., 24th Sess., sect. 7, Paleontology, p. 238–245.
Reyment, R. A., 1974, The age of zap: Syracuse Univ., Geol. Contr. 2, in press.
Robison, R. A., 1967, Ontogeny ofBathyriscus fimbriatus and its bearing on affinities of corynexochid trilobites: Jour. Paleontology v. 41, no. 1, p. 213–231.
Seal, H., 1964, Multivariate statistical analysis for biologists. Methuen and Co., London, 209 p.
Sneath, P. H. A., and Sokal, R. R., 1973, Numerical taxonomy, the principles and practice of numerical classification: W. H. Freeman and Co., San Francisco, 573 p.
Van de Geer, J. P., 1971, Introduction to multivariate analysis for the social sciences: W. H. Freeman and Co., San Francisco, 293 p.
Veldman, D. J., 1967, FORTRAN programming for the behavioral sciences: Holt, Rinehart and Winston Inc., New York, 406 p.
Whittington, H. B., 1957, The ontogeny of trilobites: Biol. Reviews, v. 32, no. 4, p. 421–469.
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Brower, J.C., Veinus, J. The statistical zap versus the shotgun approach. Mathematical Geology 6, 311–332 (1974). https://doi.org/10.1007/BF02082354
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DOI: https://doi.org/10.1007/BF02082354