A primer of correction of quantitative data of extinct shrews Crocidosoricinae (Lipotyphla: Soricidae) using statistic tests

L.L. Voyta and V.S. Zazhigin

Proceedings of the Zoological Institute RAS, 2017, 321(3): 326–338 · https://doi.org/10.31610/trudyzin/2017.321.3.326

Full text

Abstract

This article presents an example of using the parametrics (Shapiro-Wilk and Jarque-Bera) and non-parametrics (Anderson-Darling) criteria for exploratory analysis on a sample homogeneity hypothesis, and estimate the suitability of metric features for interspecific comparisons. Grubbs and Tukey tests were used for detecting of the outliers of metric features. The analyzed fossil material is represented by bone fragments and isolated teeth (n = 218) of an unknown crocidosoricine shrew †Crocidosoricinae indet. (Lipotyphla: Soricidae) from the middle Miocene Sharga 2 locality (Mongolia), and. Based on the results of the study, three measurements (MRWc, HC and W(m3)) are not recommended for interspecies comparisons while working with Crocidosoricinae indet. In addition, a homogeneity analysis of 25 metric characters of Crocidosoricinae indet. from Sharga 2 locality showed that all remains are likely to belong to a single general sample (local population), remains of which accumulated during relatively short period.

Key words

discriminant analysis, Anderson-Darling test, Grubbs test, Tukey test, Shapiro-Wilk test, Jarque-Bera test, Crocidosoricinae, Soricidae

Submitted June 2, 2017 · Accepted August 26, 2017 · Published September 25, 2017

References

Anderson T.W. and Darling D.A. 1952. Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. The Annals of Mathematical Statistics, 23: 193–212. https://doi.org/10.1214/aoms/1177729437

Ghasemi A. and Zahedials S. 2012. Normality test for statistical analysis: A guide for non-statisticians. International Journal of Endocrinology and Metabolism, 10: 486–489. https://doi.org/10.5812/ijem.3505

Hammer Ø. 2002. Morphometrics – brief notes. 49 pp. Paläontologisches Institut und Museum, Zürich. Available from: http://folk.uio.no/ohammer/past/morphometry.pdf (accessed 17 June 2015).

Hummer Ø., Harper D.A.T. and Ryan P.D. 2001. PAST: Paleontological Statistics software package for and data analysis. Palaeontologica Electronica, 4: 1–9.

Hammer Ø., Harper D.A.T. and Ryan P.D. 2008. PAST: Paleontological STatistics, ver. 1.87. 1–88. Available from: http://www.academia.edu/2683729/PAST_PAlaeontological_STatistics_ver._1.87

Kobzar’ A.I. 2006. Applied mathematical statistics. Fizmatlit, Moscow, 238 p. [In Russian].

Lemeshko B.Ju. and Lemeshko S.B. 2009. The models of distributions of statistics of nonparametric acceptance criteria for testing complex hypotheses using maximum likelihood estimates. Part I. Мeasurement Techniques, 6: 6–11. [In Russian].

Lopatin A.V. and Zazhigin V.S. 2003. New Brachyericinae (Erinaceidae, Insectivora, Mammalia) from the Oligocene and Miocene of Asia. Paleontological Journal, 37: 62–75.

Öztuna D., Elhan A.H. and Tüccar E. 2006. Investigation of four different normality tests in terms of type 1 error rate and power under different distributions. Turkish Journal of Medical Sciences, 36: 171–176.

Puzachenko Yu.G. 2004. Mathematics methods in ecological and geographical studies. Akademia, Moscow, 416 p. [In Russian].

Reumer J.W.F. 1984. Ruscinian and early Pleistocene Soricidae (Insectivora, Mammalia) from Tegelen (The Netherlands) and Hungary. Scripta Geologica, 73: 1–173.

Rohlf F.G. and Slice D.E. 1990. Extension of the Procrustes method for the optimal superimposition of landmarks. Systematic Zoology, 39: 40–59. https://doi.org/10.2307/2992207

Shapiro S.S. and Wilk M.B. 1965. An analysis of variance test for normality. Biometrika, 52: 591–611. https://doi.org/10.1093/biomet/52.3-4.591

Stefansky W. 1972. Rejecting Outliers in Factorial Designs. Technometrics, 14: 469–479. https://doi.org/10.1080/00401706.1972.10488930

Tukey J. 1949. Comparing Individual Means in the Analysis of Variance. Biometrics, 5: 99–114. https://doi.org/10.2307/3001913

Zaitsev M.V., Voyta L.L. and Sheftel B.I. 2014. The mammals of Russia and adjacent territories. Lipotyphlans. Nauka, Saint Petersburg, 391 p. [In Russian].

Zazhigin V.S. and Lopatin A.V. 2000. The history of the Dipodoidea (Rodentia, Mammalia) in the Miocene of Asia: 1. Heterosminthus (Lophocricetinae). Paleontological Journal, 34: 319–332.

Zidarova S. 2015. Is there sexual size dimorphism in shrews? A case study of six European species of the family Soricidae. Acta Zoologica Bulgarica, 67: 19–34.