Prescription for Abnormal Distribution and Interdependence of Observations Using Randomization Tests and Mantel Correlation Coefficient – the Example of Human Resources Distribution in the Regions of France

  • Sławomir Dorocki Uniwersytet Pedagogiczny w Krakowie, Instytut Geografii, Zakład Przedsiębiorczości i Gospodarki Przestrzennej
  • Bartosz Jenner Reckitt Benckiser
Keywords: France, human capital, Mantel test, randomization, R-package, statistical methods


Using statistical methods in geographical research, researchers are often faced with the problem that their data do not comply with the assumptions required by a number of statistical tests. For example, many parametric statistical tests are based on the assumption of normal distribution of data. In practice, however, this supposition is often not met, and the serious deviation of data distribution from the normal distribution (e.g., J-shaped distribution) can lead to quite absurd values of confidence limits (for example, the confidence interval). Another common problem with data from geographical research is the interdependence of observations. Mutual correlation of data can, for example, reflect the spatial distance between the places where that information was obtained. Therefore, the results of measurements from sites located in close proximity to each other may be more alike than observations from places more distant from each other. In such a situation, estimated p-values for tests investigating the relationships between variables (e.g. Pearson correlation) can be very confusing, because the “classical” statistical methods assume independence of the variables. In these situations, the researcher can use randomisation tests that allow him to “get around” the assumptions of normal distribution and independence of observations. These methods, along with the ability to perform complex calculations using computer tools, are becoming increasingly popular among researchers. The article explains the logic of randomisation tests and two examples of their use: estimating the interval for the mean and calculating Mantel correlation along with testing its significance. Calculations have shown that in both cases, disregard of the statistical assumptions leads to false results. In order to illustrate these statistical methods, data used in this paper show the volume and share of human resources in science and technology (HRST) in regions of France and the pace of changes in these values over time and space. Calculations were conducted using the free statistical software R Project and Excel spreadsheet.


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Author Biographies

Sławomir Dorocki, Uniwersytet Pedagogiczny w Krakowie, Instytut Geografii, Zakład Przedsiębiorczości i Gospodarki Przestrzennej
Sławomir Dorocki, Ph.D., Department of Entrepreneurship and Spatial Management, Institute of Geography,Pedagogical University of Cracow. Sławomir Dorocki, graduated from the Pedagogical University of Cracow,MA degree in geography, Ph.D. in history (Institute of European Studies of the Jagiellonian University). AssociateProfessor at the Pedagogical University of Cracow, Institute of Geography. His research interests aretied with regional problems and processes of socio-economic regionalization, with particular emphasis on the diversity of Europe, processes of European integration, historical conditions and application computerand statistical methods in the study of diversity of space.
Bartosz Jenner, Reckitt Benckiser
Bartosz Jenner, graduated from the Department of Biology and Earth Sciences of the Jagiellonian Universityin Krakow (2001) – he also temporarily studied biology at the University of Wolverhampton – UK. He currentlyworks as a statistician at the Global Medical Affairs of Reckitt Benckiser (UK). In the past he worked asepidemiologist at the Department of Toxicology of the Jagiellonian University Medical College and completed1 year post-doc fellowship in Max Planck Institute for Demographic Research in Germany. He has acquiredexperience in various research studies, clinical trials and GCP procedures. He is co-author of 20 papers. Heis a member of International Society of Clinical Biostatistics (ISCB) and Statisticians in the PharmaceuticalIndustry (PSI).


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How to Cite
DorockiS., & JennerB. (2016). Prescription for Abnormal Distribution and Interdependence of Observations Using Randomization Tests and Mantel Correlation Coefficient – the Example of Human Resources Distribution in the Regions of France. Studies of the Industrial Geography Commission of the Polish Geographical Society, 30(2), 186-197.

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