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

Abstract

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.