Quantitative methods based on mathematics and statistics have been increasingly applied in finance and banking industry in recent years. However, it should be stated that the selection of specific statistical methods has many prerequisites to be met in order for the application to be correct and justified. Moreover, simple methods of statistical description and conclusions, e.g. parametric or non-parametric tests, make it possible to draw deeper conclusions and verify empirical results of the application of complex econometric models. However, the examination of specific assumptions for the applicability of statistical methods is rarely used, and frequently even omitted. It often happens that analysts omit the assumptions on the normal distribution of estimators and apply methods in which such an assumption is necessary in order to use a particular statistical analysis tool.

The article presents an example of a correctly applied selected statistical test to check the "certainty" of results of performance measures obtained through the Data Envelopment Analysis (DEA) of mergers and acquisitions in the Polish banking sector in 2002-2003. The analysis focused on one group of premises for mergers and acquisitions, i.e. the economies of scale. Thus an attempt was made to answer the following question: whether the ongoing consolidation of banks is still favourable to their performance by using growing economies of scale, i.e. the synergy. The article, on the basis of analysis of the banks' performance measures, tried thus to justify the thesis that commercial banks benefited from the economies of scale in Poland in late 2002 and in 2003, which would contribute to the continuation of mergers and acquisitions in the sector favouring the increase of the banks' performance. The thesis was verified empirically with the use of statistical tests.

The test presented in the example represents the group of parametric tests, also known as tests related to the distribution of parameters in a population (regarding for instance an arithmetic mean). The example shows its correct application, which supported the conclusions following DEA in the assessment of the bank performance in 2002-2003.