## 1 Introduction
[11] proposed testing procedures for each parameter of the gamma distribution individually, that is, for the scale parameter, shape parameter, and also the mean of the distribution (a different problem). [PERSON], [PERSON], and [PERSON] [12] presented a bootstrap-based procedure to test the equality of more gamma distribution means. This is a paper of interest that will be used for comparative analysis in this text. Other mentions can also include the possibility of using nonparametric tests for the subject of interest, such as the Wilcoxon rank-sum test, approximate in nature for small samples, however, or [PERSON]'s [13] test of the homogeneity of gamma distributions, based on combining the likelihood ratio and score statistics: Their behavior is yet again known only for large samples. It seems that some theoretical outcomes are available even though they result either from mathematical approximations or resampling techniques [12; 14], such as the bootstrap. It is worth noting that resampling techniques also rely on large-sample properties. It can also be seen that the two-sample testing of means has not always been the subject matter under scrutiny. This text adopts a different and more \"hands-on\" approach compared to the two just mentioned and focuses on smaller- and medium-sized data samples for which the testing problem is more pressing. The findings presented in this text are based on simulations that try to identify properties of the true distribution of \(\overline{X}-\overline{Y}\) under \(H_{\rm o}\), striving to avoid various approximations that result either from complicated mathematical operations or potentially also from resampling techniques. Additionally, one of the major objectives of this paper is to provide as simple a testing technique as possible so that it can be used by practitioners without the need to code ad-hoc simulations or comprehend and evaluate more complex mathematical theories and the implied algorithms. As with any simulation-based research, the limitation of the presented technique lies in the fact that not all theoretically conceivable combinations of the gamma parameters can be handled while deriving the testing procedure, naturally, since there is an infinite number of them, but many of them are handled in this text. Regarding the number of parameter combinationscovered in this text, a certain aggregation of the results had to be adopted in the end when formulating the final recommendations due to a large number of simulation-based outcomes. The individual results are available in the attached datasets, however. The logic of the entire procedure is discussed below in the methodology section. Although the aggregation of results can be looked at as a way to blur back the detailed and more precise simulation outcomes, the resulting testing procedure based on the aggregation is still subject to verification so that its potential is indicated. Last but not least, the aim of the paper is not to criticize the techniques presented so far in the literature--quite the opposite. This paper is regarded as their complement, which, after all, will be obvious once the method is validated, as it shows good potential in many situations, while in others, it may be less desirable. In summary, a simpler method with desirable statistical properties for many smaller- and medium-sized samples and a reasonable range of the gamma-distribution parameters is the objective of this paper.