Classical and Modern Statistical Tests for Two-Sample Location Problems for Continuous Data: A Comprehensive Review

Author (s)

Israa Abdulameer Resen

Abstract

The area of statistical analysis has been evolving steadily over time to cope with the complexity of comparing two samples, especially in location problems. This comprehensive review attempts to discuss both classical and modern statistical methods for comparing two samples and analyse their strengths and weaknesses. Classical methods have been successfully used to evaluate mean differences between two samples for a long period of time. However, the assumption of normality of the distribution of data and equality of variances makes them less usable in practice. Modern methods that do not make such assumptions should be considered when comparing two samples of data. The Mann-Whitney U test is one of the most popular among nonparametric statistics. Another example of modern statistics is the permutation method used to estimate the significance of the difference in the mean values between two groups. Advantages of these methods include the opportunity to analyse heterogeneous data or small samples, that are the reason for using nonparametric statistics. The use of advanced computational techniques and new software in the area of statistical testing is also worth discussing. Resampling methods can be used for generating more precise confidence intervals and p-values. Machine learning algorithms and other computational methods can be used in addition to classical statistical theory to improve the prediction of results. For example, the use of support vector machines in the area of two-sample comparison will increase the accuracy of results.  Numerous studies address classical and modern approaches to comparing two samples; however, there is a lack of systematic comparison regarding the advantages and disadvantages of these methods. Most studies rely on the results of a single type of test to compare two data samples in real-world contexts, without considering whether the underlying assumptions are met. Furthermore, the evolution of statistical theory necessitates a discussion of new data types and their impact on the selection of statistical methods for comparison; indeed, comparing classical approaches with modern computational methods can contribute to the future advancement of statistical theory. Therefore, this review outlines the key frameworks that integrate classical and modern approaches for comparing two samples.

Key words: Statistical Tests, Location of Two Samples, Resampling Methods, Normality Assumption, Bootstrapping Methods, Permutation Methods, Bayesian Methods, Machine Learning.

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Cite This Article:

Resen, I. A. (2026). Classical and Modern Statistical Tests for Two-Sample Location Problems for Continuous Data: A Comprehensive Review, Journal of Scientific Reports, 15(1), 180-191. DOI: https://doi.org/10.58970/JSR.1246

About Author (s)

Israa Abdulameer Resen, Department of Mobile Communications and Computing Engineering, College of Engineering, University of Information Technology and Communications (UoITC), Baghdad, Iraq. ORCID: https://orcid.org/0009-0004-5590-010X

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DOI: https://doi.org/10.58970/JSR.1246

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