Ciclo di seminari: from Classical ANOVA to ANOVA with Random Sample Sizes: An Overview and Applications

Analysis of variance (ANOVA) is one of the most widely used statistical analyses in practical applications, with relevance across fields such as Medical and Biomedical Sciences, Agriculture, and Social Sciences, to name just a few. In its classical formulation, ANOVA assumes that sample sizes are fixed in advance. However, in many real-world situations, this assumption is not realistic, for instance when data are collected within a fixed time period defined in advance or are subject to observation failures, such as non-response or missing observations.

In this seminar, we first revisit the classical ANOVA framework, focusing on one-way and multi-way fixed effects models, as a basis for the developments that follow. In particular, we highlight the underlying assumption that sample sizes are fixed. We then show how situations in which this assumption does not hold can be addressed by performing ANOVA while treating the sample sizes as realizations of independent random variables.

This approach requires an appropriate choice of the distributions of these random variables. In particular, we consider two families of distributions, depending on the existence of an upper bound for the sample sizes: the Poisson distribution for unbounded cases and the Binomial distribution for bounded cases.

The applicability of the proposed methodology is illustrated through applications involving real and simulated data, with particular emphasis on the comparison between the classical ANOVA and the proposed framework. This comparison highlights its impact on statistical inference, particularly in terms of hypothesis testing and the control of false rejections.

With this seminar, we intend to provide an accessible overview of recent advances in the field of “ANOVA with random sample sizes”, focusing primarily on one-way models, followed by multi-way fixed effects models, while briefly mentioning possible extensions to mixed effects models.