Beyond p < .05: a critical review of new Bayesian proposals for assessing the p-value.

This paper reviews recent contributions from a Bayesian-oriented perspective, after the ASA statement on p-values (2016). We classify proposals that (i) supplement the p-value; (ii) modify the p-value itself. In the first group, we review the Bayes factor, the False Positive risk, the rejection odds and the analysis of credibility from both Matthews' and Held's point of view. We also put forth and discuss a new index of credibility, about which we conduct a delimited simulation study. In the second group, we discuss Gannon's modification of the p-value based on the Bayes factor and the second-generation p-value. The theory is illustrated with two case studies on pharmacotherapy in infectious diseases. Contemporary authors still refer to the p-value as a statistical indicator but have abandoned the perspective of evaluating p-values with fixed thresholds. Statistical societies worldwide should target new strategies to disseminate the debate on p-values in all applied fields of knowledge, as well as they may promote the use of different statistical procedures to supplement p-values.

Best uses of p-values and complementary measures in medical research: Recent developments in the frequentist and Bayesian frameworks.

The p-value is a classical proposal of statistical inference, dating back to the seminal contributions by Fisher, Neyman and E. Pearson. However, p-values have been frequently misunderstood and misused in practice, and medical research is not an exception. In recent years, in several statistical and applied journals, a debate erupted about the need of clear guidelines in reporting p-values, which culminated with the publication of the ASA statement in 2016. In this paper, we assess strengths and limitations of p-values and we assert that in applied research the p-value should be supplemented by other measures, such as the Bayes factor, the Bayes false discovery rate and the local Bayes false discovery rate. We also review a recent proposal by Bayarri et al. from a Bayesian perspective that has the advantage of introducing an indicator, the rejection odds, which keeps into account both pre- and post-experimental information, and could also have a straightforward frequentist interpretation. We conduct a delimited numerical study that investigates on the relation of the Bayes factor with its maximum, and of the local Bayes false discovery rate with its minimum under different distributional assumptions and parameter choices. We illustrate the concepts expressed in theory with an example in clinical oncology, namely a randomized trial on the effectiveness of a new chemotherapy for patients with AIDS and Kaposi's sarcoma.

Fuzzy Analysis of Students' Ratings.

BACKGROUND: Intuitionistic fuzzy sets (IFS) represent a methodology for quantifying latent variables in questionnaire analysis through membership and non-membership functions, which are linked by an uncertainty function. OBJECTIVES: We aim to apply an IFS approach to the problem of students' satisfaction of university teaching. Such framework can take into account a source of uncertainty related to items and another related to subjects. RESULTS: A new technique for IFS analysis is set forth and generalized to a multivariate scenario. Potential advantages of the IFS perspective with respect to other nonfuzzy approaches are provided. APPLICATION: We apply this method to a national program of university courses evaluation and we focus, in particular, on the outcomes of two Masters in Statistics.

Assessing the inter-rater agreement for ordinal data through weighted indexes.

Assessing the inter-rater agreement between observers, in the case of ordinal variables, is an important issue in both the statistical theory and biomedical applications. Typically, this problem has been dealt with the use of Cohen's weighted kappa, which is a modification of the original kappa statistic, proposed for nominal variables in the case of two observers. Fleiss (1971) put forth a generalization of kappa in the case of multiple observers, but both Cohen's and Fleiss' kappa could have a paradoxical behavior, which may lead to a difficult interpretation of their magnitude. In this paper, a modification of Fleiss' kappa, not affected by paradoxes, is proposed, and subsequently generalized to the case of ordinal variables. Monte Carlo simulations are used both to testing statistical hypotheses and to calculating percentile and bootstrap-t confidence intervals based on this statistic. The normal asymptotic distribution of the proposed statistic is demonstrated. Our results are applied to the classical Holmquist et al.'s (1967) dataset on the classification, by multiple observers, of carcinoma in situ of the uterine cervix. Finally, we generalize the use of s* to a bivariate case.