Riko Kelter

• University of Siegen

Bayesian design of experiments and sample size calculations usually rely on complex Monte Carlo simulations in practice. Obtaining bounds on Bayesian notions of the false-positive rate and power therefore often lack closed-form or approximate numerical solutions. In this paper, we focus on the sample size calculation in the binomial setting via Bay...

The $$\chi ^{2}$$ χ 2 test is among the most widely used statistical hypothesis tests in medical research. Often, the statistical analysis deals with the test of row-column independence in a $$2\times 2$$ 2 × 2 contingency table, and the statistical parameter of interest is the odds ratio. A novel Bayesian analogue to the frequentist $$\chi ^{2}$$...

In clinical research, the initial efficacy of a new agent is typically assessed in a phase IIA study. Bayesian group-sequential designs are often based on predictive probability of trial success. In this paper, the novel Bayesian group-sequential predictive evidence value design is introduced, and we prove that the predictive probability approach i...

Testing a precise hypothesis can lead to substantially different results in the frequentist and Bayesian approach, a situation which is highlighted by the Jeffreys-Lindley paradox. While there exist various explanations why the paradox occurs, this article extends prior work by placing the less well-studied point-null-zero-probability paradox at th...

The success of preclinical research hinges on exploratory and confirmatory animal studies. Traditional null hypothesis significance testing is a common approach to eliminate the chaff from a collection of drugs, so that only the most promising treatments are funneled through to clinical research phases. Balancing the number of false discoveries and...

There is a variety of empirical evidence that the coverage of paradoxes in mathematics education helps to support thorough understanding of probabilistic and statistical concepts. However, existing literature often focuses on extensive analysis of a specific paradox, provides new perspectives or an analysis from a different angle. Often neglected a...

Statistical simulation studies are becoming increasingly popular to demonstrate the performance or superiority of new computational procedures and algorithms. Despite this status quo, previous surveys of the literature have shown that the reporting of statistical simulation studies often lacks relevant information and structure. The latter applies...

Interval estimation is one of the most frequently used methods in statistical science, employed to provide a range of credible values a parameter is located in after taking into account the uncertainty in the data. However, while this interpretation only holds for Bayesian interval estimates, these suffer from two problems. First, Bayesian interval...

Background Causal inference has seen an increasing popularity in medical research. Estimation of causal effects from observational data allows to draw conclusions from data when randomized controlled trials cannot be conducted. Although the identification of structural causal models (SCM) and the calculation of structural coefficients has received...

The Full Bayesian Significance Test (FBST) has been proposed as a convenient method to replace frequentist p-values for testing a precise hypothesis. Although the FBST enjoys various appealing properties, the purpose of this paper is to investigate two aspects of the FBST which are sometimes observed as measure-theoretic inconsistencies of the proc...

Testing differences between a treatment and control group is common practice in biomedical research like randomized controlled trials (RCT). The standard two-sample t test relies on null hypothesis significance testing (NHST) via p values, which has several drawbacks. Bayesian alternatives were recently introduced using the Bayes factor, which has...

Hypothesis testing is an essential statistical method in experimental psychology and the cognitive sciences. The problems of traditional null hypothesis significance testing (NHST) have been discussed widely, and among the proposed solutions to the replication problems caused by the inappropriate use of significance tests and p-values is a shift to...

Hypothesis testing is a central statistical method in psychology and the cognitive sciences. However, the problems of null hypothesis significance testing (NHST) and p values have been debated widely, but few attractive alternatives exist. This article introduces the R package, which implements the Full Bayesian Significance Test (FBST) to test a s...

Background Null hypothesis significance testing (NHST) is among the most frequently employed methods in the biomedical sciences. However, the problems of NHST and p -values have been discussed widely and various Bayesian alternatives have been proposed. Some proposals focus on equivalence testing, which aims at testing an interval hypothesis instea...

Hypothesis testing is a central statistical method in the biomedical sciences. The ongoing debate about the concept of statistical significance and the reliability of null hypothesis significance tests (NHST) and p-values has brought the advent of various Bayesian hypothesis tests as possible alternatives, which often employ the Bayes factor. Howev...

The Full Bayesian Significance Test (FBST) and the Bayesian evidence value recently have received increasing attention across a variety of sciences including psychology. Ly and Wagenmakers (2021) have provided a critical evaluation of the method and concluded that it suffers from four problems which are mostly attributed to the asymptotic relations...

Testing for differences between two groups is among the most frequently carried out statistical methods in empirical research. The traditional frequentist approach is to make use of null hypothesis significance tests which use p values to reject a null hypothesis. Recently, a lot of research has emerged which proposes Bayesian versions of the most...

Student's two-sample t-test is often used in medical research like randomized controlled trials. To control type I errors, normality of the observed data needs to be assessed. In practice, a two-stage procedure is acknowledged: First, a preliminary test for normality is conducted. If the test is not significant, the two-sample t-test is applied, an...

Comparison of competing statistical models is an essential part of psychological research. From a Bayesian perspective, various approaches to model comparison and selection have been proposed in the literature. However, the applicability of these approaches depends on the assumptions about the model space M. Also, traditional methods like leave-one...

In this book review, I offer a chapter-by-chapter recension and general comments about Richard McElreath’s second edition of Statistical Rethinking: A Bayesian Course with Examples in R and STAN. Two examples of linear regression modeling and the generalized linear model with the book’s own R package rethinking highlight the flexibility and usefuln...

Objectives: The data presented herein represents the simulated datasets of a recently conducted larger study which investigated the behaviour of Bayesian indices of significance and effect size as alternatives to traditional p-values. The study considered the setting of Student's and Welch's two-sample t-test often used in medical research. It inv...

Testing for differences between two groups is one of the scenarios most often faced by scientists across all domains and is particularly important in the medical sciences and psychology. The traditional solution to this problem is rooted inside the Neyman–Pearson theory of null hypothesis significance testing and uniformly most powerful tests. In t...

Testing differences between a treatment and control group is common practice in biomedical research like randomized controlled trials (RCT). The standard two-sample t-test relies on null hypothesis significance testing (NHST) via p-values, which has several drawbacks. Bayesian alternatives were recently introduced using the Bayes factor, which has...

Typical situations in research include the comparison of two groups regarding a metric variable, in which case usually the two-sample t-test is applied. While common frequentist two-sample t-tests focus on the difference of means of both groups via a p-value, the quantity of interest in applied research most often is the effect size. Existing Bayes...

Background: Although null hypothesis significance testing (NHST) is the agreed gold standard in medical decision making and the most widespread inferential framework used in medical research, it has several drawbacks. Bayesian methods can complement or even replace frequentist NHST, but these methods have been underutilised mainly due to a lack of...

Hypothesis testing is a central statistical method in psychology and the cognitive sciences. However, the problems of null hypothesis significance testing (NHST) and p-values have been debated widely, but few attractive alternatives exist. This article introduces the fbst R package, which implements the Full Bayesian Significance Test (FBST) to tes...

Hypothesis testing is a central statistical method in psychological research and the cognitive sciences. While the problems of null hypothesis significance testing (NHST) have been debated widely, few attractive alternatives exist. In this paper, we provide a tutorial on the Full Bayesian Significance Test (FBST) and the e-value, which is a fully B...

Hypothesis testing is an essential statistical method in psychology and the cognitive sciences. The problems of traditional null hypothesis significance testing (NHST) have been discussed widely, and among the proposed solutions to the replication problems caused by the inappropriate use of significance tests and $p$-values is a shift towards Bayes...

Comparison of competing statistical models is an essential part of psychological research. From a Bayesian perspective, various approaches to model comparison and selection have been proposed in the literature. However, the applicability of these approaches strongly depends on the assumptions about the model space $\mathcal{M}$, the so-called model...

Background: The replication crisis hit the medical sciences about a decade ago, but today still most of the flaws inherent in null hypothesis significance testing (NHST) have not been solved. While the drawbacks of p-values have been detailed in endless venues, for clinical research, only a few attractive alternatives have been proposed to replace...

Survival analysis is an important analytic method in the social and medical sciences. Also known under the name time-to-event analysis, this method provides parameter estimation and model fitting commonly conducted via maximum-likelihood. Bayesian survival analysis offers multiple advantages over the frequentist approach for measurement practitione...

Teaching and learning programming is a challenge. Although several learning and programming environments have been proposed for classes, there seems to be more dissent than consensus as to which tools are preferable over others. This paper investigates teachers’ perspectives on popular learning and programming environments used in secondary compute...

The object-oriented programming (OOP) paradigm is quite prominent in German secondary schools. To challenge and overcome possible difficulties in the learning process it is vital for educators to have knowledge about possible (mis-)conceptions. Traditionally, these are gathered by investigating the mental models of students, e.g. towards object-ori...