On robust estimation of the location parameter

Coronavirus disease 2019 (COVID-19) is characterized by distinct patterns of disease progression suggesting diverse host immune responses. We performed an integrated immune analysis on a cohort of 50 COVID-19 patients with various disease severity. A unique phenotype was observed in severe and critical patients, consisting of a highly impaired interferon (IFN) type I response (characterized by no IFN-β and low IFN-α production and activity), associated with a persistent blood viral load and an exacerbated inflammatory response. Inflammation was partially driven by the transcriptional factor NF-κB and characterized by increased tumor necrosis factor (TNF)-α and interleukin (IL)-6 production and signaling. These data suggest that type-I IFN deficiency in the blood could be a hallmark of severe COVID-19 and provide a rationale for combined therapeutic approaches.

https://science.sciencemag.org/content/sci/early/2020/07/10/science.abc6027.full.pdf

Impaired type I interferon activity and inflammatory responses in severe COVID-19 patients.

Likert questionnaires are widely used in survey research, but it is unclear whether the item data should be investigated by means of parametric or nonparametric procedures. This study compared the Type I and II error rates of the t test versus the Mann-Whitney-Wilcoxon (MWW) for five-point Likert items. Fourteen population distributions were defined and pairs of samples were drawn from the populations and submitted to the t test and the t test on ranks, which yields the same results as MWW. The results showed that the two tests had equivalent power for most of the pairs. MWW had a power advantage when one of the samples was drawn from a skewed or peaked distribution. Strong power differences between the t test and MWW occurred when one of the samples was drawn from a multimodal distribution. Notably, the Type I error rate of both methods was never more than 3% above the nominal rate of 5%, even not when sample sizes were highly unequal. In conclusion, for five-point Likert items, the t test and MWW generally have similar power, and researchers do not have to worry about finding a difference whilst there is none in the population.

Five-Point Likert Items: t test versus Mann-Whitney-Wilcoxon

The present study examined the process of shared leadership in 45 ad hoc decision-making teams. Each team member's leadership behavior (n = 180) was assessed by behaviorally coding videotapes of the teams' discussions. The within-team patterns of leadership behavior were examined using cluster analysis. Results indicated that the likelihood of a team experiencing a full range of leadership behavior increased to the extent that multiple team members shared leadership, and that teams with shared leadership experienced less conflict, greater consensus, and higher intragroup trust and cohesion than teams without shared leadership. This study supports previous findings that shared leadership contributes to overall team functioning, and begins to delineate the extent to which team members may naturally share leadership.

The Shared Leadership Process in Decision-Making Teams

In this study which was part of the DISUM-project, 224 ninth graders from 14 German classes from middle track schools (Realschule) were asked about their enjoyment, interest, value and self-efficacy expectations concerning three types of mathematical problems: intra-mathematical problems, word problems and modelling problems. Enjoyment, interest, value and self-efficacy were assessed before and after a ten-lesson teaching unit promoting modelling competency related to the topics “Pythagoras’ theorem” and “linear functions”. The study aimed to answer the following research questions: (1) Do students’ enjoyment, value, interest and self-efficacy expectations differ depending on the type of task? (2) Does the treatment of modelling problems in classroom instruction influence these variables? (3) Are there any differential effects for different ways of teaching modelling problems, including a “directive”, teacher-centred instruction and an “operative-strategic”, more student-centred instruction emphasising group work and strategic scaffolding by the teacher? The findings show that there were no differences in students’ enjoyment, interest, value and self-efficacy between the three types of tasks. However, teaching oriented towards modelling problems had positive effects on some of the student variables, with the student-centred teaching method producing the most beneficial effects.

Teaching methods for modelling problems and students’ task-specific enjoyment, value, interest and self-efficacy expectations

In psychological research sometimes non-parametric procedures are in use in cases, where the corresponding parametric procedure is preferable. This is mainly due to the fact that we pay too much attention to the possible violation of the normality assumption which is needed to derive the exact distribution of the statistic used in the parametric approach. An example is the t-test and its non-parametric counterpart, the Wilcoxon (MannWhitney) test. The Wilcoxon test compares the two distributions and may lead to significance even if the means are equal due to the fact that higher moments in the two populations differ. On the other hand the t-test is so robust against non-normality that there is nearly no need to use the Wilcoxon test. In this paper results of a systematic research of the robustness of statistical procedures against non-normality are presented. These results have been obtained in a research group in Dummerstorf (near Rostock) some years ago and have not been published systematically until now. Most of the results are based on extensive simulation experiments with 10 000 runs each. But there are also some exact mathematically derived results for very extreme deviations from normality (twoand three-point distributions). Generally the results are such that in most practical cases the parametric approach for inferences about means is so robust that it can be recommended in nearly all applications.

The robustness of parametric statistical methods

How robust are tests for two independent samples

Simultaneous confidence sets and confidence intervals for multiple ratios

Objectives: In this article, we illustrate and compare exact simultaneous confidence sets with various approximate simultaneous confidence intervals for multiple ratios as applied to many-to-one comparisons Quite different datasets are analyzed to clarify the points Methods: The methods are based on existing probability inequalities (eg, Bonferroni, Slepian and Sidak), estimation of nuisance parameters and re-sampling techniques Exact simultaneous confidence sets based on the multivariate t -distribution are constructed and compared with approximate simultaneous confidence intervals Results: It is found that the coverage probabilities associated with the various methods of constructing simultaneous confidence intervals (for ratios) in manyto- one comparisons depend on the ratios of the coefficient of variation for the mean of the control group to the coefficient of variation for the mean of the treatments If the ratios of the coefficients of variations are less than one, the Bonferroni corrected Fieller confidence intervals have almost the same coverage probability as the exact simultaneous confidence sets Otherwise, the use of Bonferroni intervals leads to conservative results Conclusions: When the ratio of the coefficient of variation for the mean of the control group to the coefficient of variation for the mean of the treatments are greater than one (eg, in balanced designs with increasing effects), the Bonferroni simultaneous confidence intervals are too conservative Therefore, we recommend not using Bonferroni for this kind of data On the other hand, the plug-in method maintains the intended confidence coefficient quite satisfactorily; therefore, it can serve as the best alternative in any case

Simultaneous confidence intervals for ratios with applications to the comparison of several treatments with a control.

In this paper, we address the problem of calculating power and sample sizes associated with simultaneous tests for non-inferiority. We consider the case of comparing several experimental treatments with an active control. The approach is based on the ratio view, where the common non-inferiority margin is chosen to be some percentage of the mean of the control treatment. Two power definitions in multiple hypothesis testing, namely, complete power and minimal power, are used in the computations. The sample sizes associated with the ratio-based inference are also compared with that of a comparable inference based on the difference of means for various scenarios. It is found that the sample size required for ratio-based inferences is smaller than that of difference-based inferences when the relative non-inferiority margin is less than one and when large response values indicate better treatment effects. The results are illustrated with examples.

Volker Guiard

Papers

The robustness of parametric statistical methods

How robust are tests for two independent samples

Simultaneous confidence sets and confidence intervals for multiple ratios

Simultaneous confidence intervals for ratios with applications to the comparison of several treatments with a control.

Power and sample size computations in simultaneous tests for non‐inferiority based on relative margins