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Many psychologists do not realize that exploratory use of the popular multiway analysis of variance harbors a multiple-comparison problem. In the case of two factors, three separate null hypotheses are subject to test (i.e., two main effects and one interaction). Consequently, the probability of at least one Type I error (if all null hypotheses are true) is 14 % rather than 5 %, if the three tests are independent. We explain the multiple-comparison problem and demonstrate that researchers almost never correct for it. To mitigate the problem, we describe four remedies: the omnibus F test, control of the familywise error rate, control of the false discovery rate, and preregistration of the hypotheses.

Adsorption cooling technologies driven by low-grade thermal or solar power are used as an energy-efficient alternative to conventional refrigeration and air conditioning systems. Explicit understanding of the adsorption cycles requires precise determination of the performance parameters, replication of the experimental data, and the rigorous study of the adsorption heat transformation method. Hence, the optimum adsorption isotherms model must be identified. Scientists often face difficulties in selecting the suitable isotherm model as there are many models for a particular form of adsorption isotherm. The present study introduces a novel approach for choosing the optimal models for each type of International Union of Pure and Applied Chemistry (IUPAC) classified adsorption isotherm using robust statistical methods. First, the box-and-whisker plots of error identification are employed. Tóth for Type-I(a) and Type-I(b), modified BET for Type-II, GAB for Type-III, Universal for Type-IV(a), and Type-IV(b), Sun Chakrabarty for Type-V, and Yahia et al. for Type-VI were found lower than the other candidate models in box-and-whisker plot. The optimality of our selected models was further verified using analysis of variance (ANOVA), pairwise Tukey honest significant difference (HSD) test, Kruskal–Wallis rank-sum test, and pairwise Wilcoxon rank-sum test. In short, rigorous statistical analysis was performed to identify the best model for each type of isotherm by minimizing error. Moreover, specific cooling effect (SCE) of Maxsorb III/ethanol and silica gel/water pairs were determined. Results showed that Tóth is the optimal isotherm model for the studied pairs, and the SCE values obtained from the model agree well with experimental data. The optimum isotherm model is indispensable for the precise designing of the next generation adsorption cooling cycles.

The robustness of F-test to non-normality has been studied from the 1930s through to the present day. However, this extensive body of research has yielded contradictory results, there being evidence both for and against its robustness. This study provides a systematic examination of F-test robustness to violations of normality in terms of Type I error, considering a wide variety of distributions commonly found in the health and social sciences. We conducted a Monte Carlo simulation study involving a design with three groups and several known and unknown distributions. The manipulated variables were: Equal and unequal group sample sizes; group sample size and total sample size; coefficient of sample size variation; shape of the distribution and equal or unequal shapes of the group distributions; and pairing of group size with the degree of contamination in the distribution. The results showed that in terms of Type I error the F-test was robust in 100% of the cases studied, independently of the manipulated conditions.

This paper shows the novel approach of Taguchi-Based Grey Relational Analysis of Ti6Al4V Machining parameter. Ti6Al4V metal matrix composite has been fabricated using the powder metallurgy route. Here, all the components of TI6Al4V machining forces, including longitudinal force (Fx), radial force (Fy), tangential force (Fz), surface roughness and material removal rate (MRR) are measured during the facing operation. The effect of three process parameters, cutting speed, tool feed and cutting depth, is being studied on the matching responses. Orthogonal design of experiment (Taguchi L9) has been adopted to execute the process parameters in each level. To validate the process output parameters, the Grey Relational Analysis (GRA) optimization approach was applied. The percentage contribution of machining parameters to the parameter of response performance was interpreted through variance analysis (ANOVA). Through the GRA process, the emphasis was on the fact that for TI6Al4V metal matrix composite among all machining parameters, tool feed serves as the highest contribution to the output responses accompanied by the cutting depth with the cutting speed in addition. From optimal testing, it is found that for minimization of machining forces, maximization of MRR and minimization of Ra, the best combinations of input parameters are the 2nd stage of cutting speed (175 m/min), the 3rd stage of feed (0.25 mm/edge) as well as the 2nd stage of cutting depth (1.2 mm). It is also found that hardness of Ti6Al4V MMC is 59.4 HRA and composition of that material remain the same after milling operation.

Contrast analysis has become prevalent in experimental accounting research since Buckless and Ravenscroft (1990) introduced it to the accounting literature over 25 years ago. Since its initial introduction, the scope of contrast testing has expanded, yet guidance as to the most appropriate methods of specifying, conducting, interpreting, and exhibiting these tests has not. We survey the use of contrast analysis in the recent literature and propose a three-part testing approach that provides a more comprehensive picture of contrast results. Our approach considers three pieces of complementary evidence: the visual evaluation of fit, traditional significance testing, and quantitative evaluation of the contrast variance residual. Our measure of the contrast variance residual, 𝑞², is proposed for the first time in this work. After proposing our approach, we walk through six common contrast testing scenarios where current practices may fall short and our approach may guide researchers. We extend Buckless and Ravenscroft (1990) and contribute to the accounting research methods literature by documenting current contrast analysis practices that result in elevated Type I error and by proposing a potential solution to mitigate these concerns.

Climate change impacts on water availability and hydrological extremes are major concerns as regards the Sustainable Development Goals. Impacts on hydrology are normally investigated as part of a modelling chain, in which climate projections from multiple climate models are used as inputs to multiple impact models, under different greenhouse gas emissions scenarios, which result in different amounts of global temperature rise. While the goal is generally to investigate the relevance of changes in climate for the water cycle, water resources or hydrological extremes, it is often the case that variations in other components of the model chain obscure the effect of climate scenario variation. This is particularly important when assessing the impacts of relatively lower magnitudes of global warming, such as those associated with the aspirational goals of the Paris Agreement. In our study, we use ANOVA (analyses of variance) to allocate and quantify the main sources of uncertainty in the hydrological impact modelling chain. In turn we determine the statistical significance of different sources of uncertainty. We achieve this by using a set of five climate models and up to 13 hydrological models, for nine large scale river basins across the globe, under four emissions scenarios. The impact variable we consider in our analysis is daily river discharge. We analyze overall water availability and flow regime, including seasonality, high flows and low flows. Scaling effects are investigated by separately looking at discharge generated by global and regional hydrological models respectively. Finally, we compare our results with other recently published studies. We find that small differences in global temperature rise associated with some emissions scenarios have mostly significant impacts on river discharge-however, climate model related uncertainty is so large that it obscures the sensitivity of the hydrological system.

This study investigated the effect of crushed corn cob reinforcement on the compressive strength of composite materials with a hybrid matrix based on dammar (60%) and a synthetic epoxy (Resoltech 1050 with 1058s hardener). While previous research has explored mechanical and chemical properties of such composites, as well as the role of dammar resin, the specific impact of crushed corn cob on compressive strength had not yet been addressed. Materials with reinforcement mass fractions between 50% and 67% were fabricated, each with 15 samples. Power Analysis confirmed the sample size was statistically valid. A null hypothesis—stating that crushed corn cob has no significant influence on compressive strength—was tested and rejected (p < 0.05) using one-way ANOVA. Welch ANOVA confirmed the result (Fw > 2.49), and Kolmogorov-Smirnov tests showed data normality (p > 0.05). Post hoc ANOVA with Bonferroni correction confirmed significant differences between groups. The key finding was that beyond 66% crushed corn cob content, the materials lose engineering relevance due to inadequate compressive strength.

Repeated measures designs are commonly used in health and social sciences research. Although there are other, more advanced, statistical analyses, the F-statistic of repeated measures analysis of variance (RM-ANOVA) remains the most widely used procedure for analyzing differences in means. The impact of the violation of normality has been extensively studied for between-subjects ANOVA, but this is not the case for RM-ANOVA. Therefore, studies that extensively and systematically analyze the robustness of RM-ANOVA under the violation of normality are needed. This paper reports the results of two simulation studies aimed at analyzing the Type I error and power of RM-ANOVA when the normality assumption is violated but sphericity is fulfilled. Study 1 considered 20 distributions, both known and unknown, and we manipulated the number of repeated measures (3, 4, 6, and 8) and sample size (from 10 to 300). Study 2 involved unequal distributions in each repeated measure. The distributions analyzed represent slight, moderate, and severe deviation from normality. Overall, the results show that the Type I error and power of the F-statistic are not altered by the violation of normality. RM-ANOVA is generally robust to non-normality when the sphericity assumption is met.

The a priori calculation of statistical power has become common practice in behavioral and social sciences to calculate the necessary sample size for detecting an expected effect size with a certain probability (i.e., power). In multi-factorial repeated measures ANOVA, these calculations can sometimes be cumbersome, especially for higher-order interactions. For designs that only involve factors with two levels each, the paired t test can be used for power calculations, but some pitfalls need to be avoided. In this tutorial, we provide practical advice on how to express main and interaction effects in repeated measures ANOVA as single difference variables. In particular, we demonstrate how to calculate the effect size Cohen’s d of this difference variable either based on means, variances, and covariances of conditions or by transforming η p 2 or ω p 2 from the ANOVA framework into d . With the effect size correctly specified, we then show how to use the t test for sample size considerations by means of an empirical example. The relevant R code is provided in an online repository for all example calculations covered in this article.