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Instead of relying on null-hypothesis significance testing (NHST), researchers are consistently advised to use effect sizes (ESs) and confidence intervals (CIs) to convey research findings. However, typical ES measures for most linear models (e.g., multiple regression) assume data normality, a condition that is often violated in behavioral research. This may lead to inaccurate interpretation of ES. In multiple regression models, Cohen's f2, R2 and R adj 2 are employed by researchers, but no study has systematically evaluated their robustness in practice. Thus, this Monte Carlo simulation study evaluates the robustness of f2, R2 and R adj 2 and the associated CIs based on manipulated levels of sample sizes, magnitudes of ESs, numbers of predictors, and data violations (i.e., heavy-tailed, skewed, contaminated, lognormal, and heteroscedastic distributions of errors). This study offers guidelines regarding how robust these ESs are so that researchers can report the most appropriate ES in their research studies. [ABSTRACT FROM AUTHOR]

One of the indicators for evaluating the capability of a process is the process capability index. In this article, bootstrap confidence intervals of the generalized process capability index (GPCI) proposed by Maiti et al. are studied through simulation, when the underlying distributions are Lindley and Power Lindley distributions. The maximum likelihood method is used to estimate the parameters of the models. Three bootstrap confidence intervals namely, standard bootstrap (SB), percentile bootstrap (PB), and bias-corrected percentile bootstrap (BCPB) are considered for obtaining confidence intervals of GPCI. A Monte Carlo simulation has been used to investigate the estimated coverage probabilities and average width of the bootstrap confidence intervals. Simulation results show that the estimated coverage probabilities of the percentile bootstrap confidence interval and the bias-corrected percentile bootstrap confidence interval get closer to the nominal confidence level than those of the standard bootstrap confidence interval. Finally, three real datasets are analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

One standard summary of a clinical trial is a confidence limit for the effect of the treatment. Unfortunately, standard approximate limitsmay have poor frequentist properties, even for quite large sample sizes. It has been known since Buehler (1957) that an imperfect confidence limit can be adjusted to have exact coverage. These "tight" limits are the gold standard frequentist confidence limit. Computing tight limits requires exact calculation of certain tail probabilities and optimisation of potentially erratic functions of the nuisance parameter. Naive implementation is both computationally unreliable and highly burdensome, and perhaps explains why they are not in common use. For clinical trials however, where the data and parameter have dimension two, the difficulties can be fully surmounted. This paper brings together several results in the area and applies them to simple two dimensional problems. It is shown how to reduce the computational burden by an order of magnitude. Difficulties with the optimisation reliability are mitigated by applying two different computational strategies,which tend to break down under different conditions, and taking the less stringent of the two computed limits. This paper specifically develops limits for the relative risk in a clinical trial, but it should be clear to the reader that the method extends to arbitrary measures of treatment effect without essential modification. [ABSTRACT FROM AUTHOR]

This study aims to provide a reliable confidence interval for assessing the process incapability index [Cpp]. The concept of the generalized pivotal quantities is utilized for constructing the generalized confidence interval for [Cpp]. And, simulations are performed for demonstrating our proposed method and one existent method. The results show that the empirical confidences of these two methods are significantly affected by the degree of process departure. Therefore, we suggest the practitioners to select proper one for capability testing purpose based on the information of degree of process departure. [ABSTRACT FROM AUTHOR]

In this study, we consider the construction of the confidence interval for the population proportion while using group testing with misclassification. We propose two confidence intervals based on Cornish-Fisher expansion and a modified Wilson's interval based on a newly developed estimator. We investigate the performance of these intervals extensively and also apply the methods to real datasets. Our newly derived methods have competitive performance compared with existing methods. [ABSTRACT FROM AUTHOR]

In the estimation of a proportion p by group testing (pooled testing), retesting of units within positive groups has received little attention due to the minimal gain in precision compared to testing additional units. If acquisition of additional units is impractical or too expensive, and testing is not destructive, we show that retesting can be a useful option. We propose the retesting of a random grouping of units from positive groups, and compare it with nested halving procedures suggested by others. We develop an estimator of p for our proposed method, and examine its variance properties. Using simulation we compare retesting methods across a range of group testing situations, and show that for most realistic scenarios, our method is more efficient. [ABSTRACT FROM AUTHOR]