To obtain reliable measures researchers prefer multiple-item questionnaires rather than single-item tests. Multiple-item questionnaires may be costly however and timeconsuming for participants to complete. They therefore frequently administer twoitem measures, the reliability of which is commonly assessed by computing a reliability coefficient. There is some disagreement, however, what the most appropriate indicator of scale reliability is when a measure is composed of two items.The most frequently reported reliability statistic for multiple-item scales is Cronbach's coefficient alpha and many researchers report this coefficient for their two-item measure 1,2,3,4 . Others however claim that coefficient alpha is inappropriate and meaningless for two-item scales. Instead, they recommend using the Pearson correlation coefficient as a measure of reliability 5,6,7,8 . Still others argue that the interitem correlation equals the split-half reliability estimate for the two-item measure and they advocate the use of the Spearman-Brown formula to estimate the reliability of the total scale 9 . As these recommendations are reported without elaborating, there is considerable confusion among end users as to the best reliability coefficient for twoitem measures. This note aims to clarify the issue.It is important to emphasize at the outset that it is not our intention in this paper to promote the use of two-item scales. Quite the contrary, having only two items to identify an underlying construct has been recognized as problematic for some time and we support the claim that using more items is better 10,11,12 . The use of multiple, heterogeneous indicators enhances construct validity in the sense that it

influence.ME provides tools for detecting influential data in mixed effects models. The application of these models has become common practice, but the development of diagnostic tools has lagged behind. influence.ME calculates standardized measures of influential data for the point estimates of generalized mixed effects models, such as DFBETAS, Cook's distance, as well as percentile change and a test for changing levels of significance. influence.ME calculates these measures of influence while accounting for the nesting structure of the data. The package and measures of influential data are introduced, a practical example is given, and strategies for dealing with influential data are suggested.

influence.ME provides tools for detecting influential data in mixed effects models. The application of these models has become common practice, but the development of diagnostic tools has lagged behind. influence.ME calculates standardized measures of influential data for the point estimates of generalized mixed effects models, such as DFBETAS, Cook's distance, as well as percentile change and a test for changing levels of significance. influence.ME calculates these measures of influence while accounting for the nesting structure of the data. The package and measures of influential data are introduced, a practical example is given, and strategies for dealing with influential data are suggested.

No abstract

No abstract

No abstract

BackgroundThe Friedman rank sum test is a widely-used nonparametric method in computational biology. In addition to examining the overall null hypothesis of no significant difference among any of the rank sums, it is typically of interest to conduct pairwise comparison tests. Current approaches to such tests rely on large-sample approximations, due to the numerical complexity of computing the exact distribution. These approximate methods lead to inaccurate estimates in the tail of the distribution, which is most relevant for p-value calculation.ResultsWe propose an efficient, combinatorial exact approach for calculating the probability mass distribution of the rank sum difference statistic for pairwise comparison of Friedman rank sums, and compare exact results with recommended asymptotic approximations. Whereas the chi-squared approximation performs inferiorly to exact computation overall, others, particularly the normal, perform well, except for the extreme tail. Hence exact calculation offers an improvement when small p-values occur following multiple testing correction. Exact inference also enhances the identification of significant differences whenever the observed values are close to the approximate critical value. We illustrate the proposed method in the context of biological machine learning, were Friedman rank sum difference tests are commonly used for the comparison of classifiers over multiple datasets.ConclusionsWe provide a computationally fast method to determine the exact p-value of the absolute rank sum difference of a pair of Friedman rank sums, making asymptotic tests obsolete. Calculation of exact p-values is easy to implement in statistical software and the implementation in R is provided in one of the Additional files and is also available at http://www.ru.nl/publish/pages/726696/friedmanrsd.zip.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-017-1486-2) contains supplementary material, which is available to authorized users.

When parameterized in terms of Pearson correlations, the two variance inflation factors give quantitative insight into the impact of the number of clusters, subjects and evaluations on power. Moreover, subject matter knowledge as well as ICCs from 2-level cluster randomized trials can be incorporated in the sample size calculation, when empirical estimates of variance components or ICCs from a pilot or comparable 3-level study are lacking.