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Hedges d, an existing unbiased effect size of the difference between means, assumes the variance equality. However, the assumption of the variance equality is fragile, and is often violated in practical applications. Here, we define e, a new effect size of the difference between means, which does not assume the variance equality. In addition, another novel statistic c is defined as an effect size of the difference between a mean and a known constant. Hedges g, our c, and e correspond to Students unpaired two-sample t test, Students one-sample t test, and Welchs t test, respectively. An R package is also provided to compute these effect sizes with their variance and confidence interval.
Comparing the differences in outcomes (that is, in dependent variables) between two subpopulations is often most informative when comparing outcomes only for individuals from the subpopulations who are similar according to independent variables. The
Many predictions are probabilistic in nature; for example, a prediction could be for precipitation tomorrow, but with only a 30 percent chance. Given both the predictions and the actual outcomes, reliability diagrams (also known as calibration plots)
Causal variance decompositions for a given disease-specific quality indicator can be used to quantify differences in performance between hospitals or health care providers. While variance decompositions can demonstrate variation in quality of care, c
We study the least squares estimator in the residual variance estimation context. We show that the mean squared differences of paired observations are asymptotically normally distributed. We further establish that, by regressing the mean squared diff
The detection of differentially expressed (DE) genes is one of the most commonly studied problems in bioinformatics. For example, the identification of DE genes between distinct disease phenotypes is an important first step in understanding and devel