Kimihiro Noguchi

Western Washington University
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Abstract

Effect Size Measures and Range-Preserving Confidence Intervals

The range of values that data can take are often restricted to a subset of real numbers, such as positive numbers or numbers between 0 and 1. For such data, it is desirable to formulate confidence intervals which mathematically guarantee that any number in these intervals is in the allowable range of values. A confidence interval with this favorable property is referred to as a range-preserving confidence interval. Assessing the statistical significance visually using these range-preserving confidence intervals gives an immediate advantage of easily understanding statistical results. Moreover, a surprisingly nice relationship between the generalized Welch’s \(t\)-test and commonly used effect sizes is presented, indicating that it is possible to come up with a test statistic with a consistent effect size measure. Some simulation results, a real-life example, and current projects which extend the idea to multiple samples are presented.