Publication
Advantages of Variance Stabilization
Abstract
Variance stabilization is a simple device for normalizing a statistic. Even though its large sample properties are similar to those of studentizing, many simulation studies of confidence interval procedures show that variance stabilization works better for small samples. We investigated this question in the context of testing a null hypothesis involving a single parameter. We provide support for a measure of evidence for an alternative hypothesis that is simple to compute, calibrate and interpret. It has applications in most routine problems in statistics, and leads to more accurate confidence intervals, estimated power and hence sample size calculations than standard asymptotic methods. Such evidence is readily combined when obtained from different studies. Connections to other approaches to statistical evidence are described, with a notable link to Kullback–Leibler symmetrized divergence.
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Related concepts (35)
Statistical hypothesis testing
A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see .
Statistical significance
In statistical hypothesis testing, a result has statistical significance when a result at least as "extreme" would be very infrequent if the null hypothesis were true. More precisely, a study's defined significance level, denoted by , is the probability of the study rejecting the null hypothesis, given that the null hypothesis is true; and the p-value of a result, , is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. The result is statistically significant, by the standards of the study, when .
Sampling (statistics)
In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population, and thus, it can provide insights in cases where it is infeasible to measure an entire population.
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