<i>p</i>-Values: The Insight to Modern Statistical Inference

Fraser, D. A. S.

doi:10.1146/annurev-statistics-060116-054139

Cited by 15 publications

(10 citation statements)

References 28 publications

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“…Nuzzo discussed the key role of Pr(H a |data) in the decision making process, but she did not elaborate on how to implement a process to get to the desired outcome. Finally, Fraser (2017) demonstrates that p-values can be the bases for a complete inferential framework, and highlights the notion that the fact that p-values have been mis-used and even abused, this does not subtract from their worth as indicators of the distance between the data and a parameter value.…”

Section: Discussionmentioning

confidence: 91%

Quality Control for Scientific Research: Addressing Reproducibility, Responsiveness, and Relevance

Hubbard

Carriquiry

2019

The American Statistician

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Efforts to address a reproducibility crisis have generated several valid proposals for improving the quality of scientific research. We argue there is also need to address the separate but related issues of relevance and responsiveness. To address relevance, researchers must produce what decision makers actually need to inform investments and public policy-that is, the probability that a claim is true or the probability distribution of an effect size given the data. The term responsiveness refers to the irregularity and delay in which issues about the quality of research are brought to light. Instead of relying on the good fortune that some motivated researchers will periodically conduct efforts to reveal potential shortcomings of published research, we could establish a continuous quality-control process for scientific research itself. Quality metrics could be designed through the application of this statistical process control for the research enterprise. We argue that one quality control metric-the probability that a research hypothesis is true-is required to address at least relevance and may also be part of the solution for improving responsiveness and reproducibility. This article proposes a "straw man"solution which could be the basis of implementing these improvements. As part of this solution, we propose one way to "bootstrap" priors. The processes required for improving reproducibility and relevance can also be part of a comprehensive statistical quality control for science itself by making continuously monitored metrics about the scientific performance of a field of research.

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Section: Discussionmentioning

confidence: 91%

Quality Control for Scientific Research: Addressing Reproducibility, Responsiveness, and Relevance

Hubbard

Carriquiry

2019

The American Statistician

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“…Both ( ) and ( ) are asymptotically 2 . As defined in Fraser [7], the significance function for is defined as ( ) = ( 2 ≤ ( )) or ( ) = ( 2 ≤ ( )) can be used to obtain inference concerning where ( ) and ( ) are the observed values of ( ) and ( ), respectively. In particular, the (1− )100% confidence region of is…”

Section: Proposed Methodsmentioning

confidence: 99%

Improved Small Sample Inference on the Ratio of Two Coefficients of Variation of Two Independent Lognormal Distributions

Jiang¹

2019

Journal of Probability and Statistics

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Without the ability to use research tools and procedures that yield consistent measurements, researchers would be unable to draw conclusions, formulate theories, or make claims about generalizability of their results. In statistics, the coefficient of variation is commonly used as the index of reliability of measurements. Thus, comparing coefficients of variation is of special interest. Moreover, the lognormal distribution has been frequently used for modeling data from many fields such as health and medical research. In this paper, we proposed a simulated Bartlett corrected likelihood ratio approach to obtain inference concerning the ratio of two coefficients of variation for lognormal distribution. Simulation studies show that the proposed method is extremely accurate even when the sample size is small.

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“…Both approximations have third-order accuracy and are equivalent up to thirdorder accuracy (Fraser and Reid , 1995). Thus, as discussed in Fraser (2017), either approximation of the p-value function can be used to obtain inference for ψ.…”

Section: Saddlepoint Approximation For the Poisson-exponential Distrimentioning

confidence: 99%

Accurate Inference for the Mean of the Poisson-Exponential Distribution

Lin

2020

JIRSS

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Although the random sum distribution has been well-studied in probability theory, inference for the mean of such distribution is very limited in the literature. In this paper, two approaches are proposed to obtain inference for the mean of the Poisson-Exponential distribution. Both proposed approaches require the log-likelihood function of the Poisson-Exponential distribution, but the exact form of the log-likelihood function is not available. An approximate form of the log-likelihood function is then derived by the saddlepoint method. Inference for the mean of the Poisson-Exponential distribution can either be obtained from the modified signed likelihood root statistic or from the Bartlett corrected likelihood ratio statistic. The explicit form of the modified signed likelihood root statistic is derived in this paper, and a systematic method to numerically approximate the Bartlett correction factor, hence the Bartlett corrected likelihood ratio statistic is proposed. Simulation studies show that both methods are extremely accurate even when the sample size is small.

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p-Values: The Insight to Modern Statistical Inference

Cited by 15 publications

References 28 publications

Quality Control for Scientific Research: Addressing Reproducibility, Responsiveness, and Relevance

Quality Control for Scientific Research: Addressing Reproducibility, Responsiveness, and Relevance

Improved Small Sample Inference on the Ratio of Two Coefficients of Variation of Two Independent Lognormal Distributions

Accurate Inference for the Mean of the Poisson-Exponential Distribution

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