Personal Computers, p-Values, and Hypothesis Testing

1984 ◽  
Vol 77 (6) ◽  
pp. 473-478
Author(s):  
Larry A. Morgan ◽  
Frank W. Morgan
Keyword(s):  
Hypothesis Testing ◽  
Mathematics Teacher ◽  
Personal Computers ◽  
P Values ◽  
Probability And Statistics

The increasing availability of microcomputers in schools throughout the nation enables today's mathematics teacher to introduce students to the ideas of probability and statistics in creative and challenging ways.

scholarly journals Model Averaging with AIC Weights for Hypothesis Testing of Hormesis at Low Doses

Dose-Response ◽  
2017 ◽  
Vol 15 (2) ◽  
pp. 155932581771531
Author(s):  
Steven B. Kim ◽  
Nathan Sanders
Keyword(s):  
Hypothesis Testing ◽  
Dose Response ◽  
Statistical Power ◽  
Parametric Model ◽  
Semiparametric Models ◽  
Parametric Models ◽  
Large Sample Size ◽  
Low Doses ◽  
P Values ◽  
The Impact

For many dose–response studies, large samples are not available. Particularly, when the outcome of interest is binary rather than continuous, a large sample size is required to provide evidence for hormesis at low doses. In a small or moderate sample, we can gain statistical power by the use of a parametric model. It is an efficient approach when it is correctly specified, but it can be misleading otherwise. This research is motivated by the fact that data points at high experimental doses have too much contribution in the hypothesis testing when a parametric model is misspecified. In dose–response analyses, to account for model uncertainty and to reduce the impact of model misspecification, averaging multiple models have been widely discussed in the literature. In this article, we propose to average semiparametric models when we test for hormesis at low doses. We show the different characteristics of averaging parametric models and averaging semiparametric models by simulation. We apply the proposed method to real data, and we show that P values from averaged semiparametric models are more credible than P values from averaged parametric methods. When the true dose–response relationship does not follow a parametric assumption, the proposed method can be an alternative robust approach.

Mathematics and Statistics in Anesthesiology

2018 ◽  
Author(s):  
Daniel Mortlock
Keyword(s):  
Probability Theory ◽  
Data Analysis ◽  
Survey Design ◽  
Probability Distributions ◽  
Statistical Tests ◽  
Real World Data ◽  
Mathematical Functions ◽  
P Values ◽  
Bayesian Data Analysis ◽  
Probability And Statistics

Mathematics is the language of quantitative science, and probability and statistics are the extension of classical logic to real world data analysis and experimental design. The basics of mathematical functions and probability theory are summarized here, providing the tools for statistical modeling and assessment of experimental results. There is a focus on the Bayesian approach to such problems (ie, Bayesian data analysis); therefore, the basic laws of probability are stated, along with several standard probability distributions (eg, binomial, Poisson, Gaussian). A number of standard classical tests (eg, p values, the t-test) are also defined and, to the degree possible, linked to the underlying principles of probability theory. This review contains 5 figures, 1 table, and 15 references. Keywords: Bayesian data analysis, mathematical models, power analysis, probability, p values, statistical tests, statistics, survey design

scholarly journals Making Decisions with Data: Understanding Hypothesis Testing & Statistical Significance

2019 ◽  
Vol 81 (8) ◽  
pp. 535-542
Author(s):  
Robert A. Cooper
Keyword(s):  
Hypothesis Testing ◽  
Statistical Methods ◽  
Scientific Literacy ◽  
Statistical Significance ◽  
Statistical Hypothesis ◽  
Statistical Hypothesis Testing ◽  
P Values ◽  
Using Data ◽  
Science Classes ◽  
Practice Of Science

Statistical methods are indispensable to the practice of science. But statistical hypothesis testing can seem daunting, with P-values, null hypotheses, and the concept of statistical significance. This article explains the concepts associated with statistical hypothesis testing using the story of “the lady tasting tea,” then walks the reader through an application of the independent-samples t-test using data from Peter and Rosemary Grant's investigations of Darwin's finches. Understanding how scientists use statistics is an important component of scientific literacy, and students should have opportunities to use statistical methods like this in their science classes.

Bayesian Hypothesis Testing for Hospitality and Tourism Research

2020 ◽  
pp. 109634802094732
Author(s):  
A. George Assaf ◽  
Mike Tsionas
Keyword(s):  
Hypothesis Testing ◽  
Bayesian Approach ◽  
Prior Distributions ◽  
P Values ◽  
Tourism Research ◽  
Bayesian Hypothesis Testing ◽  
Main Challenge ◽  
Hospitality And Tourism ◽  
Practical Recommendations ◽  
The Bayesian Approach

In hospitality and tourism research, p-values continue to be the most common approach to hypothesis testing. In this article, we elaborate on some of the misconceptions associated with p-values. We discuss the advantages of the Bayesian approach and provide several important practical recommendations and considerations for Bayesian hypothesis testing. With the main challenge of Bayesian hypothesis testing being the sensitivity of the results to prior distributions, we present in this article several priors that can be used for that purpose and illustrate their performance in a regression context.

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