Theoretical Backgrounds of the Statistical Methods. Underlying Probabiilty Model Used in Making a Statistical Inference.

1951 ◽  
Vol 43 (6) ◽  
pp. 1295-1297 ◽  
Author(s):  
Frederick Mosteller
Keyword(s):  
Statistical Inference ◽  
Statistical Methods

scholarly journals Simple methods for estimating confidence levels, or tentative probabilities, for hypotheses instead of p values

2019 ◽  
Vol 12 (1) ◽  
pp. 205979911982651
Author(s):  
Michael Wood
Keyword(s):  
Statistical Inference ◽  
Confidence Intervals ◽  
Statistical Methods ◽  
Null Hypothesis ◽  
Significance Tests ◽  
P Values ◽  
Confidence Levels ◽  
Alternative Approach ◽  
Degree Of Certainty ◽  
Natural Way

In many fields of research, null hypothesis significance tests and p values are the accepted way of assessing the degree of certainty with which research results can be extrapolated beyond the sample studied. However, there are very serious concerns about the suitability of p values for this purpose. An alternative approach is to cite confidence intervals for a statistic of interest, but this does not directly tell readers how certain a hypothesis is. Here, I suggest how the framework used for confidence intervals could easily be extended to derive confidence levels, or “tentative probabilities,” for hypotheses. I also outline four quick methods for estimating these. This allows researchers to state their confidence in a hypothesis as a direct probability, instead of circuitously by p values referring to a hypothetical null hypothesis—which is usually not even stated explicitly. The inevitable difficulties of statistical inference mean that these probabilities can only be tentative, but probabilities are the natural way to express uncertainties, so, arguably, researchers using statistical methods have an obligation to estimate how probable their hypotheses are by the best available method. Otherwise, misinterpretations will fill the void.

scholarly journals Statistical inferences about injury and persistence of environmentally stressed bacteria

1975 ◽  
Vol 74 (2) ◽  
pp. 149-155 ◽  
Author(s):  
Martin A. Hamilton ◽  
Gary K. Bissonnette
Keyword(s):  
Statistical Inference ◽  
Poisson Distribution ◽  
Statistical Methods ◽  
Standard Technique ◽  
Binomial Data ◽  
Selective Media ◽  
Statistical Inferences ◽  
Table Data

SUMMARYA standard technique for ascertaining the survival characteristics of bacteria after being environmentally stressed is to incubate the bacteria on both selective and non-selective media and count the colonies produced. Based on these colony counts, indexes of injury and persistence of the bacteria are calculated. To compare the stress of two different environments, a persistence ratio is calculated. In this paper, methods of statistical inference concerning these indexes and ratios are presented. These statistical methods use well-known procedures for analysis of binomial data and 2 × 2 table data, and are appropriate when the colony counts follow a Poisson distribution.

Some Comments on Teaching Biostatistics in Medical and Health Sciences

1990 ◽  
Vol 29 (01) ◽  
pp. 41-43 ◽  
Author(s):  
H. Sahai
Keyword(s):  
Statistical Inference ◽  
Statistical Methods ◽  
Medical Diagnosis ◽  
Health Sciences ◽  
Diagnosis And Prognosis ◽  
Teachers And Students ◽  
Health Sciences Students

AbstractThe role of statistical methods is now well recognized in health sciences since these disciplines are concerned with the study of communities or populations where the principles of sampling and statistical inference are clearly applicable. However, many medical and health sciences teachers and students have been slower to perceive the need for knowledge of biostatistical methods, even though all aspects of medical diagnosis and prognosis are governed by the laws of probability. Some of them are still skeptical about the value and importance of biostatistical principles to their fields and raise questions about the meaning, content, and nature of biostatistics and relevance of its teaching to health sciences disciplines. The purpose of this essay is to address some of these issues with the hope to invoke comments and responses from other biostatistics instructors who have encountered similar predicaments in their teaching and consulting roles to health sciences students and professionals.

scholarly journals About Statistical Thinking in Pedagogics. On the Margin of the Reading of Wiesław Szymczak’s book The practice of Statistical Inference

2020 ◽  
Vol 43 (1) ◽  
pp. 251-261
Author(s):  
Sławomir Pasikowski
Keyword(s):  
Statistical Theory ◽  
Statistical Inference ◽  
Statistical Methods ◽  
Statistical Thinking

Summary The article is devoted to the issue of statistical thinking in pedagogy and research conducted in this discipline. Inspired by the readings of the book by Wiesław Szymczak, The Practice of Statistical Inference, it contains comments on popular associations and misunderstandings about what statistics is, what its principles and goals are, and therefore also comments on the using of statistical methods inconsistently with the underlying assumptions of statistical theory.

Non-Standard Parametric Statistical Inference

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Statistical Inference ◽  
Statistical Methods ◽  
Model Building ◽  
Parametric Bootstrap ◽  
Basic Knowledge ◽  
Standard Theory ◽  
Regularity Conditions ◽  
Parameter Estimates ◽  
Bootstrap Resampling ◽  
Distributional Properties

This book discusses the fitting of parametric statistical models to data samples. Emphasis is placed on (i) how to recognize situations where the problem is non-standard, when parameter estimates behave unusually, and (ii) the use of parametric bootstrap resampling methods in analysing such problems. Simple and practical model building is an underlying theme. A frequentist viewpoint based on likelihood is adopted, for which there is a well-established and very practical theory. The standard situation is where certain widely applicable regularity conditions hold. However, there are many apparently innocuous situations where standard theory breaks down, sometimes spectacularly. Most of the departures from regularity are described geometrically in the book, with mathematical detail only sufficient to clarify the non-standard nature of a problem and to allow formulation of practical solutions. The book is intended for anyone with a basic knowledge of statistical methods typically covered in a university statistical inference course who wishes to understand or study how standard methodology might fail. Simple, easy-to-understand statistical methods are presented which overcome these difficulties, and illustrated by detailed examples drawn from real applications. Parametric bootstrap resampling is used throughout for analysing the properties of fitted models, illustrating its ease of implementation even in non-standard situations. Distributional properties are obtained numerically for estimators or statistics not previously considered in the literature because their theoretical distributional properties are too hard to obtain theoretically. Bootstrap results are presented mainly graphically in the book, providing easy-to-understand demonstration of the sampling behaviour of estimators.

scholarly journals Statistical Methods for Establishing Personalized Treatment Rules in Oncology

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Junsheng Ma ◽  
Brian P. Hobbs ◽  
Francesco C. Stingo
Keyword(s):  
Data Analysis ◽  
Personalized Medicine ◽  
Statistical Inference ◽  
Statistical Methods ◽  
Treatment Strategies ◽  
Optimal Treatment ◽  
Personalized Treatment ◽  
Statistical Software ◽  
Genetic Features ◽  
Treatment Rules

The process for using statistical inference to establish personalized treatment strategies requires specific techniques for data-analysis that optimize the combination of competing therapies with candidate genetic features and characteristics of the patient and disease. A wide variety of methods have been developed. However, heretofore the usefulness of these recent advances has not been fully recognized by the oncology community, and the scope of their applications has not been summarized. In this paper, we provide an overview of statistical methods for establishing optimal treatment rules for personalized medicine and discuss specific examples in various medical contexts with oncology as an emphasis. We also point the reader to statistical software for implementation of the methods when available.

scholarly journals Statistics for Sleep and Biological Rhythms Research

2016 ◽  
Vol 32 (1) ◽  
pp. 7-17 ◽  
Author(s):  
Matt T. Bianchi ◽  
Andrew J. K. Phillips ◽  
Wei Wang ◽  
Elizabeth B. Klerman
Keyword(s):  
Sample Size ◽  
Statistical Inference ◽  
Statistical Methods ◽  
Biological Rhythms ◽  
Statistical Distribution ◽  
Causal Relationships ◽  
Sleep Research ◽  
Power Calculations ◽  
Case Examples

The Journal of Biological Rhythms will be publishing articles exploring analysis and statistical topics relevant to researchers in biological rhythms and sleep research. The goal is to provide an overview of the most common issues that arise in the analysis and interpretation of data in these fields. By using case examples and highlighting the pearls and pitfalls of statistical inference, the authors will identify and explain ways in which experimental scientists can avoid common analytical and statistical mistakes and use appropriate analytical and statistical methods in their research. In this first article, we address the first steps in analysis of data: understanding the underlying statistical distribution of the data and establishing associative versus causal relationships. These ideas are then applied to sample size, power calculations, correlation testing, differences between description and prediction, and the narrative fallacy.

Using Genomic Data to Infer Historic Population Dynamics of Nonmodel Organisms

2018 ◽  
Vol 49 (1) ◽  
pp. 433-456 ◽  
Author(s):  
Annabel C. Beichman ◽  
Emilia Huerta-Sanchez ◽  
Kirk E. Lohmueller
Keyword(s):  
Population Dynamics ◽  
Statistical Inference ◽  
Statistical Methods ◽  
Genome Sequence ◽  
Sequence Data ◽  
Demographic History ◽  
Genomic Data ◽  
Underlying Theory ◽  
History Of ◽  
Pros And Cons

Genome sequence data are now being routinely obtained from many nonmodel organisms. These data contain a wealth of information about the demographic history of the populations from which they originate. Many sophisticated statistical inference procedures have been developed to infer the demographic history of populations from this type of genomic data. In this review, we discuss the different statistical methods available for inference of demography, providing an overview of the underlying theory and logic behind each approach. We also discuss the types of data required and the pros and cons of each method. We then discuss how these methods have been applied to a variety of nonmodel organisms. We conclude by presenting some recommendations for researchers looking to use genomic data to infer demographic history.

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