scholarly journals Statistical Hypothesis Testing for Asymmetric Tolerance Index

2021 ◽  
Vol 11 (14) ◽  
pp. 6249
Author(s):  
Kuen-Suan Chen ◽  
Shui-Chuan Chen ◽  
Chang-Hsien Hsu ◽  
Wei-Zong Chen
Keyword(s):  
Standard Deviation ◽  
Confidence Interval ◽  
Hypothesis Testing ◽  
Confidence Region ◽  
Target Function ◽  
Statistical Hypothesis ◽  
Feasible Region ◽  
Tolerance Index ◽  
Statistical Hypothesis Testing ◽  
Asymmetric Tolerances

Many of the nominal-the-best quality characteristics of important machine tool components, such as inner or outer diameters, have asymmetric tolerances. An asymmetric tolerance index is a function for the average of the process and the standard deviation. Unfortunately, it is difficult to obtain the 100 (1 − α)% confidence interval of the index. Therefore, this study adopts Boole’s inequality and DeMorgan’s theorem to find the combined confidence region for the average of the process as well as the standard deviation. Next, using the asymmetric tolerance index for the target function and the combined confidence region for the feasible region, this study applies mathematical programming to find the confidence interval as well as employs this confidence interval for statistical hypothesis testing. Lastly, this study demonstrates the applicability of the proposed approach with an illustrative example.

Multiple Hypothesis Testing for Data Mining

2011 ◽  
pp. 1390-1395
Author(s):  
Sach Mukherjee
Keyword(s):  
Data Mining ◽  
Hypothesis Testing ◽  
Conventional Treatment ◽  
Statistical Significance ◽  
Multiple Hypothesis Testing ◽  
Statistical Hypothesis ◽  
Single Variable ◽  
Statistical Hypothesis Testing ◽  
Computationally Efficient ◽  
Error Probabilities

A number of important problems in data mining can be usefully addressed within the framework of statistical hypothesis testing. However, while the conventional treatment of statistical significance deals with error probabilities at the level of a single variable, practical data mining tasks tend to involve thousands, if not millions, of variables. This Chapter looks at some of the issues that arise in the application of hypothesis tests to multi-variable data mining problems, and describes two computationally efficient procedures by which these issues can be addressed.

Discrepancy to Variability

2019 ◽  
pp. 245-264
Author(s):  
Steven J. Osterlind
Keyword(s):  
Hypothesis Testing ◽  
Thought Experiment ◽  
Latin Squares ◽  
Lewis Carroll ◽  
Statistical Hypothesis ◽  
Late Nineteenth Century ◽  
Statistical Hypothesis Testing ◽  
Research Designs ◽  
Late Nineteenth ◽  
Charles Dodgson

This chapter describes quantification during the late nineteenth century. Then, most ordinary people were gaining an overt awareness, and probability notions were seeping into everyday conversation and decision-making. However, new forms of abstract mathematics were being developed, albeit with some opposition from Lewis Carroll (Charles Dodgson), who wanted to preserve traditionalist views of Euclidian geometry. The chapter introduces William Gossett, who worked in the laboratory of the Guinness brewery and developed “t-distribution,” which was published as “Student’s t-test.” It also describes his friendship with Sir Ronald Fisher, who developed many statistical hypothesis testing methods, published in The Design of Experiments, such as the ANOVA procedure, and the F ratio. Fisher also developed many research designs for hypothesis testing, both simple and complex, including the Latin squares design, as well as providing a classic description of inferential testing in the thought experiment called “the lady tasting tea.”

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