Evidential Analysis: An Alternative to Hypothesis Testing in Normal Linear Models
Statistical hypothesis testing, as formalized by 20th century statisticians and taught in college statistics courses, has been a cornerstone of 100 years of scientific progress. Nevertheless, the methodology is increasingly questioned in many scientific disciplines. We demonstrate in this paper how...
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MDPI AG
2024-11-01
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| author | Brian Dennis Mark L. Taper José M. Ponciano |
| author_facet | Brian Dennis Mark L. Taper José M. Ponciano |
| author_sort | Brian Dennis |
| collection | DOAJ |
| description | Statistical hypothesis testing, as formalized by 20th century statisticians and taught in college statistics courses, has been a cornerstone of 100 years of scientific progress. Nevertheless, the methodology is increasingly questioned in many scientific disciplines. We demonstrate in this paper how many of the worrisome aspects of statistical hypothesis testing can be ameliorated with concepts and methods from evidential analysis. The model family we treat is the familiar normal linear model with fixed effects, embracing multiple regression and analysis of variance, a warhorse of everyday science in labs and field stations. Questions about study design, the applicability of the null hypothesis, the effect size, error probabilities, evidence strength, and model misspecification become more naturally housed in an evidential setting. We provide a completely worked example featuring a two-way analysis of variance. |
| format | Article |
| id | doaj-art-b6c43a378e0e4da9a1e89a89764aab07 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj-art-b6c43a378e0e4da9a1e89a89764aab072024-11-26T18:03:14ZengMDPI AGEntropy1099-43002024-11-01261196410.3390/e26110964Evidential Analysis: An Alternative to Hypothesis Testing in Normal Linear ModelsBrian Dennis0Mark L. Taper1José M. Ponciano2Department of Fish and Wildlife Sciences, University of Idaho, Moscow, ID 83844, USADepartment of Ecology, Montana State University, Bozeman, MT 59717, USADepartment of Biology, University of Florida, Gainesville, FL 32611, USAStatistical hypothesis testing, as formalized by 20th century statisticians and taught in college statistics courses, has been a cornerstone of 100 years of scientific progress. Nevertheless, the methodology is increasingly questioned in many scientific disciplines. We demonstrate in this paper how many of the worrisome aspects of statistical hypothesis testing can be ameliorated with concepts and methods from evidential analysis. The model family we treat is the familiar normal linear model with fixed effects, embracing multiple regression and analysis of variance, a warhorse of everyday science in labs and field stations. Questions about study design, the applicability of the null hypothesis, the effect size, error probabilities, evidence strength, and model misspecification become more naturally housed in an evidential setting. We provide a completely worked example featuring a two-way analysis of variance.https://www.mdpi.com/1099-4300/26/11/964evidenceevidence functionslinear modelsNeyman–Pearsonhypothesis testingKullback–Leibler |
| spellingShingle | Brian Dennis Mark L. Taper José M. Ponciano Evidential Analysis: An Alternative to Hypothesis Testing in Normal Linear Models Entropy evidence evidence functions linear models Neyman–Pearson hypothesis testing Kullback–Leibler |
| title | Evidential Analysis: An Alternative to Hypothesis Testing in Normal Linear Models |
| title_full | Evidential Analysis: An Alternative to Hypothesis Testing in Normal Linear Models |
| title_fullStr | Evidential Analysis: An Alternative to Hypothesis Testing in Normal Linear Models |
| title_full_unstemmed | Evidential Analysis: An Alternative to Hypothesis Testing in Normal Linear Models |
| title_short | Evidential Analysis: An Alternative to Hypothesis Testing in Normal Linear Models |
| title_sort | evidential analysis an alternative to hypothesis testing in normal linear models |
| topic | evidence evidence functions linear models Neyman–Pearson hypothesis testing Kullback–Leibler |
| url | https://www.mdpi.com/1099-4300/26/11/964 |
| work_keys_str_mv | AT briandennis evidentialanalysisanalternativetohypothesistestinginnormallinearmodels AT markltaper evidentialanalysisanalternativetohypothesistestinginnormallinearmodels AT josemponciano evidentialanalysisanalternativetohypothesistestinginnormallinearmodels |