The true probability of a confidence interval Summary
The calculation of a confidence interval, which together with the hypothesis testing is the best known procedure of inferential statistics, has as result the probability that a certain statistical parameter is contained in a certain part of the real line. However, this result does not enjoy of unanimity because it is widely believed the not be strictly a probability and that must be called only confidence. To this is added the perplexity of being able to replace, as is highlighted in the article, the said probability with many other equally reliable. Keywords: confidence interval, probability, statistics, propositional logic, set theory, combinatorics. |
INDEX 1 INTRODUCTION 2 PRELIMINARIES OF LOGIC AND SET THEORY 3 EVENTS AND PROBABILITY 3.1 Composite events 3.2 Probability 3.3 An application of composite events 4 THE PROBABILITY OF AN UNKNOWN CONSTANT 4.1 A confirmation 5 THE CALCULATION OF THE CONFIDENCE INTERVAL 5.1 The mean of a normal random variable 5.1 The variance of a normal random variable CONCLUSION REFERENCES Date of release: Sunday 1 November 2015 Language: English Number of downloads: 154 THE FULL TEXT as a 868 kilobytes PDF file (can be opened by the free Adobe Reader 6.0 and later) Related link: La vera probabilità di un intervallo di fiducia http://dx.doi.org/10.5281/zenodo.32995 http://dx.doi.org/10.13140/RG.2.1.4327.1127 http://dx.doi.org/10.5281/zenodo.31643 http://dx.doi.org/10.13140/RG.2.1.3539.5048 |