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Probability and Statistics
Probability and Statistics

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statistics - John Uebersax PhD

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... their followers did not ewlici'dy suggegt to b d o n that concept of probability which had prevailed since the classical period, and to replace it by a new one. They rather believed that their concept was essentially the same a s that of all earlier authors. They merely claimed that they had given a ...
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... • Decide what p-value would be “too unlikely” • This threshold is called the alpha level. • When a sample statistic surpasses this level, the result is said to be significant. • Typical alpha levels are 0.05 and 0.01. • Alpha levels (level of significance) = probability of a type I error (the probab ...
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STAT101: A Review of the Basics

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Epistemic Complexity from an Objective Bayesian

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... H0:  =20.7, H1:   20.7 15) Plain M&M candies have a mean weight that is a least 0.8535g. H0:  <20.7, H1:   20.7 16) The percentage of workers who got a job through their college is no more than 2% H0: p>0.02, H1: p  0.02 19) Right-tailed test;a=0.01 Critical value=2.33 20) Left-tailed test;a= ...
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Inference Comparing Two Means

... There are two inference procedures for comparing means of two independent samples. I. Pooled Two-Sample t Procedures These are often emphasized in introductory mathematical statistics textbooks and in older statistics books. They make the assumptions that: • A simple random sample of size n1 is take ...
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Foundations of statistics

Foundations of statistics is the usual name for the epistemological debate in statistics over how one should conduct inductive inference from data. Among the issues considered in statistical inference are the question of Bayesian inference versus frequentist inference, the distinction between Fisher's ""significance testing"" and Neyman-Pearson ""hypothesis testing"", and whether the likelihood principle should be followed. Some of these issues have been debated for up to 200 years without resolution.Bandyopadhyay & Forster describe four statistical paradigms: ""(1) classical statistics or error statistics, (ii) Bayesian statistics, (iii) likelihood-based statistics, and (iv) the Akaikean-Information Criterion-based statistics"".Savage's text Foundations of Statistics has been cited over 10000 times on Google Scholar. It tells the following.It is unanimously agreed that statistics depends somehow on probability. But, as to what probability is and how it is connected with statistics, there has seldom been such complete disagreement and breakdown of communication since the Tower of Babel. Doubtless, much of the disagreement is merely terminological and would disappear under sufficiently sharp analysis.
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