Statistical approaches to uncertainty: p values and confidence intervals unpacked

Introduction to biostatistics: Part 3. Statistical approaches to uncertainty: P values and confidence intervals unpacked.

(the difference in risk) is estimated to be 19.6% with a 95% CI of 5.7% to 33.6%. The P value of 0.006 means that an ARR of 19.6% or more would occur only in 6 in 1000 trials if streptomycin was equally as effective as bed rest. Since the P value is less than 0.05, the results are statistically significant (i.e., it is unlikely that streptomycin is ineffective in preventing death). The 95% CI s...

Fuzzy Confidence Intervals and P -values

The optimal hypothesis tests for the binomial distribution and some other discrete distributions are uniformly most powerful (UMP) one-tailed and UMP unbiased (UMPU) two-tailed randomized tests. Conventional confidence intervals are not dual to randomized tests and perform badly on discrete data at small and moderate sample sizes. We introduce a new confidence interval notion, called fuzzy conf...

What are confidence intervals and p - values ?

Comment: Fuzzy and Randomized Confidence Intervals and P -Values

Professor Geyer and Professor Meeden have given us an intriguing article with much material for thought and exploration, and they deserve our congratulations. Although the idea of randomized procedures has long existed, this paper has revitalized the discussion on randomized confidence intervals and randomized P -values. Interval estimation of a binomial proportion is a very basic but very impo...

Comment: Fuzzy and Randomized Confidence Intervals and P -Values

We thank Professor Geyer and Professor Meeden for their thought-provoking article. We hope to also be thought-provoking in response, for we pretty much disagree with their position. The fuzzy procedures proposed by the authors result from examining the test function, φ(x,α, θ) in three different ways, as a function of each of the three variables. This is an interesting exercise, which has not b...