Let be a random sample of size 5 from an absolutely continuous distribution having median M. Let S denote the number of greater than 0. For testing against , let if if S = c, and 0 if S < c be a test of size , where and c ∈ {−1, 0, …, 5} are fixed constants. Then equals
Part BCSIR NET December 2024randomise-at-the-boundary-to-hit-the-size
Randomise at the boundary to hit the size
Related counterexample: Any interval of the form [X̄ − (S/√n)t, ∞) with a 90% quantile t is a 90% confidence interval
- runs distributionJune 2023
- one sided intervalsDecember 2023
- kolmogorov scalingDecember 2023
- the independence variance is one over n minus oneDecember 2024
- symmetry is about the mean not about mn over twoDecember 2024
- the upper tail costs no sizeDecember 2024
The chapter behind this: Standard tests and confidence intervals — free to read
From Hypothesis Testing › Likelihood ratio and standard tests