When It Seems Desirable to Ignore Data.
Abstract
An experiment designed to detect the relative motion of two astronomical objects raised the problem of testing, against shift alternatives, the hypothesis H sub o that two energy distributions are equivalent. The relevant data consist of independent Poisson counts x sub ij with means lambda sub j p sub ij T sub ij where lambda sub j is the intensity of radiation from the j-th object, p sub ij is the probability that a random photon from the j-th object has energy in a small interval centered about e sub i and T sub ij is the time duration allocated to the count x sub ij. The hypothesis H sub o implies that P sub il = P i2 for i - 1,2,..., m. A natural test uses the statistic sigma e sub i(p prime sub 12 - p prime sub il) where the p prime sub ij are estimates of p sub ij. For intervals where the p sub ij were anticipated to be small, the experimenter chose small T sub ij values and hence those p prime sub ij were highly variable. Consequently, common sense suggests that the corresponding e sub i, and X sub ij be omitted in the above statistic, a practice which may be regarded as sinful by statistical dogma. This issue and others raised by the effects of small t sub ij lead to the consideration of alternative test statistics and their relative efficiencies as well as the design problem of selecting T sub ij. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 24, 1982
- Accession Number
- ADA120059
Entities
People
- Herman Chernoff
Organizations
- Massachusetts Institute of Technology