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Even in a theory corroboration context, attention to effect
size is called for if significance testing is to be of any value. I
sketch a Popperian construal of significance tests that better fits
into scientific inference as a whole. Because of its many errors
Chow's book cannot be recommended to the novice.
Electron microscopy, and in particular low dose electron microscopy, offers interesting cases of experimental techniques where the theory of the phenomena studied and the theory of the apparatus used, are intertwined. A single primary exposure usually does not give an interpretable image, and computerized image enhancement techniques are used to create from multiple exposures a single, visually meaningful image. Some of the enhancement programs start from informed guesses at the structure of the specimen and use the primary exposures in a series of corrections to arrive at a image that can be read by trained observers.
In this paper I describe in the general deterministic case the possible relations between phenomena theory and instrument theory. I give a Bayesian criterion for when an experiment is a test of the theory of the apparatus, rather than a test of the theory of the phenomena, and describe strategies used to ensure that tests of the theory of the phenomena are possible.
The theory of personal probability must be explored with circumspection and imagination. For example, applying the theory naively one quickly comes to the conclusion that randomization is without value to statistics. This conclusion does not sound right; and it is not right.
L. J. Savage (1961, p. 585).
Randomization is a generally accepted principle of sound experimental design and common practice among working scientists. But many philosophers and some theoretical statisticians have rejected it. Bayesians have most often stated their opposition to randomization in terms of a decision theoretic argument. Not all Bayesians, however, could go along with that argument, as the above quotation by Leonard Savage testifies.
In this paper I will examine the Bayesian decision theoretic argument against randomization and show why it fails. By means of an example I will then give a partial justification of randomization in Bayesian terms.