Philosophy of Survey-Sampling Practice

Abstract

The 'induction' which philosophers have dealt with over the centuries, particularly since Hume, is illustrated popularly by the assertion, "Since the sun has risen every day over several thousand days (assuming the historical record), it will rise tomorrow". To find a general rationale behind this assertion is considered by philosophers to be the 'problem of induction'. Now philosophers of probability such as Carnap and Reichenbach have attempted to relate this 'problem of induction' with 'statistical inference'. However, in so doing they completely overlooked a central feature of 'statistical inference', namely artificial randomisation, or randomisation introduced by some suitable artifice such as random number tables and the like. Thus, in contrast to the philosopher asking, "What is the probability of the sun rising tomorrow?" the statistician was raising the problem: "Suppose balls are drawn at random (with suitable artifice of randomisation) from a bag containing one thousand black and white balls in unknown proportion; what is the probability of the nth ball being white, given that the previous n — 1 random draws have resulted in white balls?" (Kempthorne (1971) has made a somewhat similar point). This latter problem is obviously scientifically realisticwhile the former one is not. This scientifically realistic problem of "statistical inference" is generally not understood by philosophers of probability because of their rigid adherence to the framework provided by the "problem of induction" referred to above.