Resampling: The new statistics

One of the great questions in statistical inference is: How big is it? This can mean—How long? How deep? How much time? At what angle? This question about size may pertain to a single object, of which there are many measurements; an example is the location of a star in the heavens. Or the question may pertain to a varied set of elements and their measurements; examples include the effect of treatment with a given drug, and the incomes of the people of the United States in 1994. From where the observer stands, having only the evidence of a sample in hand, it often is impossible to determine whether the data represent multiple observations of a single object, or single (or multiple) observations of multiple objects. For example , from crude measurements of weight you could not know whether one person is being weighed repeatedly, or several people have been weighed once. Hence all the following discussion of point estimation is the same for both of these situations. The word " big " in the first sentence above is purposely vague, because there are many possible kinds of estimates that one might wish to make concerning a given object or collection. For a single object like a star, one surely will wish to make a best guess about its location. But about the effects of a drug treatment, or the incomes of a nation, there are many questions that one may wish to answer. The average effect or income is a frequent and important object of our interest. But one may also wish to know about the amount of dispersion in the distribution of treatment effects, or of incomes, or the sym