The astonishing increase in computer performance over the past two decades has made it possible for economists to base many statistical inferences on simulated, or bootstrap, distributions rather than on distributions obtained from asymptotic theory. In this paper, I review some of the basic ideas of bootstrap inference. The paper discusses Monte Carlo tests, several types of bootstrap test, and bootstrap confidence intervals. Although bootstrapping often works well, it does not do so in every case.

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other ("correlation" of log N with A log N) indicates density-disturbance (as defined by Nicholson 1954). Both cannot be right.The method followed by Davidson and Andrewartha is clearly set out in their two papers and in Andrewartha and Birch (p. 587). We certainly did not, and we stated clearly that we did not, infer causal relationships from our regressions. On the contrary, our independent variates were chosen to represent causal relationships which we had inferred from a prior knowledge of the biology of Thrips imaginis. If we had overlooked a causal relationship, then, because the regression accounted for a high proportion of the variance, the neglected variable would, of necessity, be highly correlated with at least one of the variables included in the regression. From the nature of the variates that were included, it seems unlikely that a substitute could be found for any of them that would be consistent with the idea of "density-dependent factors."We did not include an independent variate to represent a density-dependent factor .because we could not find one. Our study of the biology of T. imaginis established, with reasonable certainty, that shortage of food was not operating as a density-dependent factor. We searched for evidence that predators, parasites or diseases were influential but failed to find it. Nor could we find any other component of environment that might be said to act like a density-dependent factor. SUMMARY Davidson and Andrewartha (1948b) concluded that the results of their study of a population of Thrips imaginis provided no confirmation of the theory of density-dependent factors. Smith (1961) re-analyzed some of their results and reached the opposite conclusions. This paper suggests that Smith's conclusions are not acceptable because:(a) He made the logical error of inferring a causal relationship from a statistical correlation. (b) He made the statistical mistake of "correlating'' two variables that were not ascertained independently. (c) He retained two criteria that gave opposite answers to the same question.

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