This file is a short polemical essay in economic methodology by Murray N. Rothbard, appearing as a section of Making Economic Sense. Its scope is narrow but ambitious: it treats statistical inference as a discipline whose authority depends on an unproved distributional premise, then presents the bootstrap as evidence that the premise can be discarded by statisticians themselves. Rothbard opens autobiographically, locating the origin of his skepticism in graduate mathematical statistics at Columbia under Harold Hotelling.
After listening to several lectures of Hotelling, I experienced an epiphany: the sudden realization that the entire “science” of statistical inference rests on one crucial assumption, and that that assumption is utterly groundless.
The argument then explains why inference is more than data collection. Since most social and economic questions do not permit a full census, statisticians move from small samples to claims about unknown populations. Rothbard's examples—height, unemployment, and electoral polling—make the problem practical rather than abstract: the authority of margins of error and confidence levels depends on how the sample is assumed to be distributed around the population value.
In the science of statistics, the way we move from our known samples to the unknown population is to make one crucial assumption: that the samples will, in any and all cases, whether we are dealing with height or unemployment or who is going to vote for this or that candidate, be distributed around the population figure according to the so-called “normal curve.”
His central conceptual move is to recast statistical precision as conditional rhetoric. The normal curve permits the language of 90 or 95 percent confidence, but for Rothbard that language does not itself prove the curve's relevance. It gives sample-based statements an aura of exactness while concealing the assumption that makes exactness possible. Polling is his exemplary case: a margin of error seems empirical, yet its inferential force depends on the bell curve.
Well, what is the evidence for this vital assumption of distribution around a normal curve? None whatever.
Rothbard's critique is sharpened through the rifleman example, which he presents as the kind of thin analogy offered for the normal curve's universality. A pattern of shots clustering around a bullseye cannot, in his view, license broad claims about economic or political data. The essay's most important argumentative effect is therefore demystification: formal mathematics is not denied, but its epistemic authority is made to rest on an act of faith.
On this incredibly flimsy basis rests an assumption vital to the validity of all statistical inference.
The second half turns from skepticism to disciplinary reversal. Rothbard argues that bad procedures often persist until replacements exist, and he identifies Bradley Efron's bootstrap as the replacement that makes the old dependence on the bell curve unnecessary. The method's significance, as Rothbard presents it, is not merely technical: high-speed computing allows artificial data sets to be generated from the original sample, avoiding a prior universal assumption about sample distribution.
Ten years ago, Stanford statistician Bradley Efron used high-speed computers to generate “artificial data sets” based on an original sample, and to make the millions of numerical calculations necessary to arrive at a population estimate without using the normal curve, or any other arbitrary, mathematical assumption of how samples are distributed about the unknown population figure.
The closing pages use professional testimony to turn Rothbard's outsider suspicion into an insider admission. Jerome H. Friedman's praise of the bootstrap, and his concession that data often depart from bell-shaped curves, lets Rothbard portray the old normal-curve regime as exposed by the discipline it governed. The essay's relevance lies in its warning against mistaking model-dependent inference for direct knowledge: quantitative form can obscure rather than resolve assumptions about the world.
Friedman now concedes that “data don’t always follow bell-shaped curves, and when they don’t, you make a mistake” with the standard methods.
The title's question is answered polemically rather than cautiously. Statistics is shown as internally undone insofar as its own practitioners, empowered by computation, reveal that a central convention of standard inference was universal neither in evidence nor in practice. Rothbard ends by casting the moment as iconoclasm: a technical innovation becomes the death of a methodological idol.
The old mystical faith can now be abandoned; the Normal Curve god is dead at long last.
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