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38
How to improve Bayesian reasoning without instruction: Frequency formats
 Psychological Review
, 1995
"... Is the mind, by design, predisposed against performing Bayesian inference? Previous research on base rate neglect suggests that the mind lacks the appropriate cognitive algorithms. However, any claim against the existence of an algorithm, Bayesian or otherwise, is impossible to evaluate unless one s ..."
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Cited by 220 (21 self)
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Is the mind, by design, predisposed against performing Bayesian inference? Previous research on base rate neglect suggests that the mind lacks the appropriate cognitive algorithms. However, any claim against the existence of an algorithm, Bayesian or otherwise, is impossible to evaluate unless one specifies the information format in which it is designed to operate. The authors show that Bayesian algorithms are computationally simpler in frequency formats than in the probability formats used in previous research. Frequency formats correspond to the sequential way information is acquired in natural sampling, from animal foraging to neural networks. By analyzing several thousand solutions to Bayesian problems, the authors found that when information was presented in frequency formats, statistically naive participants derived up to 50 % of all inferences by Bayesian algorithms. NonBayesian algorithms included simple versions of Fisherian and NeymanPearsonian inference. Is the mind, by design, predisposed against performing Bayesian inference? The classical probabilists of the Enlightenment, including Condorcet, Poisson, and Laplace, equated probability theory with the common sense of educated people, who were known then as “hommes éclairés.” Laplace (1814/1951) declared that “the theory of probability is at bottom nothing more than good sense reduced to a calculus which evaluates that which good minds know by a sort of instinct,
Using confidence intervals in withinsubject designs
 Psychonomic Bulletin & Review
, 1994
"... Wolford, and two anonymous reviewers for very useful comments on earlier drafts of the manuscript. Correspondence may be addressed to ..."
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Cited by 178 (21 self)
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Wolford, and two anonymous reviewers for very useful comments on earlier drafts of the manuscript. Correspondence may be addressed to
Some problems connected with statistical inference
 Annals Math. Statist
, 1958
"... the nature of statistical inference. Most of the points are implicit or explicit in the literature or in current statistical practice. 2. Inferences and decision ~ For the present discussion a statistical inference ..."
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Cited by 42 (5 self)
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the nature of statistical inference. Most of the points are implicit or explicit in the literature or in current statistical practice. 2. Inferences and decision ~ For the present discussion a statistical inference
From tools to theories: A heuristic of discovery in cognitive psychology
 Psychological Review
, 1991
"... The study of scientific discovery—where do new ideas come from?—has long been denigrated by philosophers as irrelevant to analyzing the growth of scientific knowledge. In particular, little is known about how cognitive theories are discovered, and neither the classical accounts of discovery as eithe ..."
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Cited by 38 (11 self)
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The study of scientific discovery—where do new ideas come from?—has long been denigrated by philosophers as irrelevant to analyzing the growth of scientific knowledge. In particular, little is known about how cognitive theories are discovered, and neither the classical accounts of discovery as either probabilistic induction (e.g., Reichenbach, 1938) or lucky guesses (e.g., Popper, 1959), nor the stock anecdotes about sudden “eureka ” moments deepen the insight into discovery. A heuristics approach is taken in this review, where heuristics are understood as strategies of discovery less general than a supposed unique logic of discovery but more general than lucky guesses. This article deals with how scientists’ tools shape theories of mind, in particular with how methods of statistical inference have turned into metaphors of mind. The toolstotheories heuristic explains the emergence of a broad range of cognitive theories, from the cognitive revolution of the 1960s up to the present, and it can be used to detect both limitations and new lines of development in current cognitive theories that investigate the mind as an “intuitive statistician.” Scientific inquiry can be viewed as “an ocean, continuous everywhere and without a break or division ” (Leibniz, 1690/1951, p. 73). Hans Reichenbach (1938) nonetheless divided this ocean into two great seas, the context of discovery and the context of justification. Philosophers, logicians,
Severe Testing as a Basic Concept in a NeymanPearson Philosophy of Induction
 BRITISH JOURNAL FOR THE PHILOSOPHY OF SCIENCE
, 2006
"... Despite the widespread use of key concepts of the Neyman–Pearson (N–P) statistical paradigm—type I and II errors, significance levels, power, confidence levels—they have been the subject of philosophical controversy and debate for over 60 years. Both current and longstanding problems of N–P tests s ..."
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Cited by 35 (14 self)
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Despite the widespread use of key concepts of the Neyman–Pearson (N–P) statistical paradigm—type I and II errors, significance levels, power, confidence levels—they have been the subject of philosophical controversy and debate for over 60 years. Both current and longstanding problems of N–P tests stem from unclarity and confusion, even among N–P adherents, as to how a test’s (predata) error probabilities are to be used for (postdata) inductive inference as opposed to inductive behavior. We argue that the relevance of error probabilities is to ensure that only statistical hypotheses that have passed severe or probative tests are inferred from the data. The severity criterion supplies a metastatistical principle for evaluating proposed statistical inferences, avoiding classic fallacies from tests that are overly sensitive, as well as those not sensitive enough to particular errors and discrepancies.
The null ritual: What you always wanted to know about null hypothesis testing but were afraid to ask
 Handbook on Quantitative Methods in the Social Sciences. Sage, Thousand Oaks, CA
, 2004
"... No scientific worker has a fixed level of significance at which from year to year, and in all circumstances, he rejects hypotheses; he rather gives his mind to each particular case in the light of his evidence and his ideas. (Ronald A. Fisher, 1956, p. 42) It is tempting, if the only tool you have i ..."
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Cited by 11 (1 self)
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No scientific worker has a fixed level of significance at which from year to year, and in all circumstances, he rejects hypotheses; he rather gives his mind to each particular case in the light of his evidence and his ideas. (Ronald A. Fisher, 1956, p. 42) It is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail. (A. H. Maslow, 1966, pp. 15–16) One of us once had a student who ran an experiment for his thesis. Let us call him Pogo. Pogo had an experimental group and a control group and found that the means of both groups were exactly the same. He believed it would be unscientific to simply state this result; he was anxious to do a significance test. The result of the test was that the two means did not differ significantly, which Pogo reported in his thesis. In 1962, Jacob Cohen reported that the experiments published in a major psychology journal had, on average, only a 50: 50 chance of detecting a mediumsized effect if there was one. That is, the statistical power was as low as 50%. This result was widely cited, but did it change researchers’ practice? Sedlmeier and Gigerenzer (1989) checked the studies in the same journal, 24 years later, a time period that should allow for change. Yet only 2 out of 64 researchers mentioned power,
The Cult of Statistical Significance
"... difficult friend, Ronald A. Fisher (18901962), though a genius, was wrong. Fit is not the same thing as importance. Statistical significance is not the same thing as scientific importance or economic sense. But the mistaken equation is made, we find, in 8 or 9 of every 10 articles appearing in the ..."
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Cited by 11 (2 self)
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difficult friend, Ronald A. Fisher (18901962), though a genius, was wrong. Fit is not the same thing as importance. Statistical significance is not the same thing as scientific importance or economic sense. But the mistaken equation is made, we find, in 8 or 9 of every 10 articles appearing in the leading journals of science, economics to medicine. The history of this "standard error " of science involves varied characters and plot twists, but especially R. A. Fisher's canonical translation of "Student's " t. William S. Gosset aka “Student, ” who was for most of his life Head Experimental Brewer at Guinness, took an economic approach to the logic of uncertainty. Against Gosset’s wishes his friend Fisher erased the consciously economic element, Gosset's "real error. ” We want to bring it back. For the past eightyfive years it appears that some of the sciences have made a mistake, by basing decisions on statistical “significance. ” Though it looks at first like a matter of minor statistical detail, it is not. Statistics, magnitudes, coefficients are essential scientific tools. No one can credibly doubt that. And mathematical statistics is a glorious social and practical and
1985]: ‘Behavioristic, Evidentialist, and Learning Models of Statistical Testing
 Philosophy of Science
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 7 (3 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Philosophy of Statistics
 Philosophy of Science: An Encyclopedia
, 2006
"... Error statistics, as we are using that term, has a dual dimension involving philosophy and methodology. It refers to a standpoint regarding both: 1. a cluster of statistical tools, their interpretation and justification, 2. a general philosophy of science, and the roles probability plays in inductiv ..."
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Cited by 6 (4 self)
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Error statistics, as we are using that term, has a dual dimension involving philosophy and methodology. It refers to a standpoint regarding both: 1. a cluster of statistical tools, their interpretation and justification, 2. a general philosophy of science, and the roles probability plays in inductive inference. To adequately appraise the error statistical approach, and compare it to other philosophies of statistics, requires understanding the complex interconnections between the methodological and philosophical dimensions in (1) and (2) respectively. To make this entry useful while keeping to a manageable length, we restrict our main focus to (1) the error statistical philosophy. We will however aim to bring out enough of the interplay between the philosophical, methodological, and statistical issues, to elucidate longstanding conceptual, technical, and epistemological debates surrounding both these dimensions. Even with this restriction, we are identifying a huge territory marked by generations of recurring controversy about how to specify and interpret statistical methods. Understandably, standard explications
Confidence Limits: What Is The Problem? Is There The Solution?
, 2000
"... This contribution to the debate on confidence limits focuses mostly on the case of measurements with `open likelihood', in the sense that it is defined in the text. I will show that, though a priorfree assessment of confidence is, in general, not possible, still a search result can be reported in a ..."
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Cited by 4 (1 self)
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This contribution to the debate on confidence limits focuses mostly on the case of measurements with `open likelihood', in the sense that it is defined in the text. I will show that, though a priorfree assessment of confidence is, in general, not possible, still a search result can be reported in a mostly unbiased and efficient way, which satisfies some desiderata which I believe are shared by the people interested in the subject. The simpler case of `closed likelihood' will also be treated, and I will discuss why a uniform prior on a sensible quantity is a very reasonable choice for most applications. In both cases, I think that much clarity will be achieved if we remove from scientific parlance the misleading expressions `confidence intervals' and `confidence levels'.