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The earth is round (p < .05
 American Psychologist
, 1994
"... After 4 decades of severe criticism, the ritual of null hypothesis significance testing—mechanical dichotomous decisions around a sacred.05 criterion—still persists. This article reviews the problems with this practice, including its nearuniversal misinterpretation ofp as the probability that Ho is ..."
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Cited by 113 (0 self)
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After 4 decades of severe criticism, the ritual of null hypothesis significance testing—mechanical dichotomous decisions around a sacred.05 criterion—still persists. This article reviews the problems with this practice, including its nearuniversal misinterpretation ofp as the probability that Ho is false, the misinterpretation that its complement is the probability of successful replication, and the mistaken assumption that if one rejects Ho one thereby affirms the theory that led to the test. Exploratory data analysis and the use of graphic methods, a steady improvement in and a movement toward standardization in measurement, an emphasis on estimating effect sizes using confidence intervals, and the informed use of available statistical methods is suggested. For generalization, psychologists must finally rely, as has been done in all the older sciences,
Probabilistic Arithmetic
, 1989
"... This thesis develops the idea of probabilistic arithmetic. The aim is to replace arithmetic operations on numbers with arithmetic operations on random variables. Specifically, we are interested in numerical methods of calculating convolutions of probability distributions. The longterm goal is to ..."
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Cited by 13 (0 self)
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This thesis develops the idea of probabilistic arithmetic. The aim is to replace arithmetic operations on numbers with arithmetic operations on random variables. Specifically, we are interested in numerical methods of calculating convolutions of probability distributions. The longterm goal is to be able to handle random problems (such as the determination of the distribution of the roots of random algebraic equations) using algorithms which have been developed for the deterministic case. To this end, in this thesis we survey a number of previously proposed methods for calculating convolutions and representing probability distributions and examine their defects. We develop some new results for some of these methods (the Laguerre transform and the histogram method), but ultimately find them unsuitable. We find that the details on how the ordinary convolution equations are calculated are
Confidence Curves and Improved Exact Confidence Intervals for Discrete Distributions
, 2000
"... The author describes a method for improving standard "exact" confidence intervals in discrete distributions with respect to size while retaining correct level. The binomial, negative binomial, hypergeometric and Poisson distributions are considered explicitly. Contrary to other existing methods, the ..."
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Cited by 11 (0 self)
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The author describes a method for improving standard "exact" confidence intervals in discrete distributions with respect to size while retaining correct level. The binomial, negative binomial, hypergeometric and Poisson distributions are considered explicitly. Contrary to other existing methods, the author's solution possesses a natural nesting condition: if #<# # ,the 1# # confidence interval is included in the 1  # interval. Nonparametric confidence intervals for a quantile are also considered.
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
Clouds, Fuzzy Sets and Probability Intervals
 Reliable Computing, Kluwer Academic Publishers
, 2004
"... Clouds are a concept for uncertainty mediating between the concept of a fuzzy set and that of a probability distribution. A cloud is to a random variable more or less what an interval is to a number. We discuss the basic theoretical and numerical properties of clouds, and relate them to histograms, ..."
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Cited by 5 (2 self)
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Clouds are a concept for uncertainty mediating between the concept of a fuzzy set and that of a probability distribution. A cloud is to a random variable more or less what an interval is to a number. We discuss the basic theoretical and numerical properties of clouds, and relate them to histograms, cumulative distribution functions, and likelihood ratios.
A CONSONANT APPROXIMATION OF THE PRODUCT OF INDEPENDENT CONSONANT RANDOM SETS
"... ABSTRACT. The belief structure resulting from the combination of consonant and independent marginal random sets is not, in general, consonant. Also, the complexity of such a structure grows exponentially with the number of combined random sets, making it quickly intractable for computations. In this ..."
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Cited by 1 (1 self)
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ABSTRACT. The belief structure resulting from the combination of consonant and independent marginal random sets is not, in general, consonant. Also, the complexity of such a structure grows exponentially with the number of combined random sets, making it quickly intractable for computations. In this paper, we propose a simple guaranteed consonant outer approximation of this structure. The complexity of this outer approximation does not increase with the number of marginal random sets (i.e., of dimensions), making it easier to handle in uncertainty propagation. Features and advantages of this outer approximation are then discussed, with the help of some illustrative examples. 1.
October 9, 2009 12:27 WSPC/INSTRUCTION FILE PossAppRSI˙final International Journal of Uncertainty, Fuzziness and KnowledgeBased Systems c ○ World Scientific Publishing Company A CONSONANT APPROXIMATION OF THE PRODUCT OF INDEPENDENT CONSONANT RANDOM SETS
, 2009
"... The belief structure resulting from the combination of consonant and independent marginal random sets is not, in general, consonant. Also, the complexity of such a structure grows exponentially with the number of combined random sets, making it quickly intractable for computations. In this paper, we ..."
Abstract
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The belief structure resulting from the combination of consonant and independent marginal random sets is not, in general, consonant. Also, the complexity of such a structure grows exponentially with the number of combined random sets, making it quickly intractable for computations. In this paper, we propose a simple guaranteed consonant outer approximation of this structure. The complexity of this outer approximation does not increase with the number of marginal random sets (i.e., of dimensions), making it easier to handle in uncertainty propagation. Features and advantages of this outer approximation are then discussed, with the help of some illustrative examples.