Author
R. L. Plackett
Bio: R. L. Plackett is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 89 citations.
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89 citations
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TL;DR: In this paper, exact and approximate methods for computing the distribution of quadratic forms in normal variables are given for a given value x, around the probability P{Q > x}.
Abstract: In this paper exact and approximate methods are given for computing the distribution of quadratic forms in normal variables. In statistical applications the interest centres in general, for a quadratic form Q and a given value x, around the probability P{Q > x}. Methods of computation have previously been given e.g. by Box (1954), Gurland (1955) and by Grad & Solomon (1955). None of these methods is very easily applicable except, when it can be used, the finite series of Box. Furthermore, all the methods are valid only for quadratic forms in central variables. Situations occur where quadratic forms in non-central variables must be considered as well. Let x = (x1, ..., xx)' be a column random vector which follows a multidimensional normal law with mean vector 0 and covariance matrix E. Let s = (,t, . . ., ,,7)' be a constant vector, and consider the quadratic form Q = (x + ,)' A(x + ,u). If E is non-singular, one can by means of a non-singular linear transformation (Scheff6 (1959), p. 418) express Q in the form rn 2 Q =E ArXhr; (1 r=1
1,207 citations
TL;DR: The results show that the PEM had higher Spearman correlation with original authors’judgment than PND did, and the treatment was highly or at least moderately effective in synthesizing the effect of self-control training on academic and social behavior.
Abstract: The purpose of the present study is twofold: (a) to compare the validation of percentage of nonoverlapping data approach and percentage of data points exceeding the median of baseline phase (PEM) approach, and (b) to demonstrate application of the PEM approach in conducting a quantitative synthesis of single-subject research investigating the effectiveness of self-control. The results show that the PEM had higher Spearman correlation with original authors' judgment than PND did. The results of applying the PEM approach to synthesize the effect of self-control training on academic and social behavior showed that the treatment was highly or at least moderately effective.
368 citations
TL;DR: In this article, surfaces of electropolished, bright annealed and matt stainless steel and of lead stabilized PVC were exposed to running municipal drinking water (10 cm s−1) for 167 days and the total number of micro-organisms growing on the surfaces was examined with an acridine orange direct count technique at 7 sampling times.
253 citations
TL;DR: It is suggested that the reproducibility of RV measurements is adequate to detect RV hypertrophy and a low ejection fraction in the individual patient and more effort is needed to improve the reproduCibility of MR imaging measurements.
193 citations
TL;DR: In this paper, the estimation of variance components in the one-way model from a subjective Bayesian point of view is considered, and the situation in which the classical unbiased estimate of the between variance component is negative is explored in some detail.
Abstract: The estimation of variance components in the one-way model is considered from a subjective Bayesian point of view. The situation in which the classical unbiased estimate of the between variance component is negative is explored in some detail. Exact and approximate posterior distributions are obtained in both the balanced and unbalanced case. Common sense aspects of the problem are emphasized, and some contrasts with other approaches. For example, Bayesianly speaking, a large negative unbiased estimate of the between variance component indicates an uninformative experiment in which the effective likelihood for that variance component is extremely flat, instead of strong evidence that the variance component is nearly zero.
150 citations