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Objective. To compare the clinical outcome of patients presenting with symptoms of uncomplicated cystitis who were seen by a doctor, with patients who were given treatment following a diagnostic algorithm. Design. Randomized controlled trial. Setting. Out-of-hours service, Oslo, Norway. Intervention. Women with typical symptoms of uncomplicated cystitis were included in the trial in the time period September 2010-November 2011. They were randomized into two groups. One group received standard treatment according to the diagnostic algorithm, the other group received treatment after a regular consultation by a doctor. Subjects. Women (n = 441) aged 16-55 years. Mean age in both groups 27 years. Main outcome measures. Number of days until symptomatic resolution. Results. No significant differences were found between the groups in the basic patient demographics, severity of symptoms, or percentage of urine samples with single culture growth. A median of three days until symptomatic resolution was found in both groups. By day four 79% in the algorithm group and 72% in the regular consultation group were free of symptoms (p = 0.09). The number of patients who contacted a doctor again in the follow-up period and received alternative antibiotic treatment was insignificantly higher (p = 0.08) after regular consultation than after treatment according to the diagnostic algorithm. There were no cases of severe pyelonephritis or hospital admissions during the follow-up period. Conclusion. Using a diagnostic algorithm is a safe and efficient method for treating women with symptoms of uncomplicated cystitis at an out-of-hours service. This simplification of treatment strategy can lead to a more rational use of consultation time and a stricter adherence to National Antibiotic Guidelines for a common disorder. [ABSTRACT FROM AUTHOR]

Objective. To investigate prevalence, diagnostic patterns, and parallel use of daytime versus out-of-hours primary health care in a defined population (n = 23,607) in relation to mental illness including substance misuse. Design. Cross-sectional observational study. Setting. A Norwegian rural general practice cooperative providing out-of-hours care (i.e. casualty clinic) and regular general practitioners’ daytime practices (i.e. rGP surgeries) in the same catchment area. Subjects. Patients seeking medical care during daytime and out-of-hours in 2006. Main outcome measures. Patients’ diagnoses, age, gender, time of contact, and parallel use of the two services. Results. Diagnoses related to mental illness were given in 2.2% (n = 265) of encounters at the casualty clinic and in 8.9% (n = 5799) of encounters at rGP surgeries. Proportions of diagnoses related to suicidal behaviour, substance misuse, or psychosis were twice as large at the casualty clinic than at rGP surgeries. More visits to the casualty clinic occurred in months with fewer visits to rGP surgeries. Most patients with a diagnosis related to mental illness at the casualty clinic had been in contact with their rGP during the study period. Conclusion. Psychiatric illness and substance misuse have lower presentation rates at casualty clinics than at rGP surgeries. The distribution of psychiatric diagnoses differs between the services, and more serious mental illness is presented out-of-hours. The casualty clinic seems to be an important complement to other medical services for some patients with recognized mental problems. [ABSTRACT FROM AUTHOR]

Estimation of the cell probabilities in a two-way contingency table is considered when it is plausible that the table might have an independence structure relenting to the two traits. In a classical nonparametric setup, the unrestricted maximum likelihood estimators of the cell probabilities are the corresponding sample proportions; under the assumption of independence, the restricted estimators are the product of the respective row and column sample proportions. The latter estimators behave better than the former when independence actually holds, but a different picture may emerge for possible departure from the assumed independence structure; the restricted estimators may be heavily biased, inefficient, and even inconsistent. For this reason, a preliminary test on independence based on the classical contingency chi-squared statistic may be conveniently incorporated in the formulation of a preliminary test estimator of the matrix of cell probabilities. Since, typically, we have a multiparameter estimation problem, a pretest or shrinkage estimator based on the classical Stein rule may also be formulated in the same veto The primary objective of this article is to focus on the asymptotic distribution theory of all four estimators under the null hypothesis of independence as welt as local Pitman-type alternatives. The bias and risk based on suitable quadratic loss functions of these estimators are considered in the same asymptotic setup, and these are then incorporated in the shady of the asymptotic relative performance of these estimators. In the light of their asymptotic risks, neither the preliminary test nor the shrinkage estimators dominates the other, though each fares well relative... [ABSTRACT FROM AUTHOR]

The article presents a comment on a previous article related to formulating and resolving questions that illuminate the interpretation of P values in testing sharp null hypotheses that appeared in the March 1987 issue of the Journal of the American Statistical Association. According to the author statisticians James O. Berger and Thomas Sellke rightly emphasize the distinction between different aspects related to P values. In the past, and frequently in conversation, according to the author, he had used a rough value that a P value of .05 is worth a Bayes factor of only about 4 when testing a simple statistical hypothesis. Berger and Sellke get half this value, because they use a prior symmetric. The topic of max factors, mentioned by Berger and Sellke was also discussed as applied to multinomials, which of course includes binomials, and where the maximum weight of evidence is related to the chi-squared test. In the binomial case the appropriation given for the maximum weight of evidence. Sometimes a multivariate test can be reduced to a multivariate one.

The Pearson chi-square statistic for a contingency table is decomposed into a sum of components. Each component involves the Pearson chi-square statistic for tables that are formed by collapsing (i.e., combining) rows and/ or columns of the original table. Since the terms in the decomposition are necessarily nonnegative, this leads to a monotonicity in the statistic; the Pearson chi-square value for any table N is never smaller than the corresponding values for tables formed by collapsing N. The decomposition is shown to be applicable to tests for quasi-independence or quasi-homogeneity, and the monotonicity provides a coherent simultaneous test procedure. The setting for the proofs provides a probabilistic interpretation for the Pearson chi-square statistic and suggests future areas of research. [ABSTRACT FROM AUTHOR]

Motivated by the problems of detecting skewness and heavy tails in hypothetically normally distributed data, partially ordered families of alternative distributions are developed, the orderings being chosen to reflect skewness and tail weight. Optimal components of Pearson's X[sup 2], optimal in a minimax sense for detecting alternatives of this kind, are presented and their properties are discussed. Alternative approaches to the problem are also briefly discussed. [ABSTRACT FROM AUTHOR]

A method is given for adjustment of the Neyman smooth goodness-of-fit test to allow for estimation of parameters in a composite hypothesis. With this method the limiting distribution under the hypothesis is chi-squared, in contrast to a method given by Barton for this problem. The basis of the method is a standard modification of the quadratic score statistic. [ABSTRACT FROM AUTHOR]

The smooth goodness-of-fit test of Neyman (1937) was generalized to composite hypotheses by Javitz (1975) and Thomas and Pierce (1979). The test statistic is derived, as is its local asymptotic relative efficiency (LARE), which permits its comparison with other quadratic score statistic (QSS) tests, which include a Pearson-type chi[sup 2] test. For testing the negative exponential and normal distributions, the smooth test is seen to have greater LARE than the Pearson-type test and LARE comparable to certain other QSS tests for particular local alternatives. [ABSTRACT FROM AUTHOR]

We assess the probability that a table of rounded percentages adds to 100 percent. This extends work of Mosteller, Youtz, and Zabn (1967) who found that the chance of rounding to 100 percent was about 3/4 with three categories, 2/3 with four categories, and (6/pi c)1/2 with a large number c of categories. We give a mathematical treatment of this phenomenon when the table is drawn from a multinomial distribution or from a mixture of multinomial distributions. We discuss the very different small-sample behavior and treat Benford's leading digit data as an example. [ABSTRACT FROM AUTHOR]

Likelihood-ratio statistics are considered for testing a simple null hypothesis on a collection of multinomial parameters against an order-restricted alternative and for testing an order restriction against all alternatives. For the former test, the asymptotic distribution of the test statistic under the null hypothesis is a version of the chi-bar-squared distribution. This extends the work of Chacko (1966). For the latter test, homogeneity is, asymptotically, the least favorable configuration and under this hypothesis the asymptotic distribution of the test statistic has tail probabilities which are weighted averages of standard chi-squared tail probabilities. [ABSTRACT FROM AUTHOR]

The limiting distribution of the chi-square goodness-of-fit statistic Tn under alternatives is noncentral chi-square if the alternative probabilities approach the null probabilities at an appropriate rate as n → ∞. It is shown that for fixed alternative probabilities, the limiting distribution of (Tn-μn)/σn is standard normal. Both of these asymptotic results can be used to approximate the power of the goodness-of-fit test. Numerical comparisons between these two approximations indicate that for large values of the true power, the normal approximation is best, but for moderate values of power, the chi-square approximation is best. [ABSTRACT FROM AUTHOR]

Let f(x) be a probability density function with respect to the non-atomic measure mu, over the set chi. Suppose f(x) = exp [SIGMA[sup m, sub i=1] tau[sub i] phi[sub z](x) - psi[sub m](tau)] for x is an element of chi, where psi[sub m](tau) + psi[sub m] (tau[sub 1], tau[sub 2], ..., tau[sub m] is well-defined by exp [psi[sub m](tau)] = Integral of exp [SIGMA[sup m, sub i]=tau[sub i] phi[sub z](x)] d mu(x) when the right side is finite, and the integration is over chi. Let phi[sub 0](x)=1 on chi and assume {phi[sub z](x)}[sup m, sub i]=0 is a collection of functions which satisfy the Haar Condition. Using convexity properties, we obtain some results on the almost sure existence or nonexistence of the MLE for tau. [ABSTRACT FROM AUTHOR]

A two-stage estimator is proposed for the cell probabilities in a two-dimensional contingency table. Using a multivariate mean square error criterion, we show that the decision to use either the observed cell probabilities or the estimators assuming row-column independence is approximately dependent upon the noncentrality parameter of the Pearson chi-square statistic chi[sup 2]. We then derive a decision rule that says to use the independence-assumption estimators when chi[sup 2] is less than twice the number of degrees of freedom for testing independence. [ABSTRACT FROM AUTHOR]

A test of independence in a (r X c) contingency table using a specified alternative hypothesis is proposed. The test is created using Neyman's C[sub a] procedure and the approximate power computed. This test is useful when alternatives of a specific "slippage" type can be hypothesized, The usual chi[sup 2] test tends to detect all departures from randomness indiscriminately and thus not employ the added directional a priori information. [ABSTRACT FROM AUTHOR]

In this article we propose two minimum chi-square estimators for a bivariate probit model. We call one estimator the Full Information and the other Limited Information Minimum Chi-Square because the first takes account of all the a priori information while the second does not. Both estimators are shown to be consistent. Moreover, the first is shown to be asymptotically as efficient as the maximum likelihood estimator and yet is computationally much simpler. For illustration, estimates are computed for the data used by Ashford and Sowden [1970.] [ABSTRACT FROM AUTHOR]

The asymptotic non-null distribution is obtained for the modified form of the Pearson chi-square statistic studied by Dahiya and Gurland [3]. By utilizing this result the power is obtained for specific alternative distributions in testing for normality, This enables recommendations to be made as to the number of class intervals to be employed in applying the aforementioned modification of the Pearson chi-square test of normality. [ABSTRACT FROM AUTHOR]

This article shows that information partitioning in contingency tables is a very general property of exponential families, One partitioning scheme occurs when the hypotheses of interest are stated as linear expressions in the natural parameters, A second partitioning scheme is possible when the hypotheses are stated as linear in the parameter which is the expectation of the statistic in the exponent. [ABSTRACT FROM AUTHOR]

A step-by-step method is presented herein far partitioning a certain kind of hypothesis H about the m-way contingency table into (a) a series of hypotheses about marginal tables formed from the m-way table by ignoring one or more of table's m dimensions; and (b) a hypothesis about independence, conditional independence, or conditional equiprobability in the m-way table. This step-by-step method facilitates both the testing of H and the calculation of F, the estimated expected frequencies in the m-way table under FI. The method introduced herein for calculating F is easier to apply than the usual iterative-scaling method in many cases. [ABSTRACT FROM AUTHOR]

The article focuses on an inequality for a class of bivariate chi-square distributions. A recurrent problem in simultaneous inference is discussed in the article. While the joint distributions of test statistics may be known in form, these frequently depend on parameters, values of which are unknown. In such cases it is not possible to give simultaneous procedures, which hold exactly with specified probability; instead, it is expedient to give approximate procedures for which useful probability bounds can be established. Considerable effort has been expended in this direction, particularly in connection with simultaneous inference regarding means. The study is concerned with the construction of two-sided simultaneous confidence limits for variances in the bivariate case. In the p-variate normal case, researcher C.G. Khatri has given a lower bound to the simultaneous confidence coefficient associated with one-sided lower confidence limits and with additional assumptions regarding the covariance matrix, Khatri has similarly bounded the simultaneous confidence coefficient in the case of one-sided upper limits; however, two-sided limits was not examined.

If the parameters are estmated independently of the sample, the chi-square test statistic for a goodness of fit test has a limiting distribution that is stochastically larger than that of the test of fit for a completely specified distribution. Thus, if the critical values for the test of fit for a completely specified distribution are incorrectly used, the probability that we will reject the null hypothesis when it is true is greater than the desired level of significance. [ABSTRACT FROM AUTHOR]

Offers a nomogram or an alignment chart for chi square. Probability values given by the nomogram; Applications of the nomogram. [ABSTRACT FROM AUTHOR]

The article focuses on comments given by the author on topics related to 2 X 2 contingency tables. In the article two ideas are proposed. The first is that the Yates continuity correction should not be used in 2 X 2 contingency tables unless row and column totals are nonrandom. The second idea is that if row totals, or column totals, are not fixed in advance of the experiment, the Yates correction should not be used for two reasons. First, it provides poor estimates of the desired probabilities. Second, it sometimes exchanges points inside the critical region for points outside the critical region, thus providing a different test. Statistician Olli S. Miettinen points out that much of the controversy over use of a continuity correction is due to a lack of distinguishing between two distinct situations. The first situation involves estimating the exceedance probability associated with a known possible value of a discrete random variable. The second situation involves estimating the exceedance probability associated with an arbitrary real number, such as a quantile from the chi-square' distribution.