Magdalena Niewiadomska-Bugaj

On Similarity Indices and Correction for Chance Agreement

Similarity indices can be used to compare partitions (clusterings) of a data set. Many such indices were introduced in the literature over the years. We are showing that out of 28 indices we were able to track, there are 22 different ones. Even though their values differ for the same clusterings compared, after correcting for agreement attributed to chance only, their values become similar and some of them even become equivalent. Consequently, the problem of choice of the index to be used for comparing different clusterings becomes less important.

Prophylactic antibiotics with intracranial pressure monitors and external ventricular drains: a review of the evidence

BACKGROUND The role of prophylactic antibiotics (PABs) in preventing infections associated with intracranial pressure (ICP) monitors and external ventricular drains (EVD) is not well defined. METHODS This study includes an analysis of published reports and a survey of current practices regarding the use of PABs with ICP monitors and EVDs. A computerized data search and a review of the abstracts from two major national neurosurgical meetings over the past decade yielded 85 related articles. Three independent investigators, blinded to the title, author(s), institution(s), results, and conclusions of the articles used predetermined inclusion criteria to select studies for meta-analysis. Thirty-six responses were returned from 98 questionnaires (37%) mailed to university neurosurgical programs. RESULTS Among the articles reviewed, only two studies met the predetermined inclusion criteria for the meta-analysis, and they were of insufficient size to produce statistically significant results. Among the 36 programs that responded to the survey, 26 (72%) used PABs, mainly cephalosporins (46%) and semisynthetic penicillins (38%), with ICP monitors and EVDs. Twenty-two (85%) used one drug, and 4 (15%) used two drugs. Twenty-two (61%) of the total group reported intra-institutional variation in practices among individual staff neurosurgeons. Nineteen (53%) expressed interest in a retrospective study, and 27 (75%) expressed interest in a prospective study on the role of PABs in minor neurosurgical procedures. CONCLUSION No consensus regarding the use of PABs with ICP monitors and EVDs is noted. Randomized controlled trials of sufficiently large size with appropriate blinding are needed to address this issue.

Correcting Jaccard and other similarity indices for chance agreement in cluster analysis

Correcting a similarity index for chance agreement requires computing its expectation under fixed marginal totals of a matching counts matrix. For some indices, such as Jaccard, Rogers and Tanimoto, Sokal and Sneath, and Gower and Legendre the expectations cannot be easily found. We show how such similarity indices can be expressed as functions of other indices and expectations found by approximations such that approximate correction is possible. A second approach is based on Taylor series expansion. A simulation study illustrates the effectiveness of the resulting correction of similarity indices using structured and unstructured data generated from bivariate normal distributions.

MCS: A Method for Finding the Number of Clusters

This paper proposes a maximum clustering similarity (MCS) method for determining the number of clusters in a data set by studying the behavior of similarity indices comparing two (of several) clustering methods. The similarity between the two clusterings is calculated at the same number of clusters, using the indices of Rand (R), Fowlkes and Mallows (FM), and Kulczynski (K) each corrected for chance agreement. The number of clusters at which the index attains its maximum is a candidate for the optimal number of clusters. The proposed method is applied to simulated bivariate normal data, and further extended for use in circular data. Its performance is compared to the criteria discussed in Tibshirani, Walther, and Hastie (2001). The proposed method is not based on any distributional or data assumption which makes it widely applicable to any type of data that can be clustered using at least two clustering algorithms.

Optimal identification procedure for Diplostomum paracaudum (Iles, 1959) and D. pseudospathaceum Niewiadomska, 1984 metacercariae (Digenea) based on morphological characters

The diagnostic usefulness of the morphological characters of the metacercariae of two similar species of the genus Diplostomum, D. paracaudum and D. pseudospathaceum, is studied. The data are based on 203 specimens of D. paracaudum and of 153 D. pseudospathaceum from fish infected experimentally. The variability of 14 morphometric features and eight indices is analysed. It appears that no single feature or index can provide a classification (discrimination) rule with a sufficiently small percentage of misclassification. In order to increase the discriminant power, a technique based on the bootstrap method is used, which, combined with a stepwise discriminant analysis, leads to the selection of five metric features. A linear discriminant function, L, obtained for selected characters separates the two species better than any single feature. It also allows each specimen to be classified as D. paracaudum if the value of the function L is positive and as D. pseudospathaceum if negative. The accuracy of this procedure is in excess of 90%.

Comparing a New Gini Test with Other Symmetry Tests When Median Is Unknown

Although there exists an ample literature on the tests of univariate symmetry, each article provides comparison of few selected competitors only. We are comparing the performance of 15 tests recommended in the literature and two new methods introduced by Auda (2006). One of them, rank-based test RS, compares favorably with several existing procedures in controlling the Type I error as well as in power as shown in our comprehensive simulation study. An important novelty in the article are Figs. 1– 3 enabling comparison of Type I error probabilities and power of the 16 tests for 17 null and 19 alternative distributions.

Variables that Correlate with Faculty Use of Research‐Based Instructional Strategies

During the Fall of 2008 a web survey, designed to collect information about pedagogical knowledge and practices, was completed by a representative sample of 722 physics faculty across the United States (a 50.3% response rate). This paper examines how 20 predictor variables correlate with faculty knowledge about and use of research‐based instructional strategies (RBIS). Profiles were developed for each of four faculty levels of knowledge about and use of RBIS. Logistic regression analysis was used to identify a subset of the variables that could predict group membership. Five significant predictor variables were identified. High levels of knowledge and use of RBIS were associated with the following characteristics: attendee of the physics and astronomy new faculty workshop, attendee of at least one talk or workshop related to teaching in the last two years, satisfaction with meeting instructional goals, regular reader of one or more journals related to teaching, and being female. High research productivity...

A New Estimator of a Circular Median

It is well known that for distributions on the real line, the variability of sample median as an estimator of the population median remains almost the same when the sample of size 2k increases by 1 (2k + 1). Quasi medians—the averages of two symmetrically placed order statistics—were introduced by Hodges and Lehmann (1967) as alternative estimators of the location parameter, reducing the variability of the estimator in the case of samples with odd sizes. This article explores the analogous idea for the data on the circle. We propose the CQM—a circular mean of the two most central order statistics on a circle—as the estimator of a population median. The proposed estimator improves the well known Mardia median (Mardia, 1972) when the sample size is odd, and coincides with it when the sample size is even.

A New Grade Measure of Monotone Multivariate Separability

It was shown (Cifarelli and Regazzini 1987) that maximal separation of two probability measures P and Q can be assessed by a maximal concentration curve of one of the probability measures with respect to the other. In case of two univariate distributions, one can measure their monotone separation by means of a monotone concentration curve and related numerical index ar. We are extending this idea into a multivariate case. We discuss properties of a proposed index of monotone separation of multivariate distributions, especially in relation to dependence and stochastic ordering, and show examples of how the index can be used in data analysis.