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The use of statistics in the British Journal of Psychiatry.

BACKGROUND: Statistical error rates in the medical literature are generally high. METHOD: All papers published in the British Journal of Psychiatry in 1993 which presented numerical results were reviewed by the author for statistical errors. RESULTS: A total of 248 papers were published, of which 164 (66%) presented numerical results. Sixty-five (40% of 164) papers contained statistical errors. Many errors were not serious in nature, but some were serious enough to cast doubt on conclusions. The error rates are similar to those found in an earlier study. CONCLUSIONS: The statistical error rate is unacceptably high. There is no evidence of a change in the statistical error rate over time.

Bias↗

Statistical evaluation of mutagenicity test data: recommendations of the U.K. Environmental Mutagen Society.

Most of the many published guidelines on how to conduct mutagenicity tests do not give advice or references on statistical analysis of data. The U.K. Environmental Mutagen Society decided to address this omission, and in 1985 established 8 working groups comprising genetic toxicologists from all sectors of the science, plus at least 2 statisticians per group, to produce statistics guidelines on 10 different test systems. Each group gave advice on how to determine the suitability of data for distribution fitting, when data are unsuitable, when and how data should be transformed, which statistical tests are suitable for a given set of data, which factors govern the choice of statistical test, an order of preference, and some worked examples using real data. In addition, groups gave advice on statistical issues in the design of experiments. Strong recommendations were made that for in vitro tests, sufficient cells be treated and sampled to provide meaningful values of spontaneous mutant/aberration frequencies, for genuine, independent replicate treatments to be used, and that the acceptability of an experiment should be based on homogeneity between replicates as well as comparison of negative and positive control responses with historical ranges. It was recommended that most in vitro studies should include independent repeat experiments, and advice was given on how to check for consistency between experiments and then combine data for further significance testing.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗

A statistical thermodynamic model applied to experimental AFM population and location data is able to quantify DNA-histone binding strength and internucleosomal interaction differences between acetylated and unacetylated nucleosomal arrays.

Imaging of nucleosomal arrays by atomic force microscopy allows a determination of the exact statistical distributions for the numbers of nucleosomes per array and the locations of nucleosomes on the arrays. This precision makes such data an excellent reference for testing models of nucleosome occupation on multisite DNA templates. The approach presented here uses a simple statistical thermodynamic model to calculate theoretical population and positional distributions and compares them to experimental distributions previously determined for 5S rDNA nucleosomal arrays (208-12,172-12). The model considers the possible locations of nucleosomes on the template, and takes as principal parameters an average free energy of interaction between histone octamers and DNA, and an average wrapping length of DNA around the octamers. Analysis of positional statistics shows that it is possible to consider interactions between nucleosomes and positioning effects as perturbations on a random positioning noninteracting model. Analysis of the population statistics is used to determine histone-DNA association constants and to test for differences in the free energies of nucleosome formation with different types of histone octamers, namely acetylated or unacetylated, and different DNA templates, namely 172-12 or 208-12 5S rDNA multisite templates. The results show that the two template DNAs bind histones with similar affinities but histone acetylation weakens the association of histones with both templates. Analysis of locational statistics is used to determine the strength of specific nucleosome positioning tendencies by the DNA templates, and the strength of the interactions between neighboring nucleosomes. The results show only weak positioning tendencies and that unacetylated nucleosomes interact much more strongly with one another than acetylated nucleosomes; in fact acetylation appears to induce a small anticooperative occupation effect between neighboring nucleosomes.

Acetylation↗

Multi-level statistical models in studies of periodontal diseases.

Periodontal data typically have a hierarchical structure, with sites grouped within individuals, and individuals grouped within communities. Also, the occasion may be regarded as another level since the acquired knowledge indicates that periodontal disease activity may vary over time. Conventional statistical tests are based on unilevel analysis of data. However, this approach to statistical analysis is often inconvenient in periodontal research because of the variation in the outcome variables between the various levels in the hierarchy. Lately there have been important developments in the statistical theory which have made available powerful statistical techniques for analyzing multilevel or hierarchical data. This report describes a new approach for analyzing periodontal data and uses an illustrative example to build a model which explains part of the variability in the response variable. The results from this analysis are then compared to results from an earlier report which uses unilevel methods and the findings discussed. The present multilevel approach has several advantages over unilevel methods, mainly due to its statistical validity and efficiency. Further, it permits the incorporation of explanatory variables measured at the site and the subject levels, and those which vary across the time points. Multilevel analyses have a promising potential and are expected to have a significant impact on periodontal research.

Age Factors↗

Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine.

Minimal measurement error (reliability) during the collection of interval- and ratio-type data is critically important to sports medicine research. The main components of measurement error are systematic bias (e.g. general learning or fatigue effects on the tests) and random error due to biological or mechanical variation. Both error components should be meaningfully quantified for the sports physician to relate the described error to judgements regarding 'analytical goals' (the requirements of the measurement tool for effective practical use) rather than the statistical significance of any reliability indicators. Methods based on correlation coefficients and regression provide an indication of 'relative reliability'. Since these methods are highly influenced by the range of measured values, researchers should be cautious in: (i) concluding acceptable relative reliability even if a correlation is above 0.9; (ii) extrapolating the results of a test-retest correlation to a new sample of individuals involved in an experiment; and (iii) comparing test-retest correlations between different reliability studies. Methods used to describe 'absolute reliability' include the standard error of measurements (SEM), coefficient of variation (CV) and limits of agreement (LOA). These statistics are more appropriate for comparing reliability between different measurement tools in different studies. They can be used in multiple retest studies from ANOVA procedures, help predict the magnitude of a 'real' change in individual athletes and be employed to estimate statistical power for a repeated-measures experiment. These methods vary considerably in the way they are calculated and their use also assumes the presence (CV) or absence (SEM) of heteroscedasticity. Most methods of calculating SEM and CV represent approximately 68% of the error that is actually present in the repeated measurements for the 'average' individual in the sample. LOA represent the test-retest differences for 95% of a population. The associated Bland-Altman plot shows the measurement error schematically and helps to identify the presence of heteroscedasticity. If there is evidence of heteroscedasticity or non-normality, one should logarithmically transform the data and quote the bias and random error as ratios. This allows simple comparisons of reliability across different measurement tools. It is recommended that sports clinicians and researchers should cite and interpret a number of statistical methods for assessing reliability. We encourage the inclusion of the LOA method, especially the exploration of heteroscedasticity that is inherent in this analysis. We also stress the importance of relating the results of any reliability statistic to 'analytical goals' in sports medicine.

Bias↗

On a general class of chi-squared goodness-of-fit statistics.

A class of chi-squared goodness-of-fit statistics is presented as being based on the so-called divergence of one probability distribution from another. A still more general class of goodness-of-fit statistics is then presented by eliminating some of the restrictions required of divergence-based statistics. This most general class of statistics includes, as particular cases, a variety of statistics used in the published literature.

Chi-Square Distribution↗

Psychometric properties of the statistics anxiety rating scale.

The Statistics Anxiety Rating Scale has 51 items, each scored on a 5-point rating scale to measure statistics anxiety with six subscales, Worth of Statistics, Interpretation Anxiety, Test and Class Anxiety, Computational Self-concept, Fear of Asking for Help, and Fear of Statistics Teachers. Psychometric properties included analyses of construct and concurrent validities an internal consistency and test-retest reliability. 221 college students (74% women; M age=28 yr.) in elementary statistics courses at several southwestern state universities participated. The findings are consistent with previous reports and indicate adequate concurrent validity, internal consistency, and split-half reliability, but for construct validity confirmatory factor analysis yielded marginal support.

Adolescent↗

Mathematical background and attitudes toward statistics in a sample of Spanish college students.

To examine the relation of mathematical background and initial attitudes toward statistics of Spanish college students in social sciences the Survey of Attitudes Toward Statistics was given to 827 students. Multivariate analyses tested the effects of two indicators of mathematical background (amount of exposure and achievement in previous courses) on the four subscales. Analysis suggested grades in previous courses are more related to initial attitudes toward statistics than the number of mathematics courses taken. Mathematical background was related with students' affective responses to statistics but not with their valuing of statistics. Implications of possible research are discussed.

Adolescent↗

Teaching statistics to health professionals: the legal analogy.

Despite the importance of statistical concepts to health professionals, the teaching of statistics to students from this field has generally been unrewarding. We feel that a few central concepts are crucial to all statistical thinking and that, for most health professionals, the communication of these is more important than learning about complex mathematical models. A device for demonstrating the parallels between a criminal legal trial and statistical hypothesis testing is presented. We feel that it can facilitate the learning of this central statistical concept.

Curriculum↗

Statistical tests in medical research.

Various propositions have been made to improve the statistical quality of medical journals: using statistical referees, promoting better collaboration between statisticians and researchers, and teaching of basic statistics to clinicians. The most frequent errors found in medical articles are misinterpretation of p-values or non-significant results and confusion between statistical and clinical significance, inappropriate use of tests requiring precise assumptions, inappropriate or not controlled multiple testing and particularly testing of post hoc hypotheses, and overemphasis on p-values. Many errors arising from the misinterpretation of results of statistical hypothesis tests, the basic principles of this methodology are emphasized, and the usual fallacies found in the medical literature are reviewed.

Research↗

[A simulation study to evaluate the statistical noise and spatial resolution in image reconstruction of emission computed tomography--with respect to the optimization of the filter function in the convolution integral].

Filtered backprojection method has been commonly used to reconstruct images in the field of the computed tomography (CT). However, in the emission CT such as positron and single photon CT, poor counting static which are caused by limited dosage to patients, limited counting rate capacity and limited efficiency of the imaging device, produce a statistical noise in the reconstructed image. The magnitude of the statistical noise and the spatial resolution were evaluated for various shapes of the filter used in the convolution integrals of the filtered back-projection procedure. The statistical noise was proportional to the inverse of the root of the total number of counts for any filters. The high-frequency-cut characteristic of the filter reduced the statistical noise, but increased the spatial resolution in the images. It was possible to optimize the shape of the filter for given total number of counts and required statistical noise and spatial resolution.

Humans↗

Statistical issues in tumor marker studies.

CONTEXT: Inferences from tumor marker studies are complicated by a variety of statistical concerns, which can make proper interpretation of results difficult. This article focuses on important issues that should be addressed when designing, conducting, and analyzing tumor marker studies. OBJECTIVE: To highlight the importance of considering statistical significance, risk ratios, statistical power, reproducibility, multiple testing, confirmatory studies, and missing data in the design of marker studies used for prognosis. RESULTS: Suggestions are provided for more effectively conducting marker studies. These include more careful attention to adequacy of the number of subjects for a marker study and improved documentation and standardization of assay methods. The importance of complete reporting of study results and description of the statistical analysis methods used is also emphasized. CONCLUSION: Cooperation among clinicians, laboratory scientists, and statisticians will be required to conduct statistically sound tumor marker studies and to facilitate prioritizing markers for new and confirmatory studies in an environment of limited patient and specimen resources.

Biomarkers, Tumor↗

Rapid assessment of extremal statistics for gapped local alignment.

The statistical significance of gapped local alignments is characterized by analyzing the extremal statistics of the scores obtained from the alignment of random amino acid sequences. By identifying a complete set of linked clusters, "islands," we devise a method which accurately predicts the extremal score statistics by using only one to a few pairwise alignments. The success of our method relies crucially on the link between the statistics of island scores and extremal score statistics. This link is motivated by heuristic arguments, and firmly established by extensive numerical simulations for a variety of scoring parameter settings and sequence lengths. Our approach is several orders of magnitude faster than the widely used shuffling method, since island counting is trivially incorporated into the basic Smith-Waterman alignment algorithm with minimal computational cost, and all islands are counted in a single alignment. The availability of a rapid and accurate significance estimation method gives one the flexibility to fine tune scoring parameters to detect weakly homologous sequences and obtain optimal alignment fidelity.

Algorithms↗

[Problems in health statistics reporting in Bosnia-Herzegovina].

Health-statistic information system in Bosnia and Herzegovina is presented, its content, problems and reform objectives in accordance with new European trends. Adequate and prompt health information plays a key role in the policy of planning and decision-making at all health levels. Therefore, data collecting must be conducted in accordance with the country's needs aimed to the health promotion and health of the population improvement. Scope and structure of health information system varies from country to country depending on health status of population, health policy and, of course, economic capacity. Public Health Institute of Federation BH is authorized by the Law to conduct statistical research in the health sector, and, therefore, the Proposal of statistical research in health sector is made, according to these regulations. This Proposal offered 17 statistical researches for 1998. Unfortunately, only 7 researches have been carried out. The shortcomings of the existing health-statistic information system have been found out on the local, cantonal, entity and state level.

Bosnia and Herzegovina↗

[Statistical analysis of repetitive nerve stimulation test].

INTRODUCTION: Statistical properties of Repetitive Nerve Stimulation test (RNS) are studied for different variables (forth to first potentials ratio of CMAP) together with two new variables (trends of area and amplitude for series of CMAP) OBJECTIVE: To compare the variables commonly used, in order to define the best statistical properties and, in the other hand, investigate if the new variables (trends in area and amplitude) could be useful for the study of neuromuscular transmission pathology. SUBJECTS AND METHODS: Statistical properties of voltage (V4/V1(V)), area of CMAP (V4/V1(a)) and slopes of regression lines of voltage (m(V)) and area (m(a)) measures are determined for runs of 3, 10, 15 and 20 Hz series of stimuli in 13 men and 17 women healthy volunteers. RESULTS: 1) The sample fits well to a normal distribution; 2) The variables that measure tendencies in CMAP series, can be reasonably fitted to linear regression functions; 3) Differences between sex and age have been not found; 4) Variables measuring tendencies have been the most stables, specially m(a); 5) The variable that fits better to normal distribution is m(V); 6) All variables behave linearly with respect frequency of stimulation. CONCLUSIONS: 1) Neuromuscular transmission is a particularly stable physiologic function; 2) The most used variable in clinical neurophysiology laboratories, V4/V1(V) have the worst statistical properties, showing a very significant variability; 3) Trends measures (m(a)) and m(V)) show very satisfactory statistical properties; this implies that these could be very useful for the study of neuromuscular transmission diseases.

Data Interpretation, Statistical↗

[Bayesian thinking on its way into medical statistics?].

BACKGROUND: Bayesian statistical analysis is a paradigm quite different from traditional statistical inference. We wanted to show the usefulness of this approach for some medical problems. MATERIALS AND METHODS: We started with Bayes equation as it is used for estimating the probability of illness based on a specific laboratory test. We also looked into a recent Cochrane report on mammography that accepted two studies as valid and five others as biased. In comparison we used examples of clinical trials from other areas that have been misinterpreted by the use of a traditional statistical approach only. RESULTS: We found that by taking into account our prior beliefs about the likely effects on breast cancer mortality of routine radiological screening programmes, the new data fit well into an estimate of a 5% mortality reduction with a 77% chance that there is a positive effect of screening. INTERPRETATION: Bayesian statistics is helpful in making decisions on the basis of experimental evidence by taking into account our prior knowledge, whereas p-values in traditional statistics only give information on how often we will end up with a false positive conclusion in the long run.

Bayes Theorem↗

Statistics in three biomedical journals.

In this paper we analyze the use of statistics and associated problems, in three Czech biological journals in the year 2000. We investigated 23 articles Folia Biologica, 60 articles in Folia Microbiologica, and 88 articles in Physiological Research. The highest frequency of publications with statistical content have used descriptive statistics and t-test. The most usual mistake concerns the absence of reference about the used statistical software and insufficient description of the data. We have compared our results with the results of similar studies in some other medical journals. The use of important statistical methods is comparable with those used in most medical journals, the proportion of articles, in which the applied method is described insufficiently is moderately low.

Czech Republic↗

[Assessment of population differentiation using DNA fingerprinting and modified Wright's Fst-statistics].

Using our results and literature data on multilocus DNA fingerprinting, we propose a method of obtaining unbiased estimates of the between--population genetic similarity index and a measure of population subdivision based on modified Wright's FST-statistics. On the basis of multiple comparison T2 Hotelling's test and Holmes' procedure, the FST-statistics was applied to assess differentiation of four (Pacific and Atlantic) subpopulations of humpback whale Megaptera novaeangliae, six populations of California island gray fox Urocyon littoralis, and geographically isolated Ob' and Yakutia populations of Siberian white crane Crus leucogeranus. It was shown that the regional humpback whale subpopulations do not constitute a single panmictic unit (P < 10(-4)). The subdivision index of the Pacific and Atlantic populations expressed in terms of FST-statistics varied from 0.101 to 0.157. The differentiation estimates for the island fox populations, which ranged from 0.2109 to 0.4027, indicate that subdivision of these populations is a function of the distance between the islands, island size, and population size. In particular, the smallest and the greatest differences were found respectively between the populations of the geographically closest northern islands (FST = 0.2157, FST = 0.2109) and between those of the most distant northern and southern islands (FST = 0.4027, FST = 0.3869). Subdivision of the island populations with minimum areas and low population number was intermediate (FST = 0.3789). Mean values of heterozygosity, within-population genetic similarity index, and the number of coinciding fragments for two random individuals of Siberian white crane from the Ob' and Yakutia population were not statistically significantly different (P > or = 0.852, (P > or = 0.491, (P > or = 0.325). However, pairwise comparisons of mean FST values indicated that the differentiation estimates for samples from these populations fall within the limits of population subdivision (P = 0.01). The subdivision estimate (0.108-0.133) of various groups of Siberian white cranes is comparable to interregional subdivision of humpback whale. Based on the results of this study, we recommend the approach based on modified Wright's FST-statistics for studying genetic population structure aimed at detecting population subdivision.

Animals↗