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Can't miss: conquer any number task by making important statistics simple. Part 6. Tests of statistical significance (z test statistic, rejecting the null hypothesis, p value), t test, z test for proportions, statistical significance versus meaningful difference.

Healthcare quality professionals need to understand and use inferential statistics to interpret sample data from their organizations. Since in quality improvement and healthcare research studies all the data from a population often are not available, investigators take samples and make inferences about that population using inferential statistics. This series of six articles will give readers an understanding of the concepts of inferential statistics as well as the specific tools for calculating confidence intervals and tests of statistical significance for samples of data. This article, Part 6, merges the four concepts of the (1) standard error of the difference between sample means, (2) the z test statistic, (3) rejecting the null hypothesis, and (4) the p value to provide a comprehensive view of tests of statistical significance. This is followed by a description of t tests, statistical tests for comparing two sample proportions, and Type I and Type II errors. The series of articles concludes with a description of statistical significance versus meaningful difference.

Confidence Intervals↗

TYPES of vital statistics available in different countries: Demographic and Social Statistics Branch, Statistical Office of the United Nations.

This article analyses the types of vital statistical data available in the 58 major statistical areas of the world, covering about half the world population. The information for the rest of the world can be assumed to be even less complete.Tables are given showing the number of areas supplying information for the various tabulations in the vital statistics section of the United Nations Demographic Yearbook, and the availability of each tabulation for each area. Other tables indicate which items of substantive interest are given on national statistical-report forms in the same areas, and with what frequency.

Birth Rate↗

Appointment of statistical editor and quality of statistics in a small medical journal.

AIM: To test if the appointment of a statistical editor improves the quality of manuscripts published in a small general medical journal. METHODS: Retrospective review of all manuscripts containing statistical data published in the Croatian Medical Journal between 1992 and 2000 (n=241). Statistical analysis and its presentation were assessed by a single observer. RESULTS: Before the appointment of statistical editor in 1996, 97 manuscripts with statistical data were published. Statistics was not satisfactory in 52 (54%) of them, including 26 definite errors in analysis and 43 in presentation. After the appointment of statistical editor, 144 manuscripts containing statistical data were published. Statistics was not satisfactory in 91 (63%) of them, with 51 definite errors in analysis and 69 in presentation. Out of 144 manuscripts, the editor-in-chief sent out 30 (21%) for statistical review. Statistics was not satisfactory in 25 of them, including 11 definite errors in analysis and 17 in presentation. Statistical editors comments improved three manuscripts. If the authors had acknowledged all statistical editors suggestions, 9 more manuscripts would have been improved. Statistical editor had a total of 195 comments on 30 published manuscripts. Most numerous were the comments concerning the presentation of the statistical analysis (51%), followed by the general comments (26%), comments on analysis (11%), study design (8%), and interpretation (4%). CONCLUSION: Appointment of a statistical editor is not a guarantee of improvement of statistics in small journals. Other measures are necessary, including strict editorial policy on statistical review, monitoring of revised manuscript versions, and enrollment of formally trained biostatisticians.

Humans↗

[The meaning of statistical data in medical science and their examination--true and false analysis of statistical data].

The subjects which are often encountered in the statistical design and analysis of data in medical science studies were discussed. The five topics examined were: Medical science and statistical methods So-called mathematical statistics and medical science Fundamentals of cross-tabulation analysis of statistical data and inference Exploratory study by multidimensional data analyses Optimal process control of individual, medical science and informatics of statistical data In I, the author's statistico-mathematical idea is characterized as the analysis of phenomena by statistical data. This is closely related to the logic, methodology and philosophy of science. This statistical concept and method are based on operational and pragmatic ideas. Self-examination of mathematical statistics is particularly focused in II and III. In II, the effectiveness of experimental design and statistical testing is thoroughly examined with regard to the study of medical science, and the limitation of its application is discussed. In III the apparent paradox of analysis of cross-tabulation of statistical data and statistical inference is shown. This is due to the operation of a simple two- or three-fold cross-tabulation analysis of (more than two or three) multidimensional data, apart from the sophisticated statistical test theory of association. In IV, the necessity of informatics of multidimensional data analysis in medical science is stressed. In V, the following point is discussed. The essential point of clinical trials is that they are not based on any simple statistical test in a traditional experimental design but on the optimal process control of individuals in the information space of the body and mind, which is based on a knowledge of medical science and the informatics of multidimensional statistical data analysis.

Statistics as Topic↗

[A review of basic statistics concepts,research design and statistical analysis methods].

Statistics is a methodology involving a great number of statistical methods. It results in confusion of many clinicians and researchers while they are meditating on how to analyze the collected data in their studies, selecting an appropriate statistical method from all. In fact, the statistical methods are closely correlated to the research design and the data types. Therefore only with a full comprehension of the design methods and the data types can we figure out a simple and practical means from diverse statistical analysis methods. Through the systematic illustration in this review, several statistical concepts, data types, design methods, and the proper way of explaining results with statistical tables and graphs will be demonstrated elaborately. It intends to help the clinicians and researchers select appropriate statistical methods and furthermore, interpret the statistical outcomes accurately in their research.

Humans↗

[Statistical analysis of pharmacological data: use of cumulative chi-squared statistic].

The cumulative chi-squared statistic has been proposed for testing against ordered alternatives in various statistical models. As usual statistical tests of ordered column categorical data, the chi 2 test, Fisher's exact test and Wilcoxon test are used. Pharmacological studies often are performed by multiple dosing. Data obtained from these studies are called ordered categorical data. The cumulative chi-squared statistic, which has been proposed by Hirotsu and Shibuya for testing against ordered alternatives in various statistical models, is little used in spite of its good applicability in the field of pharmacology. This method was too difficult for the general pharmacologist and biological scientists because it requires the use of a complex matrix and a powerful computer to carry out the analysis. However since a more simple method was proposed by Matsumoto and Yoshimura this method has been used more frequently in the biological sciences. In this paper, the one way cumulative chi-squared statistic test and two way chi-squared statistic test are compared with the chi-squared statistic test and Wilcoxon test.

Data Interpretation, Statistical↗

Statistical limitations in functional neuroimaging. II. Signal detection and statistical inference.

The field of functional neuroimaging (FNI) methodology has developed into a mature but evolving area of knowledge and its applications have been extensive. A general problem in the analysis of FNI data is finding a signal embedded in noise. This is sometimes called signal detection. Signal detection theory focuses in general on issues relating to the optimization of conditions for separating the signal from noise. When methods from probability theory and mathematical statistics are directly applied in this procedure it is also called statistical inference. In this paper we briefly discuss some aspects of signal detection theory relevant to FNI and, in addition, some common approaches to statistical inference used in FNI. Low-pass filtering in relation to functional-anatomical variability and some effects of filtering on signal detection of interest to FNI are discussed. Also, some general aspects of hypothesis testing and statistical inference are discussed. This includes the need for characterizing the signal in data when the null hypothesis is rejected, the problem of multiple comparisons that is central to FNI data analysis, omnibus tests and some issues related to statistical power in the context of FNI. In turn, random field, scale space, non-parametric and Monte Carlo approaches are reviewed, representing the most common approaches to statistical inference used in FNI. Complementary to these issues an overview and discussion of non-inferential descriptive methods, common statistical models and the problem of model selection is given in a companion paper. In general, model selection is an important prelude to subsequent statistical inference. The emphasis in both papers is on the assumptions and inherent limitations of the methods presented. Most of the methods described here generally serve their purposes well when the inherent assumptions and limitations are taken into account. Significant differences in results between different methods are most apparent in extreme parameter ranges, for example at low effective degrees of freedom or at small spatial autocorrelation. In such situations or in situations when assumptions and approximations are seriously violated it is of central importance to choose the most suitable method in order to obtain valid results.

Biometry↗

The power and statistical behaviour of allele-sharing statistics when applied to models with two disease loci.

We have evaluated the power for detecting a common trait determined by two loci, using seven statistics, of which five are implemented in the computer program SimWalk2, and two are implemented in GENEHUNTER. Unlike most previous reports which involve evaluations of the power of allele-sharing statistics for a single disease locus, we have used a simulated data set of general pedigrees in which a two-locus disease is segregating and evaluated several nonparametric linkage statistics implemented in the two programs. We found that the power for detecting linkage using the S(all) statistic in GENEHUNTER (GH, version 2.1), implemented as statistic E in SimWalk2 (version 2.82), is different in the two. The P values associated with statistic E output by SimWalk2 are consistently more conservative than those from GENEHUNTER except when the underlying model includes heterogeneity at a level of 50% where the P values output are very comparable. On the other hand, when the thresholds are determined empirically under the null hypothesis, S(all) in GENEHUNTER and statistic E have similar power.

Alleles↗

Spatial statistical analysis of Chinese cancer mortality: a comparison study of the D statistic.

In this paper, we study a nonparametric spatial pattern test statistic, the D statistic. The D statistic is an effective test statistic for testing spatial patterns in regional health data. Comparison studies of the D statistic with fixed weights and random weights are illustrated on the atlas of the Chinese cancer mortality rates and on other cancer atlas. Some social, economic and environmental reasons for statistically significant spatial autocorrelations of the Chinese cancer mortality rates were given in the discussion section. The method for calculating the mean and the variance of the randomly weighted D statistic is given in the appendix.

China↗