Change point analysis of normal distribution based on the likelihood ratio principle and its application in the number of outpatients analysis / 中华地方病学杂志

Objective:The authors introduced the change point analysis of normal distribution based on the likelihood ratio principle, analyzed the number of outpatients in a hospital of Luohu District, Shenzhen, to provide scientific basis for rational allocation of health resources.Methods:The authors collected totally 636 number of outpatients' data from 8: 00 to 12: 00 a.m. at 48 time windows at 5 minutes intervals in a hospital of Luohu District, Shenzhen, and analyzed it with single change point analysis of simultaneous change of mean and variance, and discussed when the change point occurred.Results:The average number of outpatient was 13.250 0 for every time window, the change point occurred at 8: 50, the probability was 0.000 025, the average number of outpatient per 5 minutes from 8: 00 to 8: 50 was 7.000 0, the average number of outpatient per 5 minutes from 8: 50 to 12: 00 was 14.897 4, and the ratio of number of outpatients before and after the change point occurred was 1∶2.Conclusion:In the case of no need to determine the base period or compare the data, the change point analysis of normal distribution based on the principle of likelihood ratio provides a new way of statistical analysis and statistical monitoring for the rational allocation of health resources based on the number of patients.

How to use analysis of variance correctly——the tests of homogeneity of variance and SAS implementation / 四川精神卫生

The purpose of the paper was to introduce the test for homoscedasticity and the SAS implementation. The test of homogeneity of variance could be divided into the following three categories， ①analysis of variance directly based on comparison of variances， ②analysis of variance based on mean comparison was adopted for the new data from the variable transformation of the original data， ③the method of the χ2 test was used to analyze the quantitative raw data which followed the normal distribution. In the first category， a test statistic that followed the F distribution was constructed directly based on the variance ratio of the two samples. In the second category， there were a variety of different variable transformation approaches for the original data， and the new data after the transformation， which was viewed as the univariate quantitative data collected from a single-factor with multi-level design， was analyzed by using one-way ANOVA. In the third category， the χ2 test statistic was constructed for quantitative data that followed the normal distribution. The paper was based on SAS software to test the homogeneity of variances of three examples， and explained the output results.

Establishment of infrared fingerprints and multivariate statistical analysis of Achyranthes bidentata / 中国药房

OBJECTIVE To establish the infrared fingerprints of Achyranthes bidentata from different producing areas ，and to conduct multivariate statistical analysis. METHODS The infrared fingerprints of 61 batches of A. bidentata samples were established by Spectrum for Window 3.02 and OMNIC 9.2 software. Taking the relative peak height of common peaks of infrared fingerprint as the variable ，the normal distribution analysis was carried out by Excel 2016 software；SPSS 22.0 software was used for cluster analysis and principal component analysis ，and the comprehensive score was calculated ；the orthogonal partial least squares-discriminant analysis was carried out by SIMCA 14.1 software，and the marker wave numbers affecting the quality of A. bidentata were screened by taking the variable importance in projection （VIP）＞1 as the standard. RESULTS The correlation coefficients of infrared spectra of 61 batches of A. bidentata samples were 0.967 2-0.997 7；there were 13 common peaks. The results of normal distribution analysis showed that the normal distribution curve of relative peak height of common peaks for A. bidentata from Henan and Hebei did not cross ，and the normal distribution curve of A. bidentata from Henan and Inner Mongolia crossed. The results of cluster analysis showed that when the distance between groups was 15，61 batches of A. bidentata samples could be clustered into 3 categories，including N 1-N12 were clustered into one category ，N13-N45 were clustered into one category，and N 46-N61 were clustered into one category. The results of principal component analysis showed that the cumulative variance contribution rate of the first three principal components was 91.121％；comprehensive score of qq.com A. bidentata （number N 40） in Jiabu village ，Jiaozuo City ， Henan Province was the highest （2.39）， and that of A.bidentata（number N 4）in Xin ’an village ，Anguo City ，Hebei Province was the lowest （－2.89）. The results of orthogonal 163.com partial least squares-discriminant analysis showed that 61 batches of A. bidentata samples were divided into three categories ，including N 1-N12 were clustered into one category ，N13-N28 were clustered into one category and N 29-N61 were clustered into one category. Seven marker wave numbers affecting the quality were selected. The corresponding wave numbers of VIP from large to small were 1 059，927，2 933，813，1 732，1 128 and 3 367 cm－1，1 732 cm－1 was the characteristic obsorption peak of saponins ，1 059，1 128，927 cm－1 were the characteristic obsorption peaks of glycosides. CONCLUSIONS Infrared fingerprint combined with normal distribution analysis ，cluster analysis ，principal component analysis and orthogonal partial least squares-discriminant analysis can be used to identify A. bidentata from different producing areas.

How to use χ2 test correctly——χ2 distribution and the related contents / 四川精神卫生

The purpose of this article was to introduce the χ2 distribution and related contents， including χ2 distribution and non-central χ2 distribution. It focused on showing the definition of two χ2 distributions， the graph and the main properties of the probability density function. Among them， the two most important properties were： first， the limiting distribution of the χ2 distribution was the normal distribution； second， n-1s2σ2followed the χ2 distribution with n-1 degrees of freedom.In addition， it also explained the relationship between the χ2 distribution and the normal distribution， the relationship between χ2 test statistic and Z test statistic. Finally， it illustrated the computational approaches of the χ2 distribution based on the two SAS functions in SAS software.

How to use χ2 test correctly——the analysis of a common risk difference for the data of a multiway table and the implementation of SAS software / 四川精神卫生

The purpose of this article was to introduce the risk rate difference analysis method of the g×2×2 table data and the calculation method based on the SAS software. The tasks that needed to be completed included the following two terms： first， the point estimation of the common risk rate difference and its confidence interval estimation； second， the test "whether the common risk rate difference was equal to 0". Among them， there were a total of 6 approaches for achieving the aforementioned first task； and three approaches for achieving the aforementioned second task. Based on the SAS software and an example， the article realized the point estimation， the confidence interval estimation and the hypothesis test of the common risk rate difference， respectively. Next， the SAS output results were explained and the statistical and professional conclusions were made.

How to use χ2 test correctly——the rank sum tests and the implementation of the SAS software / 四川精神卫生

The purpose of this article was to introduce the rank sum test and its SAS implementation. The concrete contents included the following three aspects： ①the simple linear rank test of two-sample data， ②the one-way ANOVA rank sum test of the multi-sample data， ③the "scoring methods" in the aforementioned two situations. In the third aspect above， there were 10 concrete scoring approaches. Based on an example and with the aid of the SAS software， the paper implemented the first-type rank sum test previously， explained the output results， and made statistical and professional conclusions.

Validación de la calculadora de la Fundación de Medicina Fetal para tamiz de preeclampsia adaptada a población mexicana / Validation of the Fetal Medicine Foundation calculator for pre-eclampsia screening test adapted to a Mexican population

Resumen OBJETIVO: Validar el rendimiento de la calculadora de la Fundación de Medicina Fetal 4.0 adaptada a población mexicana. MATERIALES Y MÉTODOS: Estudio de cohorte efectuado en embarazos con feto único, según el modelo de riesgos en competencia para preeclampsia en un centro de medicina fetal de la Ciudad de México. El riesgo a priori se calculó de acuerdo con la historia clínica. La presión arterial media, el índice de pulsatilidad medio de la arteria uterina y la proteína plasmática A asociada al embarazo se midieron a las 11 a 14 semanas de gestación con metodología estandarizada. El valor de cada marcador se transformó en múltiplos de la mediana adaptados a la población local. Se aplicaron la distribución normal multivariante y el teorema de Bayes para obtener las probabilidades posprueba individuales, que se utilizaron como clasificadores para el área bajo la curva de característica receptor-operador. RESULTADOS: La incidencia de preeclampsia fue del 5.0% (54/1078). El área bajo la curva de característica receptor-operador fue de 0.784 (0.712; 0.856) para preeclampsia a menos de 37 semanas y de 0.807 (0.762; 0.852) para preeclampsia global. CONCLUSIONES: La calculadora FMF 4.0 adaptada a población mexicana resultó válida. Si bien tuvo menor rendimiento al esperado para preeclampsia a menos de 37 semanas, el rendimiento para preeclampsia global fue satisfactorio. Se justifica desarrollar la calculadora local.

Abstract OBJECTIVE: To validate the performance of the Fetal Medicine Foundation 4.0 calculator adapted to the Mexican population. MATERIALS AND METHODS: Cohort study performed in singleton pregnancies, according to the competing risk model for preeclampsia in a fetal medicine center in Mexico City. The a priori risk was calculated according to the clinical history. Mean arterial pressure, mean uterine artery pulsatility index and pregnancy-associated plasma protein A were measured at 11 to 14 weeks of gestation with standardized methodology. The value of each marker was transformed into multiples of the median adapted to the local population. Multivariate normal distribution and Bayes' theorem were applied to obtain individual posttest probabilities, which were used as classifiers for the area under the receiver-operator characteristic curve. RESULTS: The incidence of preeclampsia was 5.0% (54/1078). The area under the receiver-operator characteristic curve was 0.784 (0.712; 0.856) for preeclampsia at less than 37 weeks and 0.807 (0.762; 0.852) for global preeclampsia. CONCLUSIONS: The FMF 4.0 calculator adapted to Mexican population proved valid. Although it had lower performance than expected for preeclampsia at less than 37 weeks, the performance for global preeclampsia was satisfactory. The development of the local calculator is justified.

More about the basic assumptions of t-test: normality and sample size / 대한마취과학회지

Most parametric tests start with the basic assumption on the distribution of populations. The conditions required to conduct the t-test include the measured values in ratio scale or interval scale, simple random extraction, normal distribution of data, appropriate sample size, and homogeneity of variance. The normality test is a kind of hypothesis test which has Type I and II errors, similar to the other hypothesis tests. It means that the sample size must influence the power of the normality test and its reliability. It is hard to find an established sample size for satisfying the power of the normality test. In the current article, the relationships between normality, power, and sample size were discussed. As the sample size decreased in the normality test, sufficient power was not guaranteed even with the same significance level. In the independent t-test, the change in power according to sample size and sample size ratio between groups was observed. When the sample size of one group was fixed and that of another group increased, power increased to some extent. However, it was not more efficient than increasing the sample sizes of both groups equally. To ensure the power in the normality test, sufficient sample size is required. The power is maximized when the sample size ratio between two groups is 1 : 1.

Normality Test in Clinical Research

In data analysis, given that various statistical methods assume that the distribution of the population data is normal distribution, it is essential to check and test whether or not the data satisfy the normality requirement. Although the analytical methods vary depending on whether or not the normality is satisfied, inconsistent results might be obtained depending on the analysis method used. In many clinical research papers, the results are presented and interpreted without checking or testing normality. According to the central limit theorem, the distribution of the sample mean satisfies the normal distribution when the number of samples is above 30. However, in many clinical studies, due to cost and time restrictions during data collection, the number of samples is frequently lower than 30. In this case, a proper statistical analysis method is required to determine whether or not the normality is satisfied by performing a normality test. In this regard, this paper discusses the normality check, several methods of normality test, and several statistical analysis methods with or without normality checks.

Survey of the use of statistical methods in Journal of the Korean Association of Oral and Maxillofacial Surgeons

OBJECTIVES: This study aimed to describe recent patterns in the types of statistical test used in original articles that were published in Journal of the Korean Association of Oral and Maxillofacial Surgeons. MATERIALS AND METHODS: Thirty-six original articles published in the Journal in 2015 and 2016 were ascertained. The type of statistical test was identified by one researcher. Descriptive statistics, such as frequency, rank, and proportion, were calculated. Graphical statistics, such as a histogram, were constructed to reveal the overall utilization pattern of statistical test types. RESULTS: Twenty-two types of statistical test were used. Statistical test type was not reported in four original articles and classified as unclear in 5%. The four most frequently used statistical tests constituted 47% of the total tests and these were the chi-square test, Student's t-test, Fisher's exact test, and Mann-Whitney test in descending order. Regression models, such as the Cox proportional hazard model and multiple logistic regression to adjust for potential confounding variables, were used in only 6% of the studies. Normality tests, including the Kolmogorov-Smirnov test, Levene test, Shapiro-Wilk test, and Scheffé's test, were used diversely but in only 10% of the studies. CONCLUSION: A total of 22 statistical tests were identified, with four tests occupying almost half of the results. Adoption of a nonparametric test is recommended when the status of normality is vague. Adjustment for confounding variables should be pursued using a multiple regression model when the number of potential confounding variables is numerous.

Técnicas de correção do teste qui-quadrado para amostras não normais / Techniques for correction the chi-square test for non-normal samples / Técnicas de corrección del test chi-cuadrado para muestras no normales

Este artigo tem o objetivo de avaliar técnicas de correções para o teste Qui-Quadrado (χ2) aplicadas a modelos da análise fatorial confirmatória (CFA) em amostras não normais. Em uma abordagem simulada e exploratória, foram mensuradas distribuições distintas em termos de curtose multivariada. Na maioria das situações verificadas, observou-se uma tendência dos testes aferidos de realizar correções diferenciadas dos valores do χ2, CFI e RMSEA em contextos similares. Como conclusão, dentre outros testes avaliados, sugere-se o uso dos seguintes: teste Elíptico com Mínimos Quadrados Reponderados (Teoria Elíptica); teste da Curtose Heterogênea com Mínimos Quadrados Reponderados (Teoria Curtose Heterogênea) e teste Escalado de Satorra-Bentler com Máxima Verossimilhança (para distribuições com excesso de assimetria e/ou curtose univariadas). Porém, devido ao fator de correção, o teste Escalado de Satorra-Bentler pode aceitar modelos moderadamente mal especificados na presença de extrema curtose. (AU)

This paper aims to evaluate techniques for correcting the chi-square test (χ2) as applied to Confirmatory Factor Analysis (CFA) models in non-normal data. In a simulated and exploratory approach, distinct distributions were analyzed in terms of multivariate kurtosis. In most situations, it was observed a tendency of the analyzed tests to produce differing corrections on the χ2 values, as well as for the CFI and RMSEA values. Among other tests evaluated, this study suggested the use of the Elliptical Test with Least Squares (Elliptical Theory), Heterogeneous Kurtosis Test with Reweighted Least Squares (Heterogeneous Kurtosis Theory) and Satorra-Bentler Scaled Test with Maximum Likelihood estimation (for distributions with excessive univariate asymmetry and/or kurtosis). However, due to the correction factor, the Satorra-Bentler Scaled test can accept moderately poorly specified models in the presence of extreme kurtosis. (AU)

Este artículo tiene por objetivo evaluar las técnicas de correcciones para la prueba chi-cuadrado (χ2) aplicadas a modelos del Análisis Factorial Confirmatorio (CFA) en muestras no normales. En un enfoque simulado y exploratorio, se midieron distribuciones distintas en términos de curtosis multivariada. En la mayoría de las situaciones verificadas, se observó una tendencia de las pruebas evaluadas de realizar correcciones diferenciadas de los valores del χ2 , CFI y RMSEA en contextos similares. En conclusión, entre otras pruebas evaluadas, se sugiere el uso de las siguientes: Prueba Elíptica con Mínimos Cuadrados Reponderados (Teoría Elíptica); Prueba de la Curtosis Heterogénea con Mínimos Cuadrados Reponderados (Teoría de la Curtosis Heterogénea) y Prueba Escalada de Satorra-Bentler con Máxima Verosimilitud (para distribuciones con exceso de asimetría y/o curtosis univariadas). No obstante, por cuenta del factor de corrección, la Prueba Escalada de Satorra-Bentler puede aceptar modelos moderadamente mal especificados en presencia de extrema curtosis. (AU)

Probable monthly rainfall associated with distinct biomes of Mato Grosso do Sul state / Precipitação mensal provável associada aos diferentes biomas do estado de Mato Grosso do Sul

The aim of this study was to determine the probable monthly rainfall for the state of Mato Grosso do Sul, considering the level of 75% probability, and study the spatial distribution associated with its different biomes. The rainfall data of 32 stations (sites) in the state of Mato Grosso do Sul were collected in the period 1954-2013. In each of the 384 series, the average monthly rainfall was calculated, for at least 30 years of observation. The Kolmogorov-Smirnov adhesion test was applied to the rainfall time series to check the fit of the data to a normal distribution. The likely fallout was estimated at 75% probability, using the normal probability distribution and, subsequently, it was adopted the method of Ordinary Kriging interpolation mathematics to spatial data. Based on the likely monthly precipitation estimated, the State of Mato Grosso do Sul possess three distinct periods, with the precipitation associated with different biomes: the rainy season (between the months November to March, where increased precipitation occurred in the Savanna biome), dry season (between the months from June to August, when the highest rainfall occurred in the Atlantic Forest) and transition period (April and May and September and October).

O objetivo estudo foi determinar a precipitação mensal provável para o Estado de Mato Grosso do Sul, considerando o nível de 75% probabilidade e estudar sua distribuição espacial associada aos seus diferentes biomas. Os dados de precipitação pluvial de 32 estações (locais) do Estado do Mato Grosso do Sul foram coletados do período de 1954 a 2013. Em cada uma das 384 séries temporais de precipitação pluvial mensal calculou-se a média, com no mínimo 30 anos de observação. Foi aplicado o teste de aderência de Kolmogorov-Smirnov nas 364 séries temporais de precipitação pluvial mensal para verificar o ajuste dos dados a distribuição normal. A precipitação provável foi estimada a 75% de probabilidade, utilizando-se a distribuição de probabilidade normal e, posteriormente, foi adotado o método de interpolação matemática da Krigagem Ordinária para espacialização dos dados. Com base na precipitação mensal provável, estimada pela distribuição normal a 75% de probabilidade, o Estado do Mato Grosso do Sul possuí três períodos distintos, estando à precipitação associada aos diferentes biomas: período chuvoso (entre os meses de novembro a março, onde as maiores precipitações ocorrem no bioma Cerrado), período seco (entre os meses de junho a agosto, onde as maiores precipitações ocorrem no bioma Mata Atlântica) e período de transição (meses de abril e maio e setembro e outubro).

Statistical Data Editing in Scientific Articles

Scientific journals are important scholarly forums for sharing research findings. Editors have important roles in safeguarding standards of scientific publication and should be familiar with correct presentation of results, among other core competencies. Editors do not have access to the raw data and should thus rely on clues in the submitted manuscripts. To identify probable errors, they should look for inconsistencies in presented results. Common statistical problems that can be picked up by a knowledgeable manuscript editor are discussed in this article. Manuscripts should contain a detailed section on statistical analyses of the data. Numbers should be reported with appropriate precisions. Standard error of the mean (SEM) should not be reported as an index of data dispersion. Mean (standard deviation [SD]) and median (interquartile range [IQR]) should be used for description of normally and non-normally distributed data, respectively. If possible, it is better to report 95% confidence interval (CI) for statistics, at least for main outcome variables. And, P values should be presented, and interpreted with caution, if there is a hypothesis. To advance knowledge and skills of their members, associations of journal editors are better to develop training courses on basic statistics and research methodology for non-experts. This would in turn improve research reporting and safeguard the body of scientific evidence.

Practical statistics in pain research

Pain is subjective, while statistics related to pain research are objective. This review was written to help researchers involved in pain research make statistical decisions. The main issues are related with the level of scales that are often used in pain research, the choice of statistical methods between parametric or nonparametric statistics, and problems which arise from repeated measurements. In the field of pain research, parametric statistics used to be applied in an erroneous way. This is closely related with the scales of data and repeated measurements. The level of scales includes nominal, ordinal, interval, and ratio scales. The level of scales affects the choice of statistics between parametric or non-parametric methods. In the field of pain research, the most frequently used pain assessment scale is the ordinal scale, which would include the visual analogue scale (VAS). There used to be another view, however, which considered the VAS to be an interval or ratio scale, so that the usage of parametric statistics would be accepted practically in some cases. Repeated measurements of the same subjects always complicates statistics. It means that measurements inevitably have correlations between each other, and would preclude the application of one-way ANOVA in which independence between the measurements is necessary. Repeated measures of ANOVA (RMANOVA), however, would permit the comparison between the correlated measurements as long as the condition of sphericity assumption is satisfied. Conclusively, parametric statistical methods should be used only when the assumptions of parametric statistics, such as normality and sphericity, are established.

Central limit theorem: the cornerstone of modern statistics / 대한마취과학회지

According to the central limit theorem, the means of a random sample of size, n, from a population with mean, µ, and variance, σ², distribute normally with mean, µ, and variance, σ²/n. Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. Compared to non-parametric tests, which do not require any assumptions about the population probability distribution, parametric tests produce more accurate and precise estimates with higher statistical powers. However, many medical researchers use parametric tests to present their data without knowledge of the contribution of the central limit theorem to the development of such tests. Thus, this review presents the basic concepts of the central limit theorem and its role in binomial distributions and the Student's t-test, and provides an example of the sampling distributions of small populations. A proof of the central limit theorem is also described with the mathematical concepts required for its near-complete understanding.

Likelihood ratio test between two groups of castor oil plant traits / Teste de razão de verossimilhança entre dois grupos de caracteres de mamoneira

ABSTRACT: The likelihood ratio test (LRT), to the independence between two sets of variables, allows to identify whether there is a dependency relationship between them. The aim of this study was to calculate the type I error and power of the LRT for determining independence between two sets of variables under multivariate normal distributions in scenarios consisting of combinations of 16 sample sizes; 40 combinations of the number of variables of the two groups; and nine degrees of correlation between the variables (for the power). The rate of type I error and power were calculate at 640 and 5,760 scenarios, respectively. A performance evaluation of the LRT was conducted by computer simulation by the Monte Carlo method, using 2,000 simulations in each scenario. When the number of variables was large (24), the TRV controlled the rate of type I errors and showed high power in sizes greater than 100 samples. For small sample sizes (25, 30 and 50), the test showed good performance because the number of variables did not exceed 12.

RESUMO: O teste de razão de verossimilhança para a independência entre dois grupos de variáveis permite-nos identificar se existe uma relação de dependência entre eles. O objetivo deste trabalho foi calcular o erro tipo I e o poder do teste de razão de verossimilhança para independência entre dois grupos de caracteres, com distribuição normal multivariada, em cenários constituídos pelas combinações de: 16 tamanhos de amostra; 40 combinações de número de caracteres dos dois grupos; e nove graus de correlação entre os caracteres (para o poder). A taxa de erro tipo I e o poder foram calculados em 640 e 5.760 cenários a taxa de erro tipo I e o poder, respectivamente. A avaliação do desempenho do teste de razão de verossimilhança foi realizada por meio de simulação computacional pelo método Monte Carlo, utilizando-se 2.000 simulações em cada um dos cenários. Quando o número de caracteres é grande (24), o teste de razão de verossimilhança controla a taxa de erro tipo I e apresenta poder elevado (próximo a 100%), em tamanhos de amostra superiores a 100. Para tamanhos amostrais pequenos (25, 30 e 50), o teste apresenta bom desempenho (erro tipo I esperado e poder elevado), desde que o número de caracteres não exceda a 12.

Functions of probability for fitting monthly rainfall in sites of Mato Grosso do Sul state / Funções de probabilidade para ajuste da chuva mensal em locais do estado de Mato Grosso do Sul

The identification of the probability distribution function for the representation of the monthly rainfall is relevant in agricultural planning, mainly regard to the establishment of crops. The aim of this work was to verify the probability distribution (exponential, gamma or normal) which best fits to data monthly rainfall of 14 sites in the state of Mato Grosso do Sul. Rainfall data of 14 stations (sites) of the State of Mato Grosso do Sul it were obtained from the National Water Agency (ANA) database, collected in the period 1975 - 2013. At each of the 168 time series of monthly rainfall was applied the Kolmogorov-Smirnov test to assess the fit to probability distributions exponential, gamma and normal. The normal probability distribution presented the best fit to monthly rainfall series of Mato Grosso do Sul and it can be used for the estimation the monthly rainfall, especially in the rainy season months (October to March). The exponential probability distribution can be used for the estimation of monthly rainfall in the driest months of the year (May to September). Thus, we recommend that these distributions be used in future research, aimed to estimate the probable rainfall for the Mato Grosso do Sul State.

A identificação da função de distribuição de probabilidade para representação da chuva mensal é relevante no planejamento agrícola, sobretudo no que diz respeito à instalação de culturas. O objetivo deste trabalho foi verificar qual a distribuição de probabilidade (exponencial, gama ou normal) se ajusta melhor aos dados de precipitação pluvial mensal de 14 locais do Estado do Mato Grosso do Sul. Os dados pluviométricos de 14 estações (locais) do Estado do Mato Grosso do Sul foram obtidos do Banco de Dados da Agência Nacional de Águas (ANA), coletados do período de 1975 a 2013. Em cada uma das 168 séries temporais de chuva mensal aplicou-se o teste de Kolmogorov-Smirnov para avaliar o ajuste às distribuições de probabilidade exponencial, gama e normal. A distribuição de probabilidade normal apresentou melhor ajuste as séries de chuva mensal do Estado de Mato Grosso do Sul, podendo ser utilizada para estimativa da precipitação pluvial mensal, principalmente, nos meses de período chuvoso (outubro a março). A distribuição de probabilidade exponencial pode ser utilizada para estimativa da chuva mensal nos meses mais secos do ano (maio a setembro). Desta forma, recomendamos que estas distribuições sejam utilizadas em futuras pesquisas, que visem estimar a precipitação provável para o Estado de Mato Grosso do Sul.

Understanding statistical concepts in laboratory quality control measures in biomedical research.

The purpose of this article is to explore the quality assurance methods in carrying out laboratory investigations on various kits and biological products and analysing the results through statistical approach. This is commonly used in the health care industry where biological investigations have become a very important part. Quality Control/Quality Assurance (QC/QA) refers to the overall management system which includes the organization, planning, data collection, quality control, documentation, evaluation and reporting activities. With the emerging health issues and availability of modern treatment modalities, it is important to provide the patient, clinical diagnosis with the relevant laboratory investigations. It is therefore, important to maintain the quality control of the testing with a standard degree of precision, which in turn is essential for the delivery of the quality patient care. In view of this, statistical approaches that can be adopted to ascertain the quality of the test have been discussed. The communication also discusses components of validity of the biomedical test and its relevance in clinical settings.

Pruebas de bondad de ajuste en distribuciones simétricas, ¿qué estadístico utilizar? / Goodness of Fit Tests for Symmetric Distributions, which Statistical Should I Use?

El uso de pruebas no paramétricas resulta recomendable cuando los datos a analizar no cumplen los supuestos de normalidad y homocedasticidad. Sin embargo, la suposición de la normalidad de los datos o el empleo de pruebas de bondad de ajuste que no son adecuadas para el tamaño muestral empleado son aspectos habituales. Este hecho implica, en muchas ocasiones, el uso de pruebas estadísticas no ajustadas al tipo de distribución real y, consecuentemente, el establecimiento de conclusiones erróneas. Por ello, en el presente estudio se ha analizado el poder de detección de cinco pruebas de bondad de ajuste (Kolmogorov-Smirnov, Kolmogorov-Smirnov-Lilliefors, Shapiro-Wilk, Anderson-Darling y Jarque-Bera) en distribuciones simétricas con seis tamaños muestrales entre 30 y 1000 participantes generados mediante una simulación Monte Carlo. Los resultados muestran una tendencia conservadora generalizada a medida que se incrementa el tamaño muestral. En cuanto a los tamaños muestrales, las pruebas con un mejor poder de detección de la no normalidad son Kolmogorov-Smirnov-Lilliefors y Anderson-Darling para muestra pequeñas, la prueba de Kolmogorov-Smirnov si se emplean tamaños muestrales medios (200 participantes) y la prueba de Shapiro-Wilk cuando se analizan muestras superiores a 500 participantes. Además, la prueba clásica de Kolmogorov-Smirnov se considera absolutamente ineficaz independientemente del tamaño muestral.

The use of nonparametric tests is recommended when the data do not meet the assumptions of normality and homoscedasticity. However, the assumptions of normality of the data or the use of goodness of fit tests that are not appropriate for the assessed sample are common aspects. In many cases, this implies the use of statistical tests unadjusted for the real data distribution and, consequently, the establishment of inaccurate conclusions. Therefore, in this paper the detection power of five tests of goodness of fit (Kolmogorov-Smirnov-Lilliefors, Kolmogorov-Smirnov, Shapiro-Wilk, Anderson-Darling and Jarque -Bera) in symmetric distributions is analysed in six sample sizes between 30 and 1000 participants generated by Monte Carlo simulation. Results show a marked conservative tendency as the sample size becomes larger. Regarding sample sizes to detect non-normality: analysing small samples the best results are provided by Kolmogorov-Smirnov-Lilliefors and Anderson-Darling tests, if the sample is medium-sized (200 participants) the Kolmogorov-Smirnov, and when samples are over 500 participants the Shapiro-Wilk test is recommended. In addition, the classic test of Kolmogorov-Smirnov is considered absolutely ineffective regardless the sample size.

t-Student: Usos y abusos / Student's t: Uses and abuses

La prueba t-Student se fundamenta en dos premisas; la primera: en la distribución de normalidad, y la segunda: en que las muestras sean independientes. Permite comparar muestras, N ≤ 30 y/o establece la diferencia entre las medias de las muestras. El análisis matemático y estadístico de la prueba con frecuencia se minimiza para N > 30, utilizando pruebas no paramétricas, cuando la prueba tiene suficiente poder estadístico.

Student's t test is based on two premises; first: normality of distribution and second: the independence of the samples. This allows comparing samples N ≤ 30 and/or establishes the differences between the means of the two samples. The mathematical and statistical analysis of the test is frequently minimalized N > 30, using non parametric tests, when the test has enough statistical power.