Parametric Testing Procedures Research Articles

Simultaneous inference procedures for the comparison of multiple characteristics of two survival functions.

Survival time is the primary endpoint of many randomized controlled trials, and a treatment effect is typically quantified by the hazard ratio under the assumption of proportional hazards. Awareness is increasing that in many settings this assumption is a priori violated, for example, due to delayed onset of drug effect. In these cases, interpretation of the hazard ratio estimate is ambiguous and statistical inference for alternative parameters to quantify a treatment effect is warranted. We consider differences or ratios of milestone survival probabilities or quantiles, differences in restricted mean survival times, and an average hazard ratio to be of interest. Typically, more than one such parameter needs to be reported to assess possible treatment benefits, and in confirmatory trials, the according inferential procedures need to be adjusted for multiplicity. A simple Bonferroni adjustment may be too conservative because the different parameters of interest typically show considerable correlation. Hence simultaneous inference procedures that take into account the correlation are warranted. By using the counting process representation of the mentioned parameters, we show that their estimates are asymptotically multivariate normal and we provide an estimate for their covariance matrix. We propose according to the parametric multiple testing procedures and simultaneous confidence intervals. Also, the logrank test may be included in the framework. Finite sample type I error rate and power are studied by simulation. The methods are illustrated with an example from oncology. A software implementation is provided in the R package nph.

A comparison of nonparametric methods for multivariate two-sample tests

Comparing two multivariate populations can be challenging when the distributional forms are unknown. In such a situation, parametric test procedures are not appropriate given that they require distributional assumptions. In this context, it may be useful to consider the application of nonparametric tests. Specifically, we investigate the application of NonParametric Combination (NPC) which is characterized by high flexibility in the choice of test statistic and is quite powerful in multivariate scenarios. Moreover, it has the advantage of being able to deal with low sample sizes which is a very common situation in real-world applications. The performance of NPC is compared with another nonparametric method well-known in the literature, namely the (depth-based) M-test. A simulation study is provided for the purposes of comparing the performance of the NPC and the data depth-based test. Finally, both test procedures are applied to a real case study.

The Effect of Actionbound Application on Academic Success and Attitude on 6th Grade Field Measurement

This study aims to examine the effects of activities prepared using the Actionbound application on students' academic achievement and mathematical attitude in the field measurement subject in the 6th-grade mathematics course. The study was designed using a quasi-experimental design with a control group from quantitative research methods. The study group of research consists of students studying in two different 6th grades of a secondary school in the central district of Elazığ province in the school year 2022-2023. The achievement averages of the branches in the previous semester were used in forming the experimental and control groups and in ensuring the equivalence of the branches. The research, which was conducted in parallel with the MoNE curriculum, was applied simultaneously to the experimental and control groups. The research, which used parametric testing procedures due to the normal distribution of the data, was analyzed using the SPSS package program. The results show that the digital learning game developed using Actionbound improves performance and attitude, but does not cause a significant difference between the groups. It is recommended to extend the application period of the study and continue the study for one semester.

Comparison of the performances of parametric k-sample test procedures as an alternative to one-way analysis of variance

Objectives: The performances of the Welch test, the Alexander-Govern test, the Brown-Forsythe test and the James Second-Order test, which are among the parametric alternatives of one-way analysis of variance and included in the literature, to protect the Type-I error probability determined at the beginning of the trial at a nominal level, were compared with the F test. Methods: Performance of the tests to protect Type-I error; in cases where the variances are homogeneous and heterogeneous, the sample sizes are balanced and unbalanced, the distribution of the data is in accordance with the normal distribution and the log-normal distribution, how it is affected by the change in the number of groups to be compared has been examined on simulation scenarios. Results: The Welch test, the Alexander-Govern test and the James Second-Order test were not affected by the distribution and performed well in situations where variances were heterogeneous. The Brown-Forsythe test was not affected by the distribution, it performed well when the variance was homogeneous and the sample size in the groups to be compared was not equal. Conclusions: The Welch test, the Alexander-Govern test and the James Second-Order test are the tests that can be recommended as an alternative to the F test.

Modified sequential bifurcation for simulation factor screening under skew-normal response model

Sequential bifurcation (SB) has been widely used for simulation factor screening problems to identify important factors (i.e., factors that can significantly affect system response) with high efficiency and effectiveness under the ‘sparse effects’ assumption. However, when the response is asymmetric, previous SB studies based on the assumption of normally distributed response have shown limitations in practice. In this paper, we develop a skew-normal distributed response model and propose a parametric bootstrap testing procedure that is incorporated into every ‘bifurcation’ stage of SB for testing the significance of factors. Numerical experiments are provided to demonstrate the effectiveness and efficiency of the screening methods.

Estimating and Testing Quantile-based Process Capability Indices for Processes with Skewed Distributions

This article extends the recent work of V¨annman and Albing (2007) regarding the new family of quantile based process capability indices (qPCI) CMA(τ, v). We develop both asymptotic parametric and nonparametric confidence limits and testing procedures of CMA(τ, v). The kernel density estimator of process was proposed to find the consistent estimator of the variance of the nonparametric consistent estimator of CMA(τ, v). Therefore, the proposed procedure is ready for practical implementation to any processes. Illustrative examples are also provided to show the steps of implementing the proposed methods directly on the real-life problems. We also present a simulation study on the sample size required for using asymptotic results.

Kinematic analysis of gait in an underwater treadmill using land-based Vicon T 40s motion capture cameras arranged externally

Aquatic therapy for rehabilitation can be performed in a variety of environments, which can vary from a traditional swimming pool to a self-contained underwater treadmill. While kinematic analysis has been performed in large volume swimming pools using specific underwater motion capture systems, researchers may only have access to a land-based motion-capture system, which is not waterproof. Additionally, underwater motion capture systems may not fit within the confines of a smaller underwater treadmill. Thus, the purpose of this study was to design and analyze methodology to quantify lower limb kinematics during an aquatic treadmill session, using a land-based motion capture system. Kinematics of lower limb motion at different speeds was studied while walking on an underwater treadmill in comparison to walking on the same treadmill without water (empty tank). The effects of the presence of water on walking kinematics was analyzed and interpreted using parametric and non-parametric testing procedures. The results suggest significant influences of speed on knee and ankle angles (p < 0.05) in both dryland and aquatic scenarios. Knee and ankle angle measures revealed no significant differences between the dryland and water treadmill scenarios (p > 0.05). The increased time requirement in water for the full gait cycle found in this study indicates influence of resistive effects. This finding can be especially suited for muscle strengthening and stabilizing treatments for lower limbs. Also, a framework was developed to realize a potential methodology to use land-based motion capture cameras to successfully analyze the kinematics of gait in constrained aquatic volumes.

Hubungan antara banyaknya kuman (CFU/ML) dari bakteriuria dengan leukosit dari leukosituria pada pasien pasca sectio caesarea setelah kateterisasi di Bagian Obstetri dan Ginekologi Rumah Sakit Umum Daerah (RSUD) Ulin Banjarmasin

Urinary Tract Infection (UTI) is a pathologic phenomenon indicated by the presence of bacteria with a high number of CFU/ml. One of the causative measures is the constant catheterization of hospitalized patient. UTI happens easily to pregnant women whose urine will promote the growth of bacteria. The laboratory examination of UTI is carried out to observe the occurcace of bacteria and leucocytes. This study was carried out to see increases in number of bacteria in bacteriuria and number of leucocytes in leucocyturia in caesarean section patients following catheterization. The aim of this study was to examine the correlation between the number of bacteria in bacteriuria and number of lecocytes in leucocyturia from urine obtained after catheterization post caesarean section patients in the Department of Obstetrics and Gynecology of RSUD Ulin Banjarmasin during the periods of June 1st – July 31st, 2004. A descriptive method was used and regression as well as non parametric testing procedure of linear correlation were employed. The results showed a strong degree of correlation between the number of bacteria in bacteriuria and the number of leucocyte in leucocyturia after 1x24 hours (r = 0, 51089) and after 2x24 hours (r = 0, 74647). The regression analysis strongly revealed the increase number of leucocytes in leucocyturia along with the increase number of bacteria in bacteriuria.

Analysis of Means by Ranks: Modification and Application in Contract Acquisition Analysis

Analysis of Means by Ranks is a nonparametric statistical test procedure that was developed in Bakir (1989) but has rarely been applied in practice. This paper modifies and applies Analysis of Means by Ranks to a case study data involving the comparison of three contract proposals. For comparison purposes, we analyze the same data using the well-known Analysis of Variance, Analysis of Means, and the Kruskal-Wallis test. Analysis of Variance and Analysis of Means are two parametric (assume data to be samples from normal populations) test procedures whereas Kruskal-Wallis and Analysis of Means by Ranks are two nonparametric (or distribution-free) procedures. This paper shows that the parametric tests fail to detect a significant difference among three contract proposals, while the nonparametric tests do. The conclusions of the parametric tests are in doubt because a descriptive statistics analysis indicates that the required normality assumption is in doubt; the nonparametric conclusions are more trustful because the normality assumption is not required by nonparametric procedures.

Stepwise progressive parametric multiple testing procedure with correlated normal test statistics

ABSTRACTMultiple testing problems are often seen in clinical trials. An appropriate testing procedure should be specified to deal with the potential inflation of type I error rate due to multiplicity. In this article, we propose a stepwise progressive parametric multiple (SPPM) testing procedure, which constructs the testing using the products of all the combinations of local -values and the critical values are determined by numerical integrations progressively using the closure principle. We have compared the performance of SPPM to several other procedures, and demonstrate the advantage of SPPM procedure, in terms of power, for the certain situations of multiple testing.

A sequential density-based empirical likelihood ratio test for treatment effects.

In health-related experiments, treatment effects can be identified using paired data that consist of pre- and posttreatment measurements. In this framework, sequential testing strategies are widely accepted statistical tools in practice. Since performances of parametric sequential testing procedures vitally depend on the validity of the parametric assumptions regarding underlying data distributions, we focus on distribution-free mechanisms for sequentially evaluating treatment effects. In fixed sample size designs, the density-based empirical likelihood (DBEL) methods provide powerful nonparametric approximations to optimal Neyman-Pearson-type statistics. In this article, we extend the DBEL methodology to develop a novel sequential DBEL testing procedure for detecting treatment effects based on paired data. The asymptotic consistency of the proposed test is shown. An extensive Monte Carlo study confirms that the proposed test outperforms the conventional sequential Wilcoxon signed-rank test across a variety of alternatives. The excellent applicability of the proposed method is exemplified using the ventilator-associated pneumonia study that evaluates the effect of Chlorhexidine Gluconate treatment in reducing oral colonization by pathogens in ventilated patients.

Two sample comparisons including zero-inflated continuous data: A parametric approach with applications to microarray experiment

Micro-array experiments are important fields in molecular biology where zero values mixed with a continuous outcome are frequently encountered leading to a mixed distribution with a clump at zero. Comparison of two mixed populations, e.g. of a control and a treated group; of two groups with different types of cancer, to name a few, are often encountered in these contexts. Fairly skewed distribution of the continuous part coupled with small sample sizes are issues of main concern to be attended for the quality of inference in such situations while popularly used nonparametric methods rely on asymptotic distribution of the underlying test statistics which are valid only under large sample sizes. We address the aforementioned issues via a newly proposed exact test for location-scale family distributions and Generalized pivot quantity (GPQ) based parametric test procedures for non-location-scale distributions. Simulation based assessment showed their superior performance with respect to size and power in comparison to the popular two-part tests (Wilcoxon rank sum, t-test, Kolmogrov–Smirnov, Ansari–Bradley and Sigel–Tukey) more prominently for small sample sizes.

Homogeneity testing for spatially correlated data in multivariate regional frequency analysis

AbstractIdentification of homogeneous regions is a key task in regional frequency analysis (RFA) to obtain adequate quantile estimates for an event of interest. Recently, the frequently used univariate Hosking‐Wallis L‐moment homogeneity test was extended to the multivariate case. Multivariate L‐moments are used as a tool to define the test statistic and copula models to describe the statistical behavior of the analyzed dependent variables. To avoid drawbacks in fitting a parametric joint distribution to the data and a rejection threshold which is based on simulations, its nonparametric alternatives were also proposed. Although the simulation studies performed demonstrated the usefulness of both the parametric and nonparametric tests, the powers obtained were valid only for regions without intersite dependence. Examples from practice nevertheless demonstrate that intersite correlation may be expected for some kinds of data. To overcome the problem of cross correlation between stations, the parametric testing procedure is generalized using D‐vine copulas to model intersite dependence when generating synthetic homogeneous regions during the testing procedure. Monte Carlo simulations were performed and illustrate how intersite dependence negatively impacts the multivariate L‐moment homogeneity tests by significantly reducing their powers. The results of simulations also demonstrate the superiority of the proposed modification over both the original parametric and nonparametric procedures inasmuch as it improves the heterogeneity detection and avoids miscategorization of a region. The modified test is also applied in a case study for meteorological data in the Czech Republic.

A unified framework for weighted parametric multiple test procedures

We describe a general framework for weighted parametric multiple test procedures based on the closure principle. We utilize general weighting strategies that can reflect complex study objectives and include many procedures in the literature as special cases. The proposed weighted parametric tests bridge the gap between rejection rules using either adjusted significance levels or adjusted p-values. This connection is made by allowing intersection hypotheses of the underlying closed test procedure to be tested at level smaller than α. This may be also necessary to take certain study situations into account. For such cases we introduce a subclass of exact α-level parametric tests that satisfy the consonance property. When the correlation is known only for certain subsets of the test statistics, a new procedure is proposed to fully utilize this knowledge within each subset. We illustrate the proposed weighted parametric tests using a clinical trial example and conduct a simulation study to investigate its operating characteristics.

Statistical comparison of final weight scores in quality function deployment (QFD) studies

Purpose – Quality function deployment (QFD) is a methodology to translate the “voice of the customer” into engineering/technical specifications (HOWs) to be followed in designing of products or services. For the method to be effective, QFD practitioners need to be able to accurately differentiate between the final weights (FWs) that have been assigned to HOWs in the house of quality matrix. The paper aims to introduce a statistical testing procedure to determine whether the FWs of HOWs are significantly different and investigate the robustness of different rating scales used in QFD practice in contributing to these differences. Design/methodology/approach – Using a range of published QFD examples, the paper uses a parametric bootstrap testing procedure to test the significance of the differences between the FWs by generating simulated random samples based on a theoretical probability model. The paper then determines the significance or otherwise of the differences between: the two most extreme FWs and all pairs of FWs. Finally, the paper checks the robustness of different attribute rating scales (linear vs non-linear) in the context of these testing procedures. Findings – The paper demonstrates that not all of the differences that exist between the FWs of HOW attributes are in fact significant. In the absence of such a procedure, there is no reliable analytical basis for QFD practitioners to determine whether FWs are significantly different, and they may wrongly prioritise one engineering attribute over another. Originality/value – This is the first article to test the significance of the differences between FWs of HOWs and to determine the robustness of different strength of scales used in relationship matrix.

PURCHASING POWER PARITY WITH RANK TESTS FOR NONLINEAR COINTEGRATION IN AFRICAN COUNTRIES

AbstractThis study applies nonlinear cointegration to assess exchange rates with the corresponding relative prices and aggregate price levels for 20 African countries. We find that a nonparametric rank test has higher power than parametric testing procedures; a true data‐generating process of exchange rate is in fact a stationary nonlinear process. We examine the validity of purchasing power parity (PPP) from the nonparametric nonlinear point of view and provide robust evidence that clearly indicates PPP holds true for these countries. Hence, the long‐run African countries exchange rate adjustments are in equilibrium with the relevant fundamentals as suggested by the PPP hypothesis in a nonlinear way.

Notes on the Goodness-of-Fit Tests for the Ordinal Response Model

In this paper we discuss some cautionary notes in using the Pearson chi-squared test statistic for the goodness-of-fit of the ordinal response model. If a model includes continuous type explanatory variables, the resulting table from the fit of a model is not a regular one in the sense that the cell boundaries are not fixed but randomly determined by some other criteria. The chi-squared statistic from this kind of table does not have a limiting chi-square distribution in general and we need to be very cautious of the use of a chi-squared type goodness-of-fit test. We also study the limiting distribution of the chi-squared type statistic for testing the goodness-of-fit of cumulative logit models with ordinal responses. The regularity conditions necessary to the limiting distribution will be reformulated in the framework of the cumulative logit model by modifying those of Moore and Spruill (1975). Due to the complex limiting distribution, a parametric bootstrap testing procedure is a good alternative and we explained the suggested method through a practical example of an ordinal response dataset.

ÇOKLU KARŞILAŞTIRMALARDA DAĞILIŞLA VE VARYANS YAPISIYLA İLGİLİ FARAZİYELERDEN AYRILIŞLARIN TEST ÖZELLİKLERİNE ETKİLERİ ÜZERİNDE BİR ARAŞTIRMA

OZET Coklu karsilastirma testlerinde,n en fazla kullanilan LSD, Duncan, SNK ve Tukey testlerinin teorik ozelliklerJ mc'elenerek temel fia.raziyelerdeki aksamalarin bu testleri nasil etkileyecegi incelenmistir. Simulasyon teknikleriyle teskil tadilen .de· nemeler yeter sayida1ekrarlanarak teist!erin h:a.ta seviyeleri degisik'populasyonlar ve ornek genislikleri ,esas alinarak tesbit edilmistir. Normal sartlar icin beklenen hata seviyeleri normal dagilis ve homojen varyans faraziyelerininbozuldugu cesitli durumlarda ortaya cikan hata seviyeleriyle karsilastirilarak hangi testlerin ne olcude etkilendigi incelenmistir. Boylece, testlerin saglamlik yonunden genel ve birbirlerine katsi durumlari ortaya konmustur. SUMMARY A Researoh on the Effects of Nonnormality and Variance Heterogeneity on the, Structure of Multiple Comparison Tests. When tihe fixed model is u-sed, the aim of the analysis of variance is to determine the differences between the pQpulation means. As the F, test used for general nulI hypotiheses is not sufficient, the analysis of variance has got . to be completed by the multiple comparison tests. in order to detect tihe differences among the population means, 'some parametric and non parametric test procedures have been developed. In this researah some properties of the parametric tests, s'llchas L.s. d., Duncan, SNK and Tukey, were investigated by using sampiing experiments. Multiple comparison tests are the main coInponents of the analysis of variance. For this rea~ son, the validity of the comparisons depends on the accuracy of the knowledge thait is essential for the analysis of variance. There fore the assuimptioll's,of the ainalysis of vaPIance can also 1?e .extended for the multiple compariison tests. The oecurance of some departures from the underlying assu,mptions invialidates the multiple compadscm tests as the F tests, and causes wrong decisions. The error rate and theoreti· cal s;tiruoture of multiple comparision procedures are 'different /from eamother. Therefore : :tJlie levels of type i and type 11 errOrs and their powers are not the SMTle. Because of the differences in tihe error rates, the decisions and the results obtained by the use of these tests are different. In tlus researc,h the sampling .experiments obtained by using Monte-Car1o methods. The error rates of the multiple comparison 'te9ts were investigated nder different conditiQns. The error rates obtained for the nonnal case have been taken as a crlterion to compare the other cases where some departures from the underlyiing assumptions. Taking two poission distribution witth the' parametres L = 2 'and L = 3, the departures from 'the nonnal1ty were considered. '57 Taking the samples of 5 groups, each with sample sizes of 3 and 7, type i error rates were estimated according to various error rate cri:teria. With the departures from the nQrmality the error rates of the Duncan, SNK, and Tukey's niethods were mareased. Th1s priaotically arises when the sample sizes are smaIl. Effeots of the heterogeneity of the variances were also mvestigated for various combinamons of the group variances. On each sampling, 4 and 5 groups ea'.ch having 3 and 7 observations were ohosen, Applying the analysis of v:ariance and the multiple 'comparison tests, type i error rates were calculated it has been revealed that high heterogeneity of variance ended up with the increase of type T error mates of multiple comparison tests except L.S.D.. In the case of low heterogeneity, however, did not prove accordingly giying slightly decreasing error rates.

Goodness-of-Fit Tests for the Ordinal Response Models with Misspecified Links

The Pearson chi-squared statistic or the deviance statistic is widely used in assessing the goodness-of-fit of the generalized linear models. But these statistics are not proper in the situation of continuous explanatory variables which results in the sparseness of cell frequencies. We propose a goodness-of-fit test statistic for the cumulative logit models with ordinal responses. We consider the grouping of a dataset based on the ordinal scores obtained by fitting the assumed model. We propose the Pearson chi-squared type test statistic, which is obtained from the cross-classified table formed by the subgroups of ordinal scores and the response categories. Because the limiting distribution of the chi-squared type statistic is intractable we suggest the parametric bootstrap testing procedure to approximate the distribution of the proposed test statistic.

Purchasing power parity in Asian economies: further evidence from rank tests for cointegration

The finding of nonlinear cointegration between Asian exchange rates with the corresponding relative prices and aggregate price levels based on Breitung's (2001) nonparametric rank tests reinforces previous validations of purchasing power parity (PPP) by the parametric testing procedures. Hence, the long-run Asian exchange rates are in equilibrium with the relevant fundamentals as suggested by the PPP hypothesis.