Classical Analysis Of Variance Research Articles

Measurement uncertainty arising from sampling and analytical steps of dissolution test of glyburide tablets

The dissolution test is an essential technique used in pharmaceutical research to assess the rate and extent of drug release from a dosage form into a dissolution medium. Accurate and reliable dissolution test results are crucial to ensure the quality and efficacy of the drug product. The aim of this study was to evaluate the measurement uncertainty arising from the sampling and analytical steps of the dissolution test for glyburide tablets. Dissolution test was performed using 900 mL of phosphate buffer pH 7.3 as dissolution medium and a dissolution apparatus equipped with paddles rotating at 75 rpm for 60 min. Quantification was performed by HPLC-UV. The uncertainty arising from sampling was estimated through classical Analysis of Variance (ANOVA), using 8-sampling targets, two samples for each sampling target and two replicas for each sample, totalizing 32 analyses. Uncertainty arising from analytical steps considered the uncertainty from dissolution step (estimated using Monte Carlo method and regression equation obtained using DoE) and uncertainty from quantification step. The overall uncertainty value was found to be 6.33 %. The sources of uncertainty contributing to the overall measurement uncertainty of the dissolution test were estimated to be 76.09 % from sampling, 22.15 % from the dissolution step, and 1.76 % from the quantification step. The study emphasizes the importance of evaluating measurement uncertainty in dissolution testing to ensure reliable and accurate drug product quality control. The results demonstrate that the dissolution test of glyburide tablets presented high sampling uncertainty and did not pass the dissolution test within the specified limits, probably due to glyburide’s low solubility. Univariate and multivariate rejection limits were calculated in order to ensure reduced particular and total producer’s risk, respectively. This study provides useful insights for pharmaceutical industries to optimize their quality control processes and ensure the efficacy and safety of their products.

Advancements in multivariate analysis of variance

The Journal of Chemometrics is pleased to announce a special issue focused on multivariate analysis of data from designed experiments. ANOVA (Analysis of Variance) is the standard method for analyzing data from experimental designs. The classical ANOVA methods are however univariate and do not handle multiple collinear response variables. Designed experiments with multivariate outputs are prevalent across various scientific disciplines, necessitating methods that appropriately consider both the experimental design and the multivariate nature of the data. Several multivariate ANOVA techniques have been presented already. The most prevalent approaches involve combining ANOVA with PCA (principal component analysis) or other exploratory component-based techniques in different ways. Some commonly used methods in this context include ASCA, ANOVA-PCA, AComDim, and fifty-fifty MANOVA. These methods integrate ANOVA and PCA in different ways to extract meaningful information from multivariate data. Additionally, there are alternative methods that replace PCA with partial least squares (PLS) regression, which allows for the utilization of PLS-specific validation and variable importance routines. One major advantage of all these methods is that they not only offer interpretation and variable importance metrics from latent variable-based methods but also provide estimates of multivariate effect sizes accompanied by corresponding significance testing. Despite the progress made in recent years, the field of multivariate analysis of data from designed experiments is still young. Several open questions remain unanswered, and there is a need to make the methodology available to a broader audience. The aim of this special issue was therefore to stimulate and explore advances in methods, applications, and software for multivariate ANOVA. The collection of papers includes methodical improvements, practical applications, a tutorial, and a software demonstration. Application areas range from spectroscopic control of fermentation processes to metabolomics and gene expressions. Overall, this issue showcases the power and applicability of multivariate ANOVA methods in a wide range of domains.

Categorical Analysis of Variance on Knowledge, Compliance and Impact of Hand Hygiene among Healthcare Professionals during COVID-19 Outbreak in South-East, Nigeria

This paper examined the knowledge, compliance and impact of hand hygiene among healthcare professionals during COVID-19 outbreak in South-East, Nigeria. The data used in this study were collected from twenty (20) hospitals in South-East, Nigeria using questionnaire with closed-type question forms. A total number of 600 questionnaires were used in this study. Two-way CATANOVA was used to examine the gender and health profession that have well knowledge, compliance and impact experience of hand hygiene during COVID-19 outbreak. The result showed no statistically significant difference in the knowledge, compliance and impact experience of hand hygiene among four major health professions (medical doctors, nurses, pharmacists, laboratory scientists) and also between the genders at a 5% significance level. The findings showed that the changing of healthcare professional from one health profession to another does not affect the knowledge, compliance and impact experience of hand hygiene. It was noticed that 599(99.8%) healthcare professionals have good knowledge of hand hygiene, 395(65.8%) practice hand hygiene every time, and 507(84.5%) have high impact experience of hand hygiene. There is enhancement in the knowledge, compliance and impact experience of hand hygiene of healthcare professionals as their years of service increase.

On Statistical Analysis of Eight Sexually Transmitted Diseases Using Categorical Analysis of Variance: A Case Study of the University of Nigeria Teaching Hospital

This paper focused on the statistical analysis of eight Sexually Transmitted Infections (STIs) reported in the University of Nigeria Teaching Hospital from 2010-2020. A population of 20,704 patients was recorded to have contracted eight (8) selected STIs. Prevalence analysis was computed to determine the most prevalent STI. Two-way CATANOVA cross-classification was computed to ascertain age group and gender that suffer more of each of these infections. Logistic regression model was fitted to predict reproductive status of patients that suffer the most prevalent STI. The prevalence analysis results showed Gonorrhea infection as the most prevalent STI. Two-way CATANOVA results for Gonorrhea and Chlamydia infections showed that there were significant difference in gender, age and interaction effects, significant difference in age and interaction effect for Trichomoniases infection, significant difference in age for Syphilis and HIV infections but no significant difference in gender, age and interaction effects for Human Papillomavirus (HPV), Hepatitis B Virus and Herpes infections. The results showed that the percentage of male that suffers STIs is more than the percentage of female, the percentage of 30-39 years that suffer STIs is more than the percentage of any other age group and the percentage of people without STIs history is more than the percentage of those that have history of them. Logistic regression results on Gonorrhea infection showed that an increase in age, body mass index, blood pressure, blood sugar, bacteria quantity, and Gonorrhea history were associated with an increased likelihood of the Gonorrhea patient being infertile.

Testing Equality of Multiple Population Means under Contaminated Normal Model Using the Density Power Divergence.

This paper considers the problem of comparing several means under the one-way Analysis of Variance (ANOVA) setup. In ANOVA, outliers and heavy-tailed error distribution can seriously hinder the treatment effect, leading to false positive or false negative test results. We propose a robust test of ANOVA using an M-estimator based on the density power divergence. Compared with the existing robust and non-robust approaches, the proposed testing procedure is less affected by data contamination and improves the analysis. The asymptotic properties of the proposed test are derived under some regularity conditions. The finite-sample performance of the proposed test is examined via a series of Monte-Carlo experiments and two empirical data examples—bone marrow transplant dataset and glucose level dataset. The results produced by the proposed testing procedure are favorably compared with the classical ANOVA and robust tests based on Huber’s M-estimator and Tukey’s MM-estimator.

Intuitionistic fuzzy two-factor variance analysis of movie ticket sales

Analysis of variance (ANOVA) is an important method in data analysis, which was developed by Fisher. There are situations when there is impreciseness in data In order to analyze such data, the aim of this paper is to introduce for the first time an intuitionistic fuzzy two-factor ANOVA (2-D IFANOVA) without replication as an extension of the classical ANOVA and the one-way IFANOVA for a case where the data are intuitionistic fuzzy rather than real numbers. The proposed approach employs the apparatus of intuitionistic fuzzy sets (IFSs) and index matrices (IMs). The paper also analyzes a unique set of data on daily ticket sales for a year in a multiplex of Cinema City Bulgaria, part of Cineworld PLC Group, applying the two-factor ANOVA and the proposed 2-D IFANOVA to study the influence of “ season ” and “ ticket price ” factors. A comparative analysis of the results, obtained after the application of ANOVA and 2-D IFANOVA over the real data set, is also presented.

Data Information in Contingency Tables: A Fallacy of Hierarchical Loglinear Models

Information identities derived from entropy and relative entropy can be useful in statistical inference. For discrete data analyses, a recent study by the authors showed that the fundamental likelihood structure with categorical variables can be expressed in different yet equivalent information decompositions in terms of relative entropy. This clarifies an essential difference between the classical analysis of variance and the analysis of discrete data, revealing a fallacy in the analysis of hierarchical loglinear models. The discussion here is focused on the likelihood information of a three-way contingency table, without loss of generality. A classical three-way categorical data example is examined to illustrate the findings.

Ambassador of People with Disabilities in the Workplace—Conducive Demographic and Professional Characteristics

This paper introduces into the analysis the concept of the ambassador of people with disability in the workplace. A kind and friendly person in the workplace, who creates a positive atmosphere around people with disabilities, may play a crucial role in their adaptation on the open labor market. Presence of such a person is especially important in entities that did not previously employ people with disabilities. It is vital that employers who would like to employ people with disability possess knowledge about demographic and professional characteristics that predispose employees to perform this special role. On the one hand, in this article we attempted to evaluate the differentiation in the perception of the issue of disability due to demographic and professional characteristics of respondents, and, on the other hand, to identify features that favor being an “ambassador of people with disabilities” in the workplace. The study was conducted in 2019 on the representative samples of Internet users from 8 European countries using Computer-Assisted Internet Interviews. For the purposes of the study, we used the Attitudes to Disability Scale WHOQOL Group test and a proprietary questionnaire. As for the methods of analysis, we relied on the classical analysis of variance and logistic regression. The conducted study showed that the perception of the issue of disability is significantly related to demographic and professional characteristics of respondents, and that the role of the ambassador is the most appropriate for a middle-aged woman with a good knowledge of disability issues, indecisive in the workplace.

A novel nested design approach for estimation of uncertainty arising from sampling in feed

Uncertainty arising from sampling is nowadays a controversial issue, if it is necessary to be taken into account in total uncertainty. As in the quantification of analysis uncertainty, there are two principal approaches in order to estimate uncertainty of sampling: the bottom-up and the top-down approach. A novel top-down approach for sampling uncertainty is proposed in this study using nested analysis of variance (ANOVA). Determination of the oxytetracycline (OTC) content in feed was utilized for estimating uncertainty arising from sampling using the new approach. The advantage of nested ANOVA is that the effect of every factor on the total uncertainty can be calculated. In the present study, factors such as physical preparation of sample, lots of production and particle diameter were examined in the experimental design. It was found that the effect of different lots had the highest uncertainty among the factors. Finally, the results of nested ANOVA were compared with the uncertainty calculated using other top-down approaches. Classical ANOVA and robust ANOVA (RANOVA) did not show significant differences in their results. On the other hand, nested ANOVA estimated higher uncertainty of sampling in comparison with the other approaches.

Evaluation of CRM homogeneity in cases of insufficient method repeatability: Comparison of Bayesian analysis with substitutes for ANOVA based estimates

Insufficient method repeatability is a problem characterising the evaluation of certified reference materials (CRMs). In investigating the homogeneity studies of 216 certified parameters from 36 CRMs released by the European Commission’s Joint Research Centre (JRC) over the last four years, it was found that in 1/3 of the cases, the method repeatability (sr) was too high to calculate the standard deviation between units (sbb) by classical analysis of variance (ANOVA). It was also found that the application of the repeatability requirement stated in the ISO Guide 35:2017 is not feasible since it would require unrealistically low repeatability standard deviations or an impossibly high number of replicates per unit.Evaluation of the uncertainty of homogeneity (ubb) as evaluated by ANOVA using both the maximum of sbb and 0, the maximum of sbb and u∗bb, the uncertainty hidden by method repeatability, the maximum of sbb and sbb/√n and Bayesian analysis, using both informative and diffuse priors, as well as the standard deviation of the unit means, were compared using simulated homogeneity studies with repeatabilities of 1–8% and sbb between 0.2 and 2.8%. It was found that using the maximum of sbb and sbb/√n as an estimate of ubb guards against severe underestimation but usually results in a severe overestimation of the between-unit variation. Using the maximum of (sbb, 0) shows the least average bias but results in a severe underestimation of ubb in a high fraction of cases. Using the maximum of (sbb, u∗bb) limits, but does not completely eliminate cases of a severe underestimation. Also, it leads to average results biased towards high values. For the range of sbb and sr investigated, Bayesian analysis performed worse than max (sbb, u∗bb) in limiting severe underestimation of ubb, but limited the average bias towards high results.A risk-based approach to cases of insufficient method repeatability is proposed where, after evaluating the other contributions to the uncertainty of certified values, the effect of severe over- and underestimation of ubb is evaluated, and an appropriate approach is chosen based on this analysis.

CATANOVA Analysis of Knowledge and Control Practices of Hepatitis B Virus Infection amongst Tertiary University Students

Frequency data, having no underlying metric, are frequently encountered in real-life situations. The analysis of such data is usually difficult as nominal data are inherently less informative than quantitative data and decisions are taken erroneously using such results.
 The objective of the research was to study the significant effect of gender, faculties and interaction using categorical data in a two-way cross classification. 
 Materials and Methods. The study applied a cross sectional study with a total sample size of 434. Multistage sampling was adopted. Categorical analysis of variance (CATANOVA) technique was used for analysis. This is suitable as it uses a two-way ANOVA with quantal responses as equivalent of a three-way contingency table in which one of the classifications is treated as responses to the other two. The study considered frequency data involving response scores of students using a scale of good, fair and poor.
 Results. Numerical results revealed poor level of student’s knowledge and control practices of hepatitis B virus infection. And it is significantly (p>0.05) the same in the study Universities. Moreover, gender and faculties, as well as interaction have no significant (p>0.05) effect on student’s knowledge and control practices of hepatitis B virus infection.

Neutrosophic analysis of variance: application to university students

The existing analysis of variance (ANOVA) test cannot be applied when the sample is selected from the population having come imprecise, fuzzy and uncertain observations. The neutrosophic statistics will be applied to analyze the data having uncertain observations or the parameters. In this paper, we will introduce the neutrosophic analysis of variance (NANONA). The NANONA is an extension of the classical ANOVA. We presented the NANONA table. We performed the NANONA to test teaching methods using data collected from the university students.

Análise de variância corrigida para a produção de matéria seca ao longo do tempo

Technical analysis experiments using repeated measures over time should consider the correlation structure between time and within time. Dry matter production with the usage of high and low nutrient concentration was analyzed in this work. (It) was found through Mauchly test the covariance matrix of the model (which) does not satisfy the criterion sphericity and do not have equal variances and zero correlations. This fact may turn the F test invalid for the analysis of variance applied to the sources of variation present in the subplot, so it used two paths to fix the respective degrees of freedom, and thus ensure that the F distribution is accurate. In the study of dry matter production, it was verified that the use of nutrients in the production of dry matter is not relevant and this fact was confirmed by classical analysis of variance and the corrected variance analysis

Bayesian analysis of homogeneity studies in the production of reference materials

For almost two decades, the batch homogeneity in the production of reference materials has been evaluated using analysis of variance (ANOVA) to determine the between-bottle standard deviation. This approach replaced at that time the use of the F-test in ANOVA to determine whether the ratio of the mean squares $${MS}_{\mathrm {between}}/{MS}_{\mathrm {within}}$$ is statistically significant. Problems arise when $${MS}_{\mathrm {between}} < {MS}_{\mathrm {within}}$$ , because classical ANOVA provides a negative between-bottle variance, which is then often set to zero. By using a Bayesian hierarchical model, based on the same assumptions as traditional ANOVA, we show that even if $${MS}_{\mathrm {between}} < {MS}_{\mathrm {within}}$$ , there can be a relevant level of between-bottle inhomogeneity to account for. The Bayesian analysis produces a nonzero value for the between-bottle standard deviation, which dismisses the practice of setting this standard deviation to 0. At the same time, it dismisses the current guidance given in ISO Guide 35 under these circumstances. Finally, it is shown that traditional ANOVA, meta-analysis methods and Bayesian analysis give very similar answers as long as $${MS}_{\mathrm {between}} > {MS}_{\mathrm {within}}$$ , so there is no need to discourage using these methods in favour of a Bayesian analysis, provided that the repeatability of the measurement method used to conduct the between-bottle homogeneity study is sufficient to characterise the dispersion across the bottles (items) in a batch of a reference material.

Analysis of variance in uncertain environments

Testing one-way analysis of variance (ANOVA) is used for experimental data analysis in which there is a continuous response variable and a single independent classification variable. In this paper, we extend one-way ANOVA to a case where observed data are imprecise numbers rather than real numbers. Several fast computable formulas are calculated for symmetric triangular and normal fuzzy data. Similar to the classical testing ANOVA, the total observed variation in the response variable is explained as the sum of observed variation due to the effects of the classification variable and the observed variation due to random error. A real case is given to clarify the proposed method.

CATANOVA for ordinal variables using orthogonal polynomials with different scoring methods

ABSTRACTIn the context of categorical data analysis, the CATegorical ANalysis Of Variance (CATANOVA) has been proposed to analyse the scheme variable-factor, both for nominal and ordinal variables. This method is based on the C statistic and allows to test the statistical significance of the tau index using its relationship with the C statistic. Through Emerson orthogonal polynomials (EOP) a useful decomposition of C statistic into bivariate moments (location, dispersion and higher order components) has been developed. In the construction of EOP the categories are replaced by scores, typically natural scores. In the paper, we provide an overview of the main scoring schemes focusing on the advantages and the statistical properties; we pay special attention to the impact of the chosen scores on the C statistic of CATANOVA and the graphical representations of doubly ordered non-symmetrical correspondence analysis. Through a real data example, we show the impact of the scoring schemes and we consider the RV and multidimensional scaling as tools to measure similarity among the results achieved with each method.

Academic performance of students from entrance to graduation via quasi U-statistics: a study at a Brazilian research university

We present novel methodology to assess undergraduate students' performance. Emphasis is given to potential dissimilar behaviors due to high school background and gender. The proposed method is based on measures of diversity and on the decomposability of quasi U-statistics to define average distances between and within groups. One advantage of the new method over the classical analysis of variance is its robustness to distributional deviation from the normality. Moreover, compared with other nonparametric methods, it also includes tests for interaction effects which are not rank transform procedures. The variance of the test statistic is estimated by jackknife and p-values are computed using its asymptotic distribution. A college education performance data is analyzed. The data set is formed by students who entered in the University of Campinas, Brazil, between 1997 and 2000. Their academic performance has been recorded until graduation or drop-out. The classical ANOVA points to significant effects of gender, type of high school and working status. However, the residual analysis indicates a highly significant deviation from normality. The quasi U-statistics nonparametric tests proposed here present significant effect of interaction between type of high school and gender but did not present a significant effect of working status. The proposed nonparametric method also results in smaller error variances, illustrating its robustness against model misspecification.

Unbalanced robust ANOVA for the estimation of measurement uncertainty at reduced cost

An empirical estimation of the random components of measurement uncertainty arising from the sampling and analytical processes can be made via an experiment involving replication. Analysis of variance (ANOVA) is then used to estimate the variance components. However, the fully balanced design is unduly costly, requiring four analyses per sampling target. This cost can be reduced by 25% by using an unbalanced design. Robust ANOVA in this context is often a useful tool, as it gives a more representative estimate of the separate variances than classical ANOVA when outlying results are encountered, but software for executing unbalanced robust ANOVA has hitherto been unavailable. This Technical Brief introduces the unbalanced design and the corresponding software provided by the AMC.

Scaling performance examination of microcontroller-based conductivity measuring instruments

Conductivity measuring instruments should only be used if they allow carrying out the measurements of required accuracy and format, and are suitable for their measuring environment. This paper introduces a statistical analysis for scaling performance examination of conductivity instruments, enabling analysts to assess if these instruments meet specified requirements. Information is given on how analysts can verify the scaling performance of the instruments using one-way classification analysis of variance and Welch’s approximate t-test. Employing these methods as a useful technique in the field of statistical inference, it was shown that there is a strong correlation between the values of relative errors of measurements and scaling performance of the tested conductivity measuring instruments.

Determination of Pulp and Paper Making Suitability Indices of Some Nigerian Species of Leguminosae: Caesalpinoideae

Uncontrolled felling of trees for domestic and industrial uses is fast depleting the tropical forests and has led to a continued exploitation of Gmelina arborea Roxb. plantations for fuel wood and timber, a development that is threatening the ecosystem and the survival of the pulp and paper making (PPM) industries in Nigeria. This study proposes an objective method for selecting hardwood species for PPM by statistically comparing the available anatomical and other related data in the reference wood (i.e G. arborea Roxb.) with those of alternative hard wood species. (i.e twelve Nigerian species of Caesalpinioideae ). Mature stem branches (8-12cm diameter ) of twelve species , representing nine genera of the family were collected at various locations in Oyo state. A similar stem branch of G. arborea Roxb. was collected as a standard raw material for pulp and paper making. Using conventional wood anatomical techniques, nine qualitative and twenty quantitative characters were determined. The means of all the quantitative characters were compared by conducting a One-way classification analysis of variance using the version 17.0 SPSS package. Also t-test conducted indicated a significant difference between data from each of the species of Caesalpinoideae and that of G. arborea. Based on the result of the comparison, a numeric value by which the PPM potential of the alternative hardwood species was precisely defined. Results show that the woods of Caesalpinioideae species investigated are highly suitable wood resources for PPM, virtually all the species can be said to be among the best substitutes for G. arborea each being at least 75% suitable for papermaking in comparison with G. arborea. The Caesalpinioideae species investigated in order of their preferences for PPM are listed as Tamarindus indica (1.5426), Delonix regia (1.2781), Brachystegia eurycoma (1.1801), Senna sieberiana (1.1565), Bauhinia rufescens (1.1119), Afzelia africana (1.0836), Senna siamea (1.0647), Danielia ogea (1.0400), Piliostigma thoningii (0.9431), Detarium senegalensis (0.9114), Danielia oliveri (0.8423) and Caesalpinia pulcherima (0.7562). DOI: 10.5901/ajis.2013.v2n13p61