Monitoring process mean and variability with one non-central chi-square chart

Traditionally, an (X) over bar -chart is used to control the process mean and an R-chart to control the process variance. However, these charts are not sensitive to small changes in process parameters. A good alternative to these charts is the exponentially weighted moving average (EWMA) control chart for controlling the process mean and variability, which is very effective in detecting small process disturbances. In this paper, we propose a single chart that is based on the non-central chi-square statistic, which is more effective than the joint (X) over bar and R charts in detecting assignable cause(s) that change the process mean and/or increase variability. It is also shown that the EWMA control chart based on a non-central chi-square statistic is more effective in detecting both increases and decreases in mean and/or variability.

Extended table of percentage points of the chi-square distribution /

"NAVWEPS report 7770. NOTS TP 2749."

The non-central chi-square chart with two-stage samplings

In this paper, we consider the non-central chi-square chart with two stage samplings. During the first stage, one item of the sample is inspected and, depending on the result, the sampling is either interrupted, or it goes on to the second stage, where the remaining sample items are inspected and the non-central chi-square statistic is computed. The proposed chart is not only more sensitive than the joint (X) over bar and R charts, but operationally simpler too, particularly when appropriate devices, such as go-no-go gauges, can be used to decide if the sampling should go on to the second stage or not. (c) 2004 Elsevier B.V. All rights reserved.

The no-central chi-square chart with two-stage samplings

Throughout this article, it is assumed that the no-central chi-square chart with two stage samplings (TSS Chisquare chart) is employed to monitor a process where the observations from the quality characteristic of interest X are independent and identically normally distributed with mean μ and variance σ2. The process is considered to start with the mean and the variance on target (μ = μ0; σ2 = σ0 2), but at some random time in the future an assignable cause shifts the mean from μ0 to μ1 = μ0 ± δσ0, δ >0 and/or increases the variance from σ0 2 to σ1 2 = γ2σ0 2, γ > 1. Before the assignable cause occurrence, the process is considered to be in a state of statistical control (defined by the in-control state). Similar to the Shewhart charts, samples of size n 0+ 1 are taken from the process at regular time intervals. The samplings are performed in two stages. At the first stage, the first item of the i-th sample is inspected. If its X value, say Xil, is close to the target value (|Xil-μ0|< w0σ 0, w0>0), then the sampling is interrupted. Otherwise, at the second stage, the remaining n0 items are inspected and the following statistic is computed. Wt = Σj=2n 0+1(Xij - μ0 + ξiσ 0)2 i = 1,2 Let d be a positive constant then ξ, =d if Xil > 0 ; otherwise ξi =-d. A signal is given at sample i if |Xil-μ0| > w0σ 0 and W1 > knia:tl, where kChi is the factor used in determining the upper control limit for the non-central chi-square chart. If devices such as go and no-go gauges can be considered, then measurements are not required except when the sampling goes to the second stage. Let P be the probability of deciding that the process is in control and P 1, i=1,2, be the probability of deciding that the process is in control at stage / of the sampling procedure. Thus P = P1 + P 2 - P1P2, P1 = Pr[μ0 - w0σ0 ≤ X ≤ μ0+ w 0σ0] P2=Pr[W ≤ kChi σ0 2], (3) During the in-control period, W / σ0 2 is distributed as a non-central chi-square distribution with n0 degrees of freedom and a non-centrality parameter λ0 = n0d2, i.e. W / σ0 2 - xn0 22 (λ0) During the out-of-control period, W / σ1 2 is distributed as a non-central chi-square distribution with n0 degrees of freedom and a non-centrality parameter λ1 = n0(δ + ξ)2 / γ2 The effectiveness of a control chart in detecting a process change can be measured by the average run length (ARL), which is the speed with which a control chart detects process shifts. The ARL for the proposed chart is easily determined because in this case, the number of samples before a signal is a geometrically distributed random variable with parameter 1-P, that is, ARL = I /(1-P). It is shown that the performance of the proposed chart is better than the joint X̄ and R charts, Furthermore, if the TSS Chi-square chart is used for monitoring diameters, volumes, weights, etc., then appropriate devices, such as go-no-go gauges can be used to decide if the sampling should go to the second stage or not. When the process is stable, and the joint X̄ and R charts are in use, the monitoring becomes monotonous because rarely an X̄ or R value fall outside the control limits. The natural consequence is the user to pay less and less attention to the steps required to obtain the X̄ and R value. In some cases, this lack of attention can result in serious mistakes. The TSS Chi-square chart has the advantage that most of the samplings are interrupted, consequently, most of the time the user will be working with attributes. Our experience shows that the inspection of one item by attribute is much less monotonous than measuring four or five items at each sampling.

Decomposition of $\rm R\times C$ contingency table chi -square: Application to binned DNA fragment size data and population structure analysis

The purpose of this research is to develop a new statistical method to determine the minimum set of rows (R) in a R x C contingency table of discrete data that explains the dependence of observations. The statistical power of the method will be empirically determined by computer simulation to judge its efficiency over the presently existing methods. The method will be applied to data on DNA fragment length variation at six VNTR loci in over 72 populations from five major racial groups of human (total sample size is over 15,000 individuals; each sample having at least 50 individuals). DNA fragment lengths grouped in bins will form the basis of studying inter-population DNA variation within the racial groups are significant, will provide a rigorous re-binning procedure for forensic computation of DNA profile frequencies that takes into account intra-racial DNA variation among populations. ^

Statnote 7: chi-square contingency tables

When the data are counts or the frequencies of particular events and can be expressed as a contingency table, then they can be analysed using the chi-square distribution. When applied to a 2 x 2 table, the test is approximate and care needs to be taken in analysing tables when the expected frequencies are small either by applying Yate’s correction or by using Fisher’s exact test. Larger contingency tables can also be analysed using this method. Note that it is a serious statistical error to use any of these tests on measurement data!

Evaluation of the Suchey-Brooks Method of age estimation in an Australian subpopulation using computed tomography of the pubic symphyseal surface

Despite the prominent use of the Suchey-Brooks (S-B) method of age estimation in forensic anthropological practice, it is subject to intrinsic limitations, with reports of differential inter-population error rates between geographical locations. This study assessed the accuracy of the S-B method to a contemporary adult population in Queensland, Australia and provides robust age parameters calibrated for our population. Three-dimensional surface reconstructions were generated from computed tomography scans of the pubic symphysis of male and female Caucasian individuals aged 15–70 years (n = 195) in Amira® and Rapidform®. Error was analyzed on the basis of bias, inaccuracy and percentage correct classification for left and right symphyseal surfaces. Application of transition analysis and Chi-square statistics demonstrated 63.9% and 69.7% correct age classification associated with the left symphyseal surface of Australian males and females, respectively, using the S-B method. Using Bayesian statistics, probability density distributions for each S-B phase were calculated, providing refined age parameters for our population. Mean inaccuracies of 6.77 (±2.76) and 8.28 (±4.41) years were reported for the left surfaces of males and females, respectively; with positive biases for younger individuals (<55 years) and negative biases in older individuals. Significant sexual dimorphism in the application of the S-B method was observed; and asymmetry in phase classification of the pubic symphysis was a frequent phenomenon. These results recommend that the S-B method should be applied with caution in medico-legal death investigations of Queensland skeletal remains and warrant further investigation of reliable age estimation techniques.

Le rôle de la sérotonine sur le développement de traits anxieux : une étude de trajectoire longitudinale

Certains gènes, modulant la sérotonine (5-hydroxytryptamine, 5-HT), ont été associés aux tempéraments liés à l'anxiété. Une limitation dans la plupart de ces études est que les études sont de nature transversale et l'anxiété a été évaluée à un seul point dans le temps. De plus, seules quelques études ont été réalisées chez les enfants. Le but de la présente étude était d'étudier le rôle des gènes HTR2A et TPH2 dans le développement des trajectoires d’anxiété durant l’enfance. Les associations entre ces gènes, ces trajectoires, le diagnostic d’anxiété à l'âge adulte et les différences entre les sexes ont été examinées dans l'Étude Longitudinale des Enfants de Maternelle au Québec, composée de 3185 enfants recrutés en 1986-1987. Leur anxiété a été cotée par leur professeur annuellement entre 6 et 12 ans. Ces cotes ont été modélisées en trajectoires comportementales. Les données genotypées de 5-HT, disponibles pour 1068 personnes, ont été analysées en utilisant les statistiques du Chi-carré, des régressions logistiques et des analyses de variance. Sur les 37 polymorphismes étudiés, plusieurs ont été associés à la trajectoire de forte anxiété, tels le 5-HTR2A (rs1328684, rs95534511, rs1745837, rs7984966, 7330636) et TPH2 (rs11179050, rs11179052, rs1386498). Bien que les trajectoires d’anxiété en enfance n’aient pas prédit le diagnostic d'anxiété à 21 ans, les relations ont été trouvées entre ce diagnostic, HTR2A et les polymorphismes du nucléotide simple (PNS) de TPH2. On remarque que les PNS associés à l’anxiété durant l’enfance et l’âge adulte ne sont pas les mêmes. La force d'association entre les gènes étudiés et l'anxiété diffère entre les garçons et les filles. Cette étude est la première à identifier une association entre les variantes TPH2, 5-HTR2A et les trajectoires d’anxiété en enfance. Les études futures devraient reproduire les résultats dans d'autres échantillons, enquêter sur l'interaction avec les facteurs de stress, et étudier la pertinence fonctionnelle de la PNS.

A relação entre o parecer de auditoria e a troca de auditores: uma investigação nas instituições financeiras brasileiras

Esta pesquisa tem como objetivo principal verificar se há relação entre a troca espontânea da auditoria independente e o parecer não limpo emitido no ano anterior e também se há relação positiva entre o rodízio de auditores e a emissão de pareceres não limpos no ano do rodízio e nos seguintes. Justifica-se este trabalho pela proposta de avaliar cientificamente o impacto da influência da administração e da adoção do rodízio de auditoria na independência do auditor externo, sem ser enviesado pelos interesses dos profissionais envolvidos, uma vez que esta é uma pesquisa exclusivamente documental. Portanto, chega-se a diversas hipóteses quanto à ocorrência de parecer não limpo como fator motivador para a troca de auditores por parte da administração e quanto ao rodízio obrigatório de auditorias propiciando a emissão de pareceres não limpos. Além da pesquisa documental, este trabalho também é composto por revisão da literatura acadêmica e especializada, que fundamentam e respaldam as principais questões abordadas. Os resultados obtidos, após as considerações e constatações observadas nas pesquisas bibliográficas, e nos resultados dos testes da estatística qui-quadrado, verificam que a administração é mais propensa a trocar a firma de auditoria quando recebe um parecer modificado por ressalvas e ênfases relevantes que quando recebe um parecer limpo da firma de auditoria atual. Outra constatação é a ausência de relação entre a adoção do rodízio obrigatório de auditoria e a emissão de pareceres modificados nos anos após esta troca.

A synthetic control chart for monitoring the process mean and variance

Purpose - The aim of this paper is to present a synthetic chart based on the non-central chi-square statistic that is operationally simpler and more effective than the joint X̄ and R chart in detecting assignable cause(s). This chart will assist in identifying which (mean or variance) changed due to the occurrence of the assignable causes. Design/methodology/approach - The approach used is based on the non-central chi-square statistic and the steady-state average run length (ARL) of the developed chart is evaluated using a Markov chain model. Findings - The proposed chart always detects process disturbances faster than the joint X̄ and R charts. The developed chart can monitor the process instead of looking at two charts separately. Originality/value - The most important advantage of using the proposed chart is that practitioners can monitor the process by looking at only one chart instead of looking at two charts separately. © Emerald Group Publishing Limted.

Analysis of sport psychology consultancy at three Olympic Games: Facts and figures

Objectives Despite many reports on best practises regarding onsite psychological services, little research has attempted to systematically explore the frequency, issues, nature and client groups of onsite sport psychology consultancy at the Olympic Games. The present paper will fill this gap through a systematic analysis of the sport psychology consultancy of the Swiss team for the Olympic Games of 2006 in Turin, 2008 in Beijing and 2010 in Vancouver. Design Descriptive research design. Methods The day reports of the official sport psychologist were analysed. Intervention issues were labelled using categories derived from previous research and divided into the following four intervention-issue dimensions: “general performance”, “specific Olympic performance”, “organisational” and “personal” issues. Data were analysed using descriptive statistics, chi square statistics and odds ratios. Results Across the Olympic Games, between 11% and 25% of the Swiss delegation used the sport psychology services. On average, the sport psychologist provided between 2.1 and 4.6 interventions per day. Around 50% of the interventions were informal interventions. Around 30% of the clients were coaches. The most commonly addressed issues were performance related. An association was observed between previous collaboration, intervention likelihood and intervention theme. Conclusions Sport psychologists working at the Olympic Games are fully engaged with daily interventions and should have developed ideally long-term relationships with clients to truly help athletes with general performance issues. Critical incidents, working with coaches, brief contact interventions and team conflicts are specific features of the onsite consultancy. Practitioners should be trained to deal with these sorts of challenges.

The prevalence of periodontal disease in Mexican American vs European American elderly in three distinct socio-economic communities in San Antonio, Texas

Purpose of the Study: This study evaluated the prevalence of periodontal disease between Mexican American elderly and European American elderly residing in three socio-economically distinct neighborhoods in San Antonio, Texas. ^ Study Group: Subjects for the original protocol were participants of the Oral Health: San Antonio Longitudinal Study of Aging (OH: SALSA), which began with National Institutes of Health (NIH) funding in 1993 (M.J. Saunders, PI). The cohort in the study was the individuals who had been enrolled in Phases I and III of the San Antonio Heart Study (SAHS). This SAHS/SALSA sample is a community-based probability sample of Mexican American and European American residents from three socio-economically distinct San Antonio neighborhoods: low-income barrio, middle-income transitional, and upper-income suburban. The OH: SALSA cohort was established between July 1993 and May 1998 by sampling two subsets of the San Antonio Heart Study (SAHS) cohort. These subsets included the San Antonio Longitudinal Study of Aging (SALSA) cohort, comprised of the oldest members of the SAHS (age 65+ yrs. old), and a younger set of controls (age 35-64 yrs. old) sampled from the remainder of the SAHS cohort. ^ Methods: The study used simple descriptive statistics to describe the sociodemographic characteristics and periodontal disease indicators of the OH: SALSA participants. Means and standard deviations were used to summarize continuous measures. Proportions were used to summarize categorical measures. Simple m x n chi square statistics was used to compare ethnic differences. A multivariable ordered logit regression was used to estimate the prevalence of periodontal disease and test ethnic group and neighborhood differences in the prevalence of periodontal disease. A multivariable model adjustment for socio-economic status (income and education), gender, and age (treated as confounders) was applied. ^ Summary: In the unadjusted and adjusted model, Mexican American elderly demonstrated the greatest prevalence for periodontitis, p < 0.05. Mexican American elderly in barrio neighborhoods demonstrated the greatest prevalence for severe periodontitis, with unadjusted prevalence rates of 31.7%, 22.3%, and 22.4% for Mexican American elderly barrio, transitional, and suburban neighborhoods, respectively. Also, Mexican American elderly had adjusted prevalence rates of 29.4%, 23.7%, and 20.4% for barrio, transitional, and suburban neighborhoods, respectively. ^ Conclusion: This study indicates that the prevalence of periodontal disease is an important oral health issue among the Mexican American elderly. The results suggest that the socioeconomic status of the residential neighborhood increased the risk for severe periodontal disease among the Mexican American elderly when compared to European American elderly. A viable approach to recognizing oral health disparities in our growing population of Mexican American elderly is imperative for the provision of special care programs that will help increase the quality of care in this minority population.^

Salient factors in child molestation: Moral development, social competence, and type of offender

The current study was designed to build on and extend the existing knowledge base of factors that cause, maintain, and influence child molestation. Theorized links among the type of offender and the offender's levels of moral development and social competence in the perpetration of child molestation were investigated. The conceptual framework for the study is based on the cognitive developmental stages of moral development as proposed by Kohlberg, the unified theory, or Four-Preconditions Model, of child molestation as proposed by Finkelhor, and the Information-Processing Model of Social Skills as proposed by McFall. The study sample consisted of 127 adult male child molesters participating in outpatient group therapy. All subjects completed a Self-Report Questionnaire which included questions designed to obtain relevant demographic data, questions similar to those used by the researchers for the Massachusetts Treatment Center: Child Molester Typology 3's social competency dimension, the Defining Issues Test (DIT) short form, the Social Avoidance and Distress Scale (SADS), the Rathus Assertiveness Schedule (RAS), and the Questionnaire Measure of Empathic Tendency (Empathy Scale). Data were analyzed utilizing confirmatory factor analysis, t-tests, and chi-square statistics. Partial support was found for the hypothesis that moral development is a separate but correlated construct from social competence. As predicted, although the actual mean score differences were small, a statistically significant difference was found in the current study between the mean DITP scores of the subject sample and that of the general male population, suggesting that child molesters, as a group, function at a lower level of moral development than does the general male population, and the situational offenders in the study sample demonstrated a statistically significantly higher level of moral development than the preferential offenders. The data did not support the hypothesis that situational offenders will demonstrate lower levels of social competence than preferential offenders. Relatively little significance is placed on this finding, however, because the measure for the social competency variable was likely subject to considerable measurement error in that the items used as indicators were not clearly defined. The last hypothesis, which involved the potential differences in social anxiety, assertion skills, and empathy between the situational and preferential offender types, was not supported by the data. ^

Mothers’ perception of recovery and satisfaction with patent medicine dealers’ treatment of childhood febrile conditions in rural communities

Background Infant mortality in rural areas of Nigeria can be minimized if childhood febrile conditions are treated by trained health personnel, deployed to primary healthcare centres (PHCs) rather than the observed preference of mothers for patent medicine dealers (PMDs). However, health service utilization/patronage is driven by consumer satisfaction and perception of services/product value. The objective of this study was to determine ‘mothers’ perception of recovery’ and ‘mothers’ satisfaction’ after PMD treatment of childhood febrile conditions, as likely drivers of mothers’ health-seeking behaviour, which must be targeted to reverse the trend. Methods Ugwuogo-Nike, in Enugu, Nigeria, has many PMDs/PHCs, and was selected based on high prevalence of childhood febrile conditions. In total, 385 consenting mothers (aged 15–45 years) were consecutively recruited at PMD shops, after purchasing drugs for childhood febrile conditions, in a cross-sectional observational study using a pre-tested instrument; 33 of them (aged 21–47 years) participated in focus group discussions (FGDs). Qualitative data were thematically analysed while a quantitative study was analysed with Z score and Chi square statistics, at p < 0.05. Results Most participants in FGDs perceived that their child had delayed recovery, but were satisfied with PMDs’ treatment of childhood febrile conditions, for reasons that included politeness, caring attitude, drug availability, easy accessibility, flexibility in pricing, shorter waiting time, their God-fearing nature, and disposition as good listeners. Mothers’ satisfaction with PMDs’ treatment is significantly (p < 0.05) associated with mothers’ perception of recovery of their child (χ2 = 192.94, df = 4; p < 0.0001; Cramer’s V = 0.7079). However, predicting mothers’ satisfaction with PMDs’ treatment from a knowledge of mothers’ perception of recovery shows a high accord (lambda[A from B] = 0.8727), unlike when predicting mothers’ perception of recovery based on knowledge of mothers’ satisfaction with PMDs’ treatment (lambda[A from B] = 0.4727). Conclusions Mothers’ satisfaction could be the key ‘driver’ of mothers’ health-seeking behaviour and is less likely to be influenced by mothers’ perception of recovery of their child. Therefore, mothers’ negative perception of their child’s recovery may not induce proportionate decline in mothers’ health-seeking behaviour (patronage of PMDs), which might be influenced mainly by mothers’ satisfaction with the positive attributes of PMDs’ personality/practice and sets an important agenda for PHC reforms.