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.

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.

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. ^

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

"NAVWEPS report 7770. NOTS TP 2749."

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!

The impact of perceived stage of cancer on carers’ anxiety and depression during the patients’ final year of life

Objective: This paper explores the effects of perceived stage of cancer (PSOC) on carers' anxiety and depression during the patients' final year. Methods: A consecutive sample of patients and carers (N=98) were surveyed at regular intervals regarding PSOC, and anxiety and depression using the Hospital Anxiety and Depression Scale. Means were compared by gender using the Mann-Whitney U-test. The chi-square was used to analyse categorical data. Agreement between carers' and patients' PSOC was estimated using kappa statistics. Correlations between carers' PSOC and their anxiety and depression were calculated using the Spearman's rank correlation. Results: Over time, an increasing proportion of carers reported that the cancer was advanced, culminating at 43% near death. Agreement regarding PSOC was fair (kappa=0.29-0.34) until near death (kappa=0.21). Carers' anxiety increased over the year; depression increased in the final 6 months. Females were more anxious (p=0.049, 6 months; p=0.009, 3 months) than males, and more depressed until 1 month to death. The proportion of carers reporting moderate-severe anxiety almost doubled over the year to 27%, with more females in this category at 6 months (p=0.05). Carers with moderate-severe depression increased from 6 to 15% over the year. Increased PSOC was weakly correlated with increased anxiety and depression. Conclusions: Carers' anxiety exceeded depression in severity during advanced cancer. Females generally experienced greater anxiety and depression. Carers were more realistic than patients regarding the ultimate outcome, which was reflected in their declining mental health, particularly near the end.

Characteristics and predictors of high-range speeding offenders

This paper examines an aspect of the data taken from a larger study evaluating the effect of speeding penalty changes on speeding recidivism in Queensland. Traffic offence data from May 1996 to August 2007 were provided to the research team for two cohorts of offenders: individuals who committed a speeding offence in May 2001; and individuals who committed a speeding offence in May 2003. Data included details of the offenders’ index offence, previous and subsequent traffic offences (speeding and other) and their demographic characteristics. Using this data the aim of this component of the research was to use demographic data and the previous traffic offences of these individuals to explore the characteristics and predictors of high-range speeding offenders. High-range offenders were identified as those individuals who committed two or more speeding offences with a recorded speed of 30 km/hr or more above the speed limit. For the purposes of comparison, low-range offenders (committed one speeding offence in the time-frame and that offence was less than 15 km/hr over the speed limit) and mid-range offenders (all other offenders) were identified. Using Chi-square and logistic regression analyses, characteristics and predictors of high-range speeding offenders were identified. The implications and limitations of this study are also discussed.

The relationship of loneliness and social anxiety with children's and adolescents' online communication

Children and adolescents are now using online communication to form and/or maintain relationships with strangers and/or friends. Relationships in real life are important for children and adolescents in identity formation and general development. However, social relationships can be difficult for those who experience feelings of loneliness and social anxiety. The current study aimed to replicate and extend research conducted by Valkenburg and Peter (2007b), by investigating differences in online communication patterns between children and adolescents with and without selfreported loneliness and social anxiety. Six hundred and twenty-six students aged 10-16 years completed a questionnaire survey about the amount of time they engaged in online communication, the topics they discussed, who they communicated with, and their purposes of online communication. Following Valkenburg and Peter (2007b), loneliness was measured with a shortened version of the UCLA Loneliness Scale (Version 3) developed by Russell (1996), whereas social anxiety was assessed with a sub-scale of the Social Anxiety Scale for Adolescents (La Greca & Lopez, 1998). The sample was divided into four groups of children and adolescents: 220 were “non-socially anxious and non-lonely”, 139 were “socially anxious but not lonely”, 107 were “lonely but not socially anxious”, and 159 were “lonely and socially anxious”. A one-way ANOVA and chi-square tests were conducted to evaluate the aforementioned differences between these groups. The results indicated that children and adolescents who reported being lonely used online communication differently from those who did not report being lonely. Essentially, the former communicated online more frequently about personal things and intimate topics, but also to compensate for their weak social skills and to meet new people. Further analyses on gender differences within lonely children and adolescents revealed that boys and girls communicated online more frequently with different partners. It was concluded that for these vulnerable individuals online communication may fulfil needs of self-disclosure, identity exploration, and social interactions. However, future longitudinal studies combining a quantitative with a qualitative approach would better address the relationship between Internet use and psychosocial well-being. The findings also suggested the need for further exploration of how such troubled children and adolescents can use the Internet beneficially.

Patterns of reporting to child protection services in Canada by healthcare and nonhealthcare professionals

Background: All Canadian jurisdictions require certain professionals to report suspected or observed child maltreatment. This study examined the types of maltreatment, level of harm and child functioning issues, controlling for family socioeconomic status, age and gender of the child reported by healthcare and non-healthcare professionals. Methods: We conducted chi-square analyses and logistic regression on a national child welfare sample from the 2003 Canadian Incidence Study of Reported Child Abuse and Neglect (CIS-2003) and compared the differences in professional reporting with its previous cycle (CIS-1998) using Bonferroni-corrected confidence intervals. Results: Our analysis of CIS-2003 data revealed that the majority of substantiated child maltreatment is reported to service agencies by non-healthcare professionals (57%), followed by non-professionals (33%) and healthcare professionals (10%). The number of professional reports increased 2.5 times between CIS-1998 and CIS-2003, while non-professionals’ increased 1.7 times. Of the total investigations, professional reports represented 59% in CIS-1998 and 67% in CIS-2003 (p<0.001). Compared to non-healthcare professionals, healthcare professionals more often reported younger children, children who experienced neglect and emotional maltreatment and those assessed as suffering harm and child functioning issues, but less often exposure to domestic violence. Conclusion: The results indicate that healthcare professionals played an important role in identifying children in need of protection considering harm and other child functioning issues. The authors discuss the reasons why underreporting is likely to remain an issue.

Trends in demographic, health behaviour factors, and self-perceived weight status : influences on obesity in Australia from 1995 to 2005

Overweight and obesity are two of the most important emerging public health issues in our time and regarded by the World Health Organisation [WHO] (1998) as a worldwide epidemic. The prevalence of obesity in the USA is the highest in the world, and Australian obesity rates fall into second place. Currently, about 60% of Australian adults are overweight (BMI „d 25kg/m2). The socio-demographic factors associated with overweight and/or obesity have been well demonstrated, but many of the existing studies only examined these relationships at one point of time, and did not examine whether significant relationships changed over time. Furthermore, only limited previous research has examined the issue of the relationship between perception of weight status and actual weight status, as well as factors that may impact on people¡¦s perception of their body weight status. Aims: The aims of the proposed research are to analyse the discrepancy between perceptions of weight status and actual weight status in Australian adults; to examine if there are trends in perceptions of weight status in adults between 1995 to 2004/5; and to propose a range of health promotion strategies and furth er research that may be useful in managing physical activity, healthy diet, and weight reduction. Hypotheses: Four alternate hypotheses are examined by the research: (1) there are associations between independent variables (e.g. socio -demographic factors, physical activity and dietary habits) and overweight and/or obesity; (2) there are associations between the same independent variables and the perception of overweight; (3) there are associations between the same independent variables and the discrepancy between weight status and perception of weight status; and (4) there are trends in overweight and/or obesity, perception of overweight, and the discrepancy in Australian adults from 1995 to 2004/5. Conceptual Framework and Methods: A conceptual framework is developed that shows the associations identified among socio -demographic factors, physical activity and dietary habits with actual weight status, as well as examining perception of weight status. The three latest National Health Survey data bases (1995 , 2001 and 2004/5) were used as the primary data sources. A total of 74,114 Australian adults aged 20 years and over were recruited from these databases. Descriptive statistics, bivariate analyses (One -Way ANOVA tests, unpaired t-tests and Pearson chi-square tests), and multinomial logistic regression modelling were used to analyse the data. Findings: This research reveals that gender, main language spoken at home, occupation status, household structure, private health insurance status, and exercise are related to the discrepancy between actual weight status and perception of weight status, but only gender and exercise are related to the discrepancy across the three time point s. The current research provides more knowledge about perception of weight status independently. Factors which affect perception of overweight are gender, age, language spoken at home, private health insurance status, and diet ary habits. The study also finds that many factors that impact overweight and/or obesity also have an effect on perception of overweight, such as age, language spoken at home, household structure, and exercise. However, some factors (i.e. private health insurance status and milk consumption) only impact on perception of overweight. Furthermore, factors that are rel ated to people’s overweight are not totally related to people’s underestimation of their body weight status in the study results. Thus, there are unknown factors which can affect people’s underestimation of their body weight status. Conclusions: Health promotion and education activities should provide education about population health education and promotion and education for particular at risk sub -groups. Further research should take the form of a longitudinal study design ed to examine the causal relationship between overweight and/or obesity and underestimation of body weight status, it should also place more attention on the relationships between overweight and/or obesity and dietary habits, with a more comprehensive representation of SES. Moreover, further research that deals with identification of characteristics about perception of weight status, in particular the underestimation of body weight status should be undertaken.

Wandering and the physical environment

Background/Rationale Guided by the need-driven dementia-compromised behavior (NDB) model, this study examined influences of the physical environment on wandering behavior. Methods Using a descriptive, cross-sectional design, 122 wanderers from 28 long-term care (LTC) facilities were videotaped 10 to 12 times; data on wandering, light, sound, temperature and humidity levels, location, ambiance, and crowding were obtained. Associations between environmental variables and wandering were evaluated with chi-square and t tests; the model was evaluated using logistic regression. Results In all, 80% of wandering occurred in the resident’s own room, dayrooms, hallways, or dining rooms. When observed in other residents’ rooms, hallways, shower/baths, or off-unit locations, wanderers were likely (60%-92% of observations) to wander. The data were a good fit to the model overall (LR [logistic regression] χ2 (5) = 50.38, P < .0001) and by wandering type. Conclusions Location, light, sound, proximity of others, and ambiance are associated with wandering and may serve to inform environmental designs and care practices.

On the nature of over-dispersion in motor vehicle crash prediction models

Statistical modeling of traffic crashes has been of interest to researchers for decades. Over the most recent decade many crash models have accounted for extra-variation in crash counts—variation over and above that accounted for by the Poisson density. The extra-variation – or dispersion – is theorized to capture unaccounted for variation in crashes across sites. The majority of studies have assumed fixed dispersion parameters in over-dispersed crash models—tantamount to assuming that unaccounted for variation is proportional to the expected crash count. Miaou and Lord [Miaou, S.P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes methods. Transport. Res. Rec. 1840, 31–40] challenged the fixed dispersion parameter assumption, and examined various dispersion parameter relationships when modeling urban signalized intersection accidents in Toronto. They suggested that further work is needed to determine the appropriateness of the findings for rural as well as other intersection types, to corroborate their findings, and to explore alternative dispersion functions. This study builds upon the work of Miaou and Lord, with exploration of additional dispersion functions, the use of an independent data set, and presents an opportunity to corroborate their findings. Data from Georgia are used in this study. A Bayesian modeling approach with non-informative priors is adopted, using sampling-based estimation via Markov Chain Monte Carlo (MCMC) and the Gibbs sampler. A total of eight model specifications were developed; four of them employed traffic flows as explanatory factors in mean structure while the remainder of them included geometric factors in addition to major and minor road traffic flows. The models were compared and contrasted using the significance of coefficients, standard deviance, chi-square goodness-of-fit, and deviance information criteria (DIC) statistics. The findings indicate that the modeling of the dispersion parameter, which essentially explains the extra-variance structure, depends greatly on how the mean structure is modeled. In the presence of a well-defined mean function, the extra-variance structure generally becomes insignificant, i.e. the variance structure is a simple function of the mean. It appears that extra-variation is a function of covariates when the mean structure (expected crash count) is poorly specified and suffers from omitted variables. In contrast, when sufficient explanatory variables are used to model the mean (expected crash count), extra-Poisson variation is not significantly related to these variables. If these results are generalizable, they suggest that model specification may be improved by testing extra-variation functions for significance. They also suggest that known influences of expected crash counts are likely to be different than factors that might help to explain unaccounted for variation in crashes across sites

Perceptions of the psychological well-being and care of older home care clients : clients and their carers

Aim. To explore and compare older home care clients’ (65+) and their professionals’ perceptions of the clients’ psychological well-being and care and to identify possible differences in these perceptions. Background. Psychological well-being is considered an important dimension of quality of life. With advancing age, older people require home care support to be able to remain in their own home. The main goal of care is to maximise their independence and quality of life. Design. Descriptive, survey design with questionnaire. Methods. A postal questionnaire was distributed to 200 older home care clients and 570 social and health care professionals in 2007. The total response rate was 63%. The questionnaire consisted of questions about clients’ psychological well-being and the provision of care by home care professionals. The differences in responses between clients and professionals were analysed using cross-tabulations, the Pearson Chi-Square Test and Fisher’s Exact Tests. Results. The professional group believed that their clients did not have plans for the future. They believed that their clients felt themselves depressed and suffering from loneliness significantly more often than the client group did. The client group were also significantly more critical of the care (motivating independent actions, physical, psychological and social care) they got from the professional group than how the professionals evaluated the care they gave. Conclusions. To be able to support older clients to continue living at home, professionals need to provide a service that meets client’s own perceptions and complex social and health care needs as well as personal sense of well-being. Relevance to clinical practice. The findings offer useful insights for the professional in planning and delivering appropriate home care services. A better understanding of differences between clients’ and professionals’ perceptions could lead to a better individualised care outcome.