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. ^

Spatial and temporal analysis of Barmah Forest virus disease in Queensland, Australia

Barmah Forest virus (BFV) disease is one of the most widespread mosquito-borne diseases in Australia. The number of outbreaks and the incidence rate of BFV in Australia have attracted growing concerns about the spatio-temporal complexity and underlying risk factors of BFV disease. A large number of notifications has been recorded continuously in Queensland since 1992. Yet, little is known about the spatial and temporal characteristics of the disease. I aim to use notification data to better understand the effects of climatic, demographic, socio-economic and ecological risk factors on the spatial epidemiology of BFV disease transmission, develop predictive risk models and forecast future disease risks under climate change scenarios. Computerised data files of daily notifications of BFV disease and climatic variables in Queensland during 1992-2008 were obtained from Queensland Health and Australian Bureau of Meteorology, respectively. Projections on climate data for years 2025, 2050 and 2100 were obtained from Council of Scientific Industrial Research Organisation. Data on socio-economic, demographic and ecological factors were also obtained from relevant government departments as follows: 1) socio-economic and demographic data from Australian Bureau of Statistics; 2) wetlands data from Department of Environment and Resource Management and 3) tidal readings from Queensland Department of Transport and Main roads. Disease notifications were geocoded and spatial and temporal patterns of disease were investigated using geostatistics. Visualisation of BFV disease incidence rates through mapping reveals the presence of substantial spatio-temporal variation at statistical local areas (SLA) over time. Results reveal high incidence rates of BFV disease along coastal areas compared to the whole area of Queensland. A Mantel-Haenszel Chi-square analysis for trend reveals a statistically significant relationship between BFV disease incidence rates and age groups (ƒÓ2 = 7587, p<0.01). Semi-variogram analysis and smoothed maps created from interpolation techniques indicate that the pattern of spatial autocorrelation was not homogeneous across the state. A cluster analysis was used to detect the hot spots/clusters of BFV disease at a SLA level. Most likely spatial and space-time clusters are detected at the same locations across coastal Queensland (p<0.05). The study demonstrates heterogeneity of disease risk at a SLA level and reveals the spatial and temporal clustering of BFV disease in Queensland. Discriminant analysis was employed to establish a link between wetland classes, climate zones and BFV disease. This is because the importance of wetlands in the transmission of BFV disease remains unclear. The multivariable discriminant modelling analyses demonstrate that wetland types of saline 1, riverine and saline tidal influence were the most significant risk factors for BFV disease in all climate and buffer zones, while lacustrine, palustrine, estuarine and saline 2 and saline 3 wetlands were less important. The model accuracies were 76%, 98% and 100% for BFV risk in subtropical, tropical and temperate climate zones, respectively. This study demonstrates that BFV disease risk varied with wetland class and climate zone. The study suggests that wetlands may act as potential breeding habitats for BFV vectors. Multivariable spatial regression models were applied to assess the impact of spatial climatic, socio-economic and tidal factors on the BFV disease in Queensland. Spatial regression models were developed to account for spatial effects. Spatial regression models generated superior estimates over a traditional regression model. In the spatial regression models, BFV disease incidence shows an inverse relationship with minimum temperature, low tide and distance to coast, and positive relationship with rainfall in coastal areas whereas in whole Queensland the disease shows an inverse relationship with minimum temperature and high tide and positive relationship with rainfall. This study determines the most significant spatial risk factors for BFV disease across Queensland. Empirical models were developed to forecast the future risk of BFV disease outbreaks in coastal Queensland using existing climatic, socio-economic and tidal conditions under climate change scenarios. Logistic regression models were developed using BFV disease outbreak data for the existing period (2000-2008). The most parsimonious model had high sensitivity, specificity and accuracy and this model was used to estimate and forecast BFV disease outbreaks for years 2025, 2050 and 2100 under climate change scenarios for Australia. Important contributions arising from this research are that: (i) it is innovative to identify high-risk coastal areas by creating buffers based on grid-centroid and the use of fine-grained spatial units, i.e., mesh blocks; (ii) a spatial regression method was used to account for spatial dependence and heterogeneity of data in the study area; (iii) it determined a range of potential spatial risk factors for BFV disease; and (iv) it predicted the future risk of BFV disease outbreaks under climate change scenarios in Queensland, Australia. In conclusion, the thesis demonstrates that the distribution of BFV disease exhibits a distinct spatial and temporal variation. Such variation is influenced by a range of spatial risk factors including climatic, demographic, socio-economic, ecological and tidal variables. The thesis demonstrates that spatial regression method can be applied to better understand the transmission dynamics of BFV disease and its risk factors. The research findings show that disease notification data can be integrated with multi-factorial risk factor data to develop build-up models and forecast future potential disease risks under climate change scenarios. This thesis may have implications in BFV disease control and prevention programs in Queensland.

Factors Contributing to Reading Performance: An In-Depth Analysis of the “Boy Crisis”

This research used a quantitative study approach to investigate the “boy crisis” in Canada. Boy crisis advocates suggest that boys are being surpassed by girls on reading assessments and promote strategies to assist male students. A feminist framework was used in this study that allowed for an investigation and discussion of the factors that mediate between gender and success at reading comprehension, interpretation, and response to text without ignoring female students. Reading scores and questionnaire data compiled by the Pan-Canadian Assessment Program were used in this research, specifically the PCAP-13 2007 assessment of approximately 30,000 13-year-old students from all Canadian provinces and Yukon Territory (CMEC, 2008). Approximately 20,000 participants wrote the reading assessment, while 30,000 students completed the questionnaire responses. Predictor variables were tested using parametric tests such as independent samples t-test, one-way ANOVA, chi-square analysis, and Pearson r. Findings from this study indicate that although boys scored lower than girls on the PCAP-13 2007 reading assessment, factors were found to influence the reading scores of both male and female students to varying degrees. Socioeconomic status, perceptions of the reading material used in language arts classrooms, reading preference, reading interest, parental involvement, parental encouragement for reading, and self-efficacy were all found to affect the reading performance of boys and girls. Relationships between variables were also found and are discussed in this research. The analysis presented in this study allows parents, educators, and policy makers to begin to critically examine and re-evaluate boy crisis literature and offers suggestions on how to improve reading performance for all students of all socioeconomic backgrounds.

HAPPINESS INDEXTHE CONSTRUCTION AND ANALYSIS

This study aims to investigate the important indicators that contribute to happiness among Beijing residence. The residents of Beijing were taken as the target population for the survey. A questionnaire was used as the main statistical instrument to collect the data from the residents in Beijing. In so doing the investigation employs Factor analyses and chi-square analyses as the main statistical tools used for the analyses in this research. The study found that Beijing residents gained greater happiness in the family, interpersonal relationships, and health status. The analysis also shows that generally, the residence of Beijing feels happier and also in terms of gender basis, females in Beijing feel happier as compare to their male counterpart. It will find that gender, age and education are statistically significant when dealing with happiness.

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.

Learning styles vary among general surgery residents: analysis of 12 years of data

PURPOSE: Understanding the learning styles of individuals may assist in the tailoring of an educational program to optimize learning. General surgery faculty and residents have been characterized previously as having a tendency toward particular learning styles. We seek to understand better the learning styles of general surgery residents and differences that may exist within the population. METHODS: The Kolb Learning Style Inventory was administered yearly to general surgery residents at the University of Cincinnati from 1994 to 2006. This tool allows characterization of learning styles into 4 groups: converging, accommodating, assimilating, and diverging. The converging learning style involves education by actively solving problems. The accommodating learning style uses emotion and interpersonal relationships. The assimilating learning style learns by abstract logic. The diverging learning style learns best by observation. Chi-square analysis and analysis of variance were performed to determine significance. RESULTS: Surveys from 1994 to 2006 (91 residents, 325 responses) were analyzed. The prevalent learning style was converging (185, 57%), followed by assimilating (58, 18%), accommodating (44, 14%), and diverging (38, 12%). At the PGY 1 and 2 levels, male and female residents differed in learning style, with the accommodating learning style being relatively more frequent in women and assimilating learning style more frequent in men (Table 1, p < or = 0.001, chi-square test). Interestingly, learning style did not seem to change with advancing PGY level within the program, which suggests that individual learning styles may be constant throughout residency training. If a resident's learning style changed, it tended to be to converging. In addition, no relation exists between learning style and participation in dedicated basic science training or performance on the ABSIT/SBSE. CONCLUSIONS: Our data suggests that learning style differs between male and female general surgery residents but not with PGY level or ABSIT/SBSE performance. A greater understanding of individual learning styles may allow more refinement and tailoring of surgical programs.

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!

Children of substance-using mothers : child health engagement and child protection outcomes

Aim: Maternal substance use has been associated with a range of child risk factors. The study investigated the relationship between engagement with child health services and child protection outcomes for children of substance using mothers. ----- ----- Methods: A sample of 119 children of mothers who disclosed opiate, amphetamine or methadone use during a maternity admission between 2000 and 2003, as included in a previous matched co-hort study1, were included in the current study. Statutory child protection agency and child health engagement information for the first two years of life, was obtained. The relationship between type of maternal substance use, child health engagement and child protection outcomes was examined. ----- ----- Results: Seventy two percent of study group infants were engaged with child health services during the first two years of life. Chi square analysis showed no significant relationship between child health engagement and child protection reports. Child health engagement was associated with decreased substantiated child protection notifications for children of methadone using mothers, but not for children of illicit substance users. ----- ----- Conclusions: Almost a quarter of identified children of substance using mothers are not accessing standard child health services in their first two years of life. This study provides support for increased attention to the provision of child health services for children of methadone using mothers. Further research into effective intervention strategies for children of illicit substance using mothers is indicated.

Physical performance profile of sub-elite juvenile Gaelic Games players and the prevalence of a Relative Age Effect (RAE)

Gaelic Games are the indigenous sports played in Ireland, the most popular being Gaelic football and hurling. The games are contact sports and the physical demands are thought to be similar to those of Australian Rules football, rugby union, rugby league, field hockey, and lacrosse (Delahunt et al., 2011). The difference in chronological age between children in a single age group is known as relative age and its consequences as the RAE, whereby younger players are disadvantaged (Del Campo et al., 2010). The purpose of this study was to describe the physical and performance profile of sub-elite juvenile Gaelic Games players and to establish if a RAE is present in this cohort and any influence physiological moderator variables may have on this. Following receipt of ethical approval (EHSREC11-45), six sub-elite county development squads (Under-14/15/16 age groups, male, n=115) volunteered to partake in the study. Anthropometric data including skin folds and girths were collected. A number of field tests of physical performance including 5 and 20m speed, vertical and broad jump distance, and an estimate of VO2max were carried out. Descriptive data are presented as Mean SD. Juvenile sub-elite Gaelic Games players aged 14.53 0.82 y were 172.87 7.63 cm tall, had a mass of 64.74 11.06 kg, a BMI of 21.57 2.82 kg.m-2 and 9.22 4.78 % body fat. Flexibility, measured by sit and reach was 33.62 6.86 cm and lower limb power measured by vertical and broad jump were 42.19 5.73 and 191.16 25.26 cm, respectively. Participant time to complete 5m, 20m and an agility test (T-Test) was 1.12 0.07, 3.31 0.30 and 9.31 0.55 s respectively. Participant’s estimated VO2max was 48.23 5.05 ml.kg.min-1. Chi-Square analysis of birth month by quartile (Q1 = January-March) revealed that a RAE was present in this cohort, whereby an over-representation of players born in Q1 compared with Q2, Q3 and Q4 was evident (2 = 14.078, df = 3, p = 0.003). Kruskal-Wallis analysis of the data revealed no significant difference in any of the performance parameters based on quartile of birth (Alpha level = 0.05).This study provides a physical performance profile of juvenile sub-elite Gaelic Games players, comparable with those of other sports such as soccer and rugby. This novel data can inform us of the physical requirements of the sport. The evidence of a RAE is similar to that observed in other contact sports such as soccer and rugby league (Carling et al, 2009; Till et al, 2010). Although a RAE exists in this cohort, this cannot be explained by any physical/physiological moderator variables. Carling C et al. (2009). Scandinavian Journal of Medicine and Science in Sport 19, 3-9. Delahunt E et al. (2011). Journal of Athletic Training 46, 241-5. Del Campo DG et al. (2010). Journal of Sport Science and Medicine 9, 190-198. Delorme N et al. (2010). European Journal of Sport Science 10, 91-96. Till K et al. (2010). Scandinavian Journal of Medicine and Science in Sports 20, 320-329.

Investigation of homocysteine-pathway-related variants in essential hypertension

Hyperhomocysteinemia (hHcy) has been associated with an increased risk of cardiovascular disease and stroke. Essential hypertension (EH), a polygenic condition, has also been associated with increased risk of cardiovascular related disorders. To investigate the role of the homocysteine (Hcy) metabolism pathway in hypertension we conducted a case-control association study of Hcy pathway gene variants in a cohort of Caucasian hypertensives and age- and sex-matched normotensives. We genotyped two polymorphisms in the methylenetetrahydrofolate reductase gene (MTHFR C677T and MTHFR A1298C), one polymorphism in the methionine synthase reductase gene (MTRR A66G), and one polymorphism in the methylenetetrahydrofolate dehydrogenase 1 gene (MTHFD1 G1958A) and assessed their association with hypertension using chi-square analysis. We also performed a multifactor dimensionality reduction (MDR) analysis to investigate any potential epistatic interactions among the four polymorphisms and EH. None of the four polymorphisms was significantly associated with EH and although we found a moderate synergistic interaction between MTHFR A1298C and MTRR A66G, the association of the interaction model with EH was not statistically significant (

Investigation of two Wnt signalling pathway single nucleotide polymorphisms in a breast cancer-affected Australian population

In the mammary gland, Wnt signals are strongly implicated in initial development of the mammary rudiments and in the ductal branching and alveolar morphogenesis that occurs during pregnancy. Previously, we identified two Wnt signaling pathway-implicated genes, PPP3CA and MARK4, as having a role in more aggressive and potentially metastatic breast tumors. In this study, we examined two SNPs within PPP3CA and MARK4 in an Australian case-control study population for a potential role in human breast cancers. 182 cases and 180 controls were successfully genotyped for the PPP3CA SNP (rs2850328) and 182 cases and 177 controls were successfully genotyped for the MARK4 SNP (rs2395) using High Resolution Melt (HRM) analysis. Genotypes of randomly selected samples for both SNPs were validated by dye terminator sequencing. Chi-square tests were performed to determine any significant differences in the genotype and allele frequencies between the cases and controls. Chi-square analysis showed no statistically significant difference (p > .05) for genotype frequencies between cases and controls for rs2850328 (χ2 = 1.2, p = .5476) or rs2395 (χ2 = .3, p = .8608). Similarly, no statistical difference was observed for allele frequencies for rs2850328 (χ2 = .68, p = .4108) or rs2395 (χ2 = .02, p = .893). Even though an association of the polymorphisms rs2850328 and rs2395 and breast cancer was not detected in our case-control study population, other variants within the PPP3CA and MARK4 genes may still be associated with breast cancer, as both genes are implicated with processes involved in the disease as well as their mutual partaking in the Wnt signaling pathway.