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 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. ^

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.

Ureaplasma parvum and ureaplasma urealyticum detected in semen after washing prior to assisted reproductive technology procedures

Objective: This study investigated: (i) the prevalence of ureaplasmas in semen and washed semen and (ii) the effect of ureaplasmas on semen andrology parameters. Design: Prospective study. Setting: IVF unit -private hospital, Brisbane, Australia. Patient(s): Three hundred and forty three men participating in an assisted reproductive technology (ART) treatment cycle. Intervention(s): Semen and washed semen tested by culture, PCR assays and indirect immunofluorescent antibody assays. Statistical differences were determined by a t-test, Wilcoxon or Pearson’s Chi- square test where appropriate. Main Outcome Measure(s): The prevalence of ureaplasmas in semen and washed semen and the effect of these microorganisms on semen andrology parameters. Result(s): Ureaplasmas were detected in 73/343 (22%) semen samples and 29/343 (8.5%) washed semen samples. Ureaplasmas adherent to the surface of spermatozoa were demonstrated by indirect immunofluorescent antibody testing. U. parvum serovar 6 (36.6%) and U. urealyticum (30%) were the most prevalent isolates in washed semen. A comparison of the semen andrology parameters of washed semen ureaplasma positive and negative groups demonstrated a lower proportion of non-motile sperm in the washed semen ureaplasma positive group. Conclusion(s): Ureaplasmas are not always removed from semen by a standard ART washing procedure and can remain adherent to the surface of spermatozoa.

The genetics of endurance : frequency of the ACTN3 R577X variant in Ironman World Championship athletes

Objectives To investigate the frequency of the ACTN3 R577X polymorphism in elite endurance triathletes, and whether ACTN3 R577X is significantly associated with performance time. Design Cross-sectional study. Methods Saliva samples, questionnaires, and performance times were collected for 196 elite endurance athletes who participated in the 2008 Kona Ironman championship triathlon. Athletes were of predominantly North American, European, and Australian origin. A one-way analysis of variance was conducted to compare performance times between genotype groups. Multiple linear regression analysis was performed to model the effect of questionnaire variables and genotype on performance time. Genotype and allele frequencies were compared to results from different populations using the chi-square test. Results Performance time did not significantly differ between genotype groups, and age, sex, and continent of origin were significant predictors of finishing time (age and sex: p < 5 × 10−6; continent: p = 0.003) though genotype was not. Genotype and allele frequencies obtained (RR 26.5%, RX 50.0%, XX 23.5%, R 51.5%, X 48.5%) were found to be not significantly different from Australian, Spanish, and Italian endurance athletes (p > 0.05), but were significantly different from Kenyan, Ethiopian, and Finnish endurance athletes (p < 0.01). Conclusions Genotype and allele frequencies agreed with those reported for endurance athletes of similar ethnic origin, supporting previous findings for an association between 577X allele and endurance. However, analysis of performance time suggests that ACTN3 does not alone influence endurance performance, or may have a complex effect on endurance performance due to a speed/endurance trade-off.

Prevalence and characteristics of Indigenous drink-driving convictions in Queensland, Australia

Alcohol-involved accidents are one of the leading contributors towards high injury rates among Indigenous Australians. However, there is limited information available to inform existing policies to change current rates. The study aims to provide information about the prevalence and the characteristics of such behaviour. Drink driving convictions from 2006-2010 were extracted from the Queensland Department of Justice and Attorney General database. Convictions were regrouped by gender, age, Accessibility/Remoteness Index of Australia classification (using court location) and sentence severity. A number of cross tabulations were carried out to identify relationships between variables. Standardised adjusted residuals were calculated for each cell in order to determine cell differences that contributed to the chi-square test results. Analysis revealed there were 9,323 convictions, of which the majority were for offences by males (77.5%). In relation to age, 52.6% of the convictions were of persons under 25 years of age. Age was significantly different across the five regions for males only (χ2=90.8, p<0.001), with a larger number of convictions in the ‘very remote’ region of persons over 40+ years of age. Increased remoteness was linked with high range BAC convictions for both males (χ2=168.4, p<0.001) and females (χ2=22.5, p=0.004). Monetary penalties were the primary sentence received for both males and females in all regions. The findings identify the Indigenous drink driving conviction rate to be 6 times that of the general Queensland rate and indicate that a multipronged approach is needed, with tailored strategies for remote offenders, young adults and offenders with alcohol misuse and dependency issues. Further attention is warranted in this area of road safety.

Analysis of the MTHFR C677T variant with migraine phenotypes

Background The methylenetetrahydrofolate reductase (MTHFR) gene variant C677T has been implicated as a genetic risk factor in migraine susceptibility, particularly in Migraine with Aura. Migraine, with and without aura (MA and MO) have many diagnostic characteristics in common. It is postulated that migraine symptomatic characteristics might themselves be influenced by MTHFR. Here we analysed the clinical profile, migraine symptoms, triggers and treatments of 267 migraineurs previously genotyped for the MTHFR C677T variant. The chi-square test was used to analyse all potential relationships between genotype and migraine clinical variables. Regression analyses were performed to assess the association of C677T with all migraine clinical variables after adjusting for gender. Findings The homozygous TT genotype was significantly associated with MA (P < 0.0001) and unilateral head pain (P = 0.002). While the CT genotype was significantly associated with physical activity discomfort (P < 0.001) and stress as a migraine trigger (P = 0.002). Females with the TT genotype were significantly associated with unilateral head pain (P < 0.001) and females with the CT genotype were significantly associated with nausea (P < 0.001), osmophobia (P = 0.002), and the use of natural remedy for migraine treatment (P = 0.003). Conversely, male migraineurs with the TT genotype experienced higher incidences of bilateral head pain (63% vs 34%) and were less likely to use a natural remedy as a migraine treatment compared to female migraineurs (5% vs 20%). Conclusions MTHFR genotype is associated with specific clinical variables of migraine including unilateral head pain, physical activity discomfort and stress.

Calibration and comparison of accelerometer cut points in preschool children

Objective The present study aimed to develop accelerometer cut points to classify physical activities (PA) by intensity in preschoolers and to investigate discrepancies in PA levels when applying various accelerometer cut points. Methods To calibrate the accelerometer, 18 preschoolers (5.8 +/- 0.4 years) performed eleven structured activities and one free play session while wearing a GT1M ActiGraph accelerometer using 15 s epochs. The structured activities were chosen based on the direct observation system Children's Activity Rating Scale (CARS) while the criterion measure of PA intensity during free play was provided using a second-by-second observation protocol (modified CARS). Receiver Operating Characteristic (ROC) curve analyses were used to determine the accelerometer cut points. To examine the classification differences, accelerometer data of four consecutive days from 114 preschoolers (5.5 +/- 0.3 years) were classified by intensity according to previously published and the newly developed accelerometer cut points. Differences in predicted PA levels were evaluated using repeated measures ANOVA and Chi Square test. Results Cut points were identified at 373 counts/15 s for light (sensitivity: 86%; specificity: 91%; Area under ROC curve: 0.95), 585 counts/15 s for moderate (87%; 82%; 0.91) and 881 counts/15 s for vigorous PA (88%; 91%; 0.94). Further, applying various accelerometer cut points to the same data resulted in statistically and biologically significant differences in PA. Conclusions Accelerometer cut points were developed with good discriminatory power for differentiating between PA levels in preschoolers and the choice of accelerometer cut points can result in large discrepancies.

Subjective reasons why immigrant patients attend the emergency department

Background Some patients visit a hospital’s emergency department (ED) for reasons other than an urgent medical condition. There is evidence that this practice may differ among patients from different backgrounds. The objective of this study was to examine the reasons why patients from a non-English speaking background (NESB) and patients with an English speaking background but not born in Australia (ESB-NBA) visit the ED, as compared to patients from English-speaking backgrounds but born in Australia (ESB-BA). Methods A cross-sectional survey was conducted at the ED of a tertiary hospital in metropolitan Brisbane, Queensland, Australia. Over a four-month period patients who were assigned an Australasian Triage Scale score of 3, 4 or 5 were surveyed. Pearson chi-square test and multivariate logistic regression analyses were performed to examine the differences between the ESB and NESB patients’ reported reasons for attending the ED. Results A total of 828 patients participated in this study. Compared to ESB-BA patients NESB patients were less likely to consider contacting a general practitioner (GP) before attending the ED (Odds Ratios (OR) 0.6 (95% Confidence Interval (CI) 0.4–0.8, p < .05) While ESB-NBA were more likely to consider contacting a GP 1.7 (1.1–2.5, p < .05). Both the NESB patients and the ESB-NBA patients were far more likely than ESB-BA patients to report that they had visited the ED either because they do not have a GP (OR 7.9, 95% CI 4.7–13.4, p < .001) and 2.2 (95% CI 1.1–4.4, p < .05) respectively and less likely to think that the ED could deal with their problem better than a GP(OR 0.5 (95% CI 0.3–0.8, p < .05) and 0.7 (0.3–0.9, p < .05) respectively. The NESB patients also thought it would take too long to make an appointment to consult a GP (OR 6.2, 95% CI 3.7–10.4, p < 0.001). Conclusions NESB patients were the least likely to consider contacting a GP before attending hospital EDs. Educational interventions may help direct NESB people to the appropriate health services and therefore reduce the burden on tertiary hospitals ED.

Comparison of visual status of Iranian military and commercial drivers

Background There is no legal requirement for Iranian military truck drivers to undergo regular visual checkups as compared to commercial truck drivers. Objectives This study aimed to evaluate the impact of drivers’ visual checkups by comparing the visual function of Iranian military and commercial truck drivers. Patients and Methods In this comparative cross-sectional study, two hundred military and 200 commercial truck drivers were recruited and their Visual Acuity (VA), Visual Field (VF), color vision and Contrast Sensitivity (CS) were assessed and compared using the Snellen chart, confrontation screening method, D15 test and Pelli-Robson letter chart, respectively. A questionnaire regarding driving exposure and history of motor-vehicle crashes (MVCs) was also filled by drivers. Results were analyzed using an independent samples t-test, one-way ANOVA (assessing difference in number of MVCs across different age groups), chi-square test and Pearson correlation at statistical significance level of P < 0.05. Results Mean age was 41.6 ± 9.2 for the military truck drivers and 43.4 ± 10.9 for commercial truck drivers (P > 0.05). No significant difference between military and commercial drivers was found in terms of driving experience, number of MVCs, binocular VA, frequency of color vision defects and CS scores. In contrast, the last ocular examination was significantly earlier in military drivers than commercial drivers (P < 0.001). In addition, 4% of military drivers did not meet the national standards to drive as opposed to 2% of commercial drivers. There was a significant but weak correlation between binocular VA and age (r = 0.175, P < 0.001). However, CS showed a significantly moderate correlation with age (r = -0.488, P < 0.001). Conclusions The absence of legal requirement for regular eye examination in military drivers caused the incompetent drivers to be missed in contrast to commercial drivers. The need for scientific revision of VA standard for Iranian drivers is also discussed. The CS measurement in visual checkups of older drivers deserves to be investigated more thoroughly.