A scaled difference chi-square test statistic for moment structure analysis

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say ${\cal M}_0$ implies on a less restricted one ${\cal M}_1$. If $T_0$ and $T_1$ denote the goodness-of-fit test statistics associated to ${\cal M}_0$ and ${\cal M}_1$, respectively, then typically the difference $T_d = T_0 - T_1$ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models ${\cal M}_0$ and ${\cal M}_1$. As in the case of the goodness-of-fit test, it is of interest to scale the statistic $T_d$ in order to improve its chi-square approximation in realistic, i.e., nonasymptotic and nonnormal, applications. In a recent paper, Satorra (1999) shows that the difference between two Satorra-Bentler scaled test statistics for overall model fit does not yield the correct SB scaled difference test statistic. Satorra developed an expression that permits scaling the difference test statistic, but his formula has some practical limitations, since it requires heavy computations that are notavailable in standard computer software. The purpose of the present paper is to provide an easy way to compute the scaled difference chi-square statistic from the scaled goodness-of-fit test statistics of models ${\cal M}_0$ and ${\cal M}_1$. A Monte Carlo study is provided to illustrate the performance of the competing statistics.

Swain: Stata module to correct the SEM chi-square overidentification test in small sample sizes or complex models. Statistical Software Components S457617, Boston College Department of Economics.

Swain corrects the chi-square overidentification test (i.e., likelihood ratio test of fit) for structural equation models whethr with or without latent variables. The chi-square statistic is asymptotically correct; however, it does not behave as expected in small samples and/or when the model is complex (cf. Herzog, Boomsma, & Reinecke, 2007). Thus, particularly in situations where the ratio of sample size (n) to the number of parameters estimated (p) is relatively small (i.e., the p to n ratio is large), the chi-square test will tend to overreject correctly specified models. To obtain a closer approximation to the distribution of the chi-square statistic, Swain (1975) developed a correction; this scaling factor, which converges to 1 asymptotically, is multiplied with the chi-square statistic. The correction better approximates the chi-square distribution resulting in more appropriate Type 1 reject error rates (see Herzog & Boomsma, 2009; Herzog, et al., 2007).

Chi-square analysis of the reduction of ATP levels in L-02 hepatocytes by hexavalent chromium

This study explored the reduction of adenosine triphosphate (ATP) levels in L-02 hepatocytes by hexavalent chromium (Cr(VI)) using chi-square analysis. Cells were treated with 2, 4, 8, 16, or 32 μM Cr(VI) for 12, 24, or 36 h. Methyl thiazolyl tetrazolium (MTT) experiments and measurements of intracellular ATP levels were performed by spectrophotometry or bioluminescence assays following Cr(VI) treatment. The chi-square test was used to determine the difference between cell survival rate and ATP levels. For the chi-square analysis, the results of the MTT or ATP experiments were transformed into a relative ratio with respect to the control (%). The relative ATP levels increased at 12 h, decreased at 24 h, and increased slightly again at 36 h following 4, 8, 16, 32 μM Cr(VI) treatment, corresponding to a "V-shaped" curve. Furthermore, the results of the chi-square analysis demonstrated a significant difference of the ATP level in the 32-μM Cr(VI) group (P < 0.05). The results suggest that the chi-square test can be applied to analyze the interference effects of Cr(VI) on ATP levels in L-02 hepatocytes. The decreased ATP levels at 24 h indicated disruption of mitochondrial energy metabolism and the slight increase of ATP levels at 36 h indicated partial recovery of mitochondrial function or activated glycolysis in L-02 hepatocytes.

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. ^

[do Elderly Individuals With A Cognitive Handicap Have Worse Oral Health?].

A comparison of the oral health of elderly people with and without a cognitive handicap was assessed. The cognitive condition, the indices of decayed, missing, filled teeth (DMFT), decayed, filled roots (DFR), the need for dental treatment, the presence of plaque (P), calculus (C), the community periodontal index (CPI), the rate of periodontal attachment loss (PAL), edentulism, prosthetic use and the need for prosthetics were evaluated in a complex probabilistic sample by conglomerates of the elderly (65-74 years). PASW(r) 17.0 was used for the statistical analyses with correction for the design effect, applying the Mann Whitney and chi-square test with 95% reliability. A total of 736 elderly individuals were interviewed and examined. Those with cognitive impairment had higher average DMFT, DFR and lower average healthy sextant CPI, a lower prevalence of sextants without plaque/calculus, use of prosthetics and higher prevalence of edentulism and need for prosthetics. Elderly individuals with a cognitive handicap had poorer oral health.

Rh, Kell, Duffy, Kidd And Diego Blood Group System Polymorphism In Brazilian Japanese Descendants.

Polymorphisms of Rh, Kell, Duffy, Kidd and Diego blood group systems were studied in 209 unrelated Brazilian Japanese descendants from South of Brazil. The methods used were multiplex-PCR, AS-PCR and RFLP-PCR. The differences in frequencies among the populations were evaluated using chi-square test. The frequencies for Rh, Kell, Kidd and Diego system were similar to those of the Japanese. RHCE(*)CC, RHCE(*)EE genotypes and FY(*)01 allele were lower and FY(*)01N.01 was higher than Japanese. These differences in the frequencies between Brazilian Japanese descendants and Japanese could indicate a gene flow in Brazilian population and reinforce the importance of this knowledge to achieve safe red blood cells.

Clinicopathological And Immunohistochemical Evaluation Of Oral And Oropharyngeal Squamous Cell Carcinoma In Chilean Population.

In oral and oropharyngeal squamous cell carcinoma (OCSCC and OPSCC) exist an association between clinical and histopathological parameters with cell proliferation, basal lamina, connective tissue degradation and surrounding stroma markers. We evaluated these associations in Chilean patients. A convenience sample of 37 cases of OCSCC (n=16) and OPSCC (n=21) was analyzed clinically (TNM, clinical stage) and histologically (WHO grade of differentiation, pattern of tumor invasion). We assessed the expression of p53, Ki67, HOXA1, HOXB7, type IV collagen (ColIV) and carcinoma-associated fibroblast (α-SMA-positive cells). Additionally we conducted a univariate/bivariate analysis to assess the relationship of these variables with survival rates. Males were mostly affected (56.2% OCSCC, 76.2% OPSCC). Patients were mainly diagnosed at III/IV clinical stages (68.8% OCSCC, 90.5% OPSCC) with a predominantly infiltrative pattern invasion (62.9% OCSCC, 57.1% OPSCC). Significant association between regional lymph nodes (N) and clinical stage with OCSCC-HOXB7 expression (Chi-Square test P < 0.05) was observed. In OPSCC a statistically significant association exists between p53, Ki67 with gender (Chi-Square test P < 0.05). In OCSCC and OPSCC was statistically significant association between ki67 with HOXA1, HOXB7, and between these last two antigens (Pearson's Correlation test P < 0.05). Furthermore OPSCC-p53 showed significant correlation when it was compared with α-SMA (Kendall's Tau-c test P < 0.05). Only OCSCC-pattern invasion and OPSCC-primary tumor (T) pattern resulted associated with survival at the end of the follow up period (Chi-Square Likelihood Ratio, P < 0.05). Clinical, histological and immunohistochemical features are similar to seen in other countries. Cancer proliferation markers were associated strongly from each other. Our sample highlights prognostic value of T and pattern of invasion, but the conclusions may be limited and should be considered with caution (small sample). Many cases were diagnosed in the advanced stages of the disease, which suggests that the diagnosis of OCSCC and OPSCC is made late.

Prevalence Of Urinary Incontinence And Its Association With Multimorbidity In Women Aged 50 Years Or Older: A Population-based Study.

To evaluate the prevalence and associated risk factors for urinary incontinence, as well as its association with multimorbidity among Brazilian women aged 50 or over. This was a secondary analysis of a cross-sectional population-based study including 622 women 50 years or older, conducted in the city of Campinas-SP-Brazil. The dependent variable was Urinary Incontinence (UI), defined as any complaint of urine loss. The independent variables were sociodemographic data, health-related habits, self-perception of health and functional capacity evaluation. Statistical analysis was carried out using the Chi-square test and Poisson regression. The mean age of the women was 64. UI was prevalent in 52.3% of these women: Mixed UI (26.6%), Urge UI (13.2%) and Stress UI (12.4%). Factors associated with a higher prevalence of UI were hypertension (OR 1.21, CI 1:01-1:47, P = 0.004), osteoarthritis (OR 1.24, CI 1:03-1:50, P = 0.022), physical activity ≥3 days/week (OR 1.21, CI 1:01-1:44, P = 0.039), BMI ≥ 25 at the time of the interview (OR 1.25, CI 1:04-1:49, P = 0.018), negative self-perception of health (OR 1.23, CI 1:06-1:44 P = 0.007) and limitations in daily living activities (PR 1:56 CI 1:16-2:10, P = 0.004). The prevalence of UI was high. Mixed incontinence was the most frequent type of UI. Many associated factors can be prevented or improved. Thus, health policies targeted at these combined factors could reduce their prevalence rate and possibly decrease the prevalence of UI. Neurourol. Urodynam. © 2014 Wiley Periodicals, Inc.