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).

Extending a model of shift-work tolerance

The present study contributes to theory and practice through the development of a model of shift-work tolerance with the potential to indicate interventions that reduce nurses' intention toward turnover and increase job satisfaction in hospital-based settings. Survey data from 1257 nurses were used to conduct structural equation modeling that examine the direct and indirect effects of supervisor and colleague support, team identity, team climate, and control over working environment on time-based work/life conflict, psychological well-being, physical symptoms, job satisfaction, and turnover intention. The analysis of the proposed model revealed a good fit The chi-square difference test was non-significant (χ2(26)=338.56), the fit indices were high (CFI=.923, NFI=.918, and NNFI=.868), the distribution of residuals was symmetric and approached zero, the average standardized residual was low (AASR=.04), and the standardized RMR was .072. In terms of the predictor variable, the final model explained 48% of the variance in turnover intention. The data revealed considerable evidence of both direct effects on adjustment and complex indirect links between levels of adjustment and work-related social support, team identity, team climate, and control. Nurses with high supervisor and coworker support experienced more positive team climates, identified more strongly with their team, and increased their perceptions of control over their work environment. This in turn lowered their appraisals of their time-based work/life conflict, which consequently increased their psychological well-being and job satisfaction and reduced their physical health symptoms and turnover intention. The type of shift schedule worked by the nurses influenced levels of turnover intention, control over work environment, time-based work/life conflict, and physical symptoms.

Testing the psychometric properties of Kidscreen-27 with Irish children of low socio-economic status

Background

Kidscreen-27 was developed as part of a cross-cultural European Union-funded project to standardise the measurement of children’s health-related quality of life. Yet, research has reported mixed evidence for the hypothesised 5-factor model, and no confirmatory factor analysis (CFA) has been conducted on the instrument with children of low socio-economic status (SES) across Ireland (Northern and Republic).

Method

The data for this study were collected as part of a clustered randomised controlled trial. A total of 663 (347 male, 315 female) 8–9-year-old children (M = 8.74, SD = .50) of low SES took part. A 5- and modified 7-factor CFA models were specified using the maximum likelihood estimation. A nested Chi-square difference test was conducted to compare the fit of the models. Internal consistency and floor and ceiling effects were also examined.

Results

CFA found that the hypothesised 5-factor model was an unacceptable fit. However, the modified 7-factor model was supported. A nested Chi-square difference test confirmed that the fit of the 7-factor model was significantly better than that of the 5-factor model. Internal consistency was unacceptable for just one scale. Ceiling effects were present in all but one of the factors.

Conclusions

Future research should apply the 7-factor model with children of low socio-economic status. Such efforts would help monitor the health status of the population.

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!

Qualidade de vida e fatores associados em idosos dependentes em uma cidade do interior do Nordeste

OBJETIVO: Este estudo tem por objetivo verificar a influência de fatores sociodemográficos, condições de saúde, capacidade funcional e dinâmica familiar na qualidade de vida de idosos dependentes residentes em domicílio em uma cidade do interior da região do Nordeste. MÉTODOS: Trata-se de uma pesquisa de caráter analítico com delineamento transversal. A amostra deste estudo foi composta por 117 idosos dependentes, cadastrados nas Unidades de Saúde da Família da área de abrangência do bairro do Jequiezinho, no município de Jequié, BA. Os instrumentos de coleta de dados utilizados foram o WHOQOL-OLD, o Índice de Barthel, o Apgar de Família e o levantamento de dados sociodemográficos e condições de saúde. RESULTADOS: Com a aplicação do Teste do qui-quadrado (x²) encontrou-se diferença estatística entre comprometimento da qualidade de vida e da dinâmica familiar, com exceção do domínio autonomia (p = 0,061) da qualidade de vida. CONCLUSÕES: Apenas o comprometimento da dinâmica familiar influencia de maneira negativa a qualidade de vida dos idosos dependentes, uma vez que, quanto mais prejudicada a funcionalidade familiar, pior a qualidade de vida desses.

Univariate versus multivariate modeling of panel data

Panel data can be arranged into a matrix in two ways, called 'long' and 'wide' formats (LFand WF). The two formats suggest two alternative model approaches for analyzing paneldata: (i) univariate regression with varying intercept; and (ii) multivariate regression withlatent variables (a particular case of structural equation model, SEM). The present papercompares the two approaches showing in which circumstances they yield equivalent?insome cases, even numerically equal?results. We show that the univariate approach givesresults equivalent to the multivariate approach when restrictions of time invariance (inthe paper, the TI assumption) are imposed on the parameters of the multivariate model.It is shown that the restrictions implicit in the univariate approach can be assessed bychi-square difference testing of two nested multivariate models. In addition, commontests encountered in the econometric analysis of panel data, such as the Hausman test, areshown to have an equivalent representation as chi-square difference tests. Commonalitiesand differences between the univariate and multivariate approaches are illustrated usingan empirical panel data set of firms' profitability as well as a simulated panel 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.

Avaliação do estresse de enfermeiros de hospitais gerais do interior paulista, considerando serem ou não acreditados

Pós-graduação em Enfermagem (mestrado profissional) - FMB

Assessment of Pharmaceutical Equivalence: Difference Test or Equivalence Test?

Pharmaceutical equivalence is an important step towards the confirmation of similarity and Interchangeability among pharmaceutical products, particularly regarding those that win not be tested for bioequivalence. The aim of this paper is to compare traditional difference testing to two one-side equivalence tests in the assessment of pharmaceutical equivalence, by means of equivalence studies between similar, generic and reference products of acyclovir cream, atropine sulfate injection, meropenem for injection, and metronidazole injection. All tests were performed in accordance with the Brazilian Pharmacopeia or the United States Pharmacopeia. All four possible combinations of results arise in these comparisons of difference testing and equivalence testing. Most of the former did not show significant difference, whereas the latter presented similarity. We concluded that equivalence testing is more appropriate than difference testing, what can make it a useful tool to assess pharmaceutical equivalence in products that will not be tested for bioequivalence.