• Journal of Integrative Natural Science
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• v.14 no.3
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• pp.123-129
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• 2021

This research examines the effect of positively skewed population distribution on the two sample t-test through simulation. For simulation work, two independent samples were selected from the same chi-square distributions with 3, 5, 10, 15, 20, 30 degrees of freedom and sample sizes 3, 5, 10, 15, 20, 30, respectively. Chi-square distribution is largely skewed to the right at small degrees of freedom and getting symmetric as the degrees of freedom increase. Simulation results show that the sampled populations are distributed positively skewed like chi-square distribution with small degrees of freedom, the F-test for the equality of variances shows poor performances even at the relatively large degrees of freedom and sample sizes like 30 for both, and so it is recommended to avoid using F-test. When two population variances are equal, the skewness of population distribution does not affect on the t-test in terms of the confidence level. However even though for the highly positively skewed distribution and small sample sizes like three or five the t-test achieved the nominal confidence level, the error limits are very large at small sample size. Therefore, if the sampled population is expected to be highly skewed to the right, it will be recommended to use relatively large sample size, at least 20.

• The Korean Journal of Rehabilitation Nursing
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• v.17 no.1
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• pp.38-47
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• 2014

Purpose: This study was performed to investigate the effects of Tai Chi exercise on physical fitness and quality of life (QOL) in elderly women. Methods: This study was designed as a quasi-experimental, nonequivalent control group pre-post test design. The subjects were elderly women over 60 years old who enrolled senior citizen centers and elderly welfare center. Thirty-three people were conveniently assigned to an experimental group (n=15) or a control group (n=18). The data were collected from September 2009 to May 2010. The experimental group was trained Tai Chi exercise for 8 weeks (one hour Tai Chi classes twice a week and once a week by themselves at home). Data were analyzed by Fisher's exact test, ${\chi}^2$-test and independent t-test. Results: The experimental group experienced significant improvements in flexibility. The experimental group experienced significant improvements in physical component summary (p=.017) and mental component summary (p=.027) of QOL. Conclusion: Tai Chi exercise can be used as a nursing intervention for improvement of physical fitness and QOL in elderly women.

• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1465-1475
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• 2013

The chi-square type test statistic is the most commonly used test in terms of measuring testing goodness-of-fit for multinomial logistic regression model, which has its grouped data (binomial data) and ungrouped (binary) data classified by a covariate pattern. Chi-square type statistic is not a satisfactory gauge, however, because the ungrouped Pearson chi-square statistic does not adhere well to the chi-square statistic and the ungrouped Pearson chi-square statistic is also not a satisfactory form of measurement in itself. Currently, goodness-of-fit in the ordinal setting is often assessed using the Pearson chi-square statistic and deviance tests. These tests involve creating a contingency table in which rows consist of all possible cross-classifications of the model covariates, and columns consist of the levels of the ordinal response. I examined goodness-of-fit tests for a proportional odds logistic regression model-the most commonly used regression model for an ordinal response variable. Using a simulation study, I investigated the distribution and power properties of this test and compared these with those of three other goodness-of-fit tests. The new test had lower power than the existing tests; however, it was able to detect a greater number of the different types of lack of fit considered in this study. I illustrated the ability of the tests to detect lack of fit using a study of aftercare decisions for psychiatrically hospitalized adolescents.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.385-392
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• 2000

Many tests for multivariate normality are based on the spherical coordinates of the scaled residuals of multivariate observations. Moore and Stubblebine's (1981) Pearson chi-square test is based on the radii of the scaled residuals, or equivalently the sample Mahalanobis distances of the observations from the sample mean vector. The chi-square statistic does not have a limiting chi-square distribution since the unknown parameters are estimated from ungrouped data. We will derive a simple closed form of the Rao-Robson chi-square test statistic and provide a self-contained proof that it has a limiting chi-square distribution. We then provide an illustrative example of application to a real data with a simulation study to show the accuracy in finite sample of the limiting distribution.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.330-335
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• 1995

The rebustness of one sample Chi-square test for multivariate normal mean vector is investigated when the multivariate normal population is mixed with another multivariate normal population with differing in the mean vector. Explicit expressions for the level of significance and power of the test are derived. Some numerical results indicate that the Chi-square test procedure is quite robust against slight mixtures of multivariate normal populations differing in location parameters.

• Journal of muscle and joint health
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• v.12 no.2
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• pp.119-131
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• 2005

Purpose: The purpose of this study was to examine effect of Tai-Chi exercise program on pain, flexibility, perceived health status and instrumental activities of daily living for osteoarthritis patients. To evaluate the effects, quasi-experimental study was used for pre and post test with a nonequivalent control group. Method: Fifty-two subjects participated in the experiment(twenty-seven for experimental group and twenty-five for control group) and they were from two different senior citizen centers in J city. The experiment period was from April 2002 through August 2002. The experiment group took part in Tai-Chi exercise program for eighteen weeks(three times a week for four weeks and five times a week for fourteen week). The exercise was performed for 50 minutes at every time (15 minutes for warm-up, 30 minutes for Tai-Chi exercise, and 5 minutes for ending). In order to pursue study purpose, the SPSS/WIN 8.0 program was chosen for the statistical analysis; ANCOVA was employed in examining test hypothesis; t-test and $X^{2}-test$ were used to examine homogeneity between experimental and control group. Result: The study results were as follows: Score of pain decreased significantly after of Tai-Chi exercise program. Score of flexibility increased significantly after of Tai-Chi exercise program. Score of perceived health status increased significantly after of Tai-Chi exercise program. Score of IADL increased significantly after of Tai-Chi exercise program. Conclusion: As shown in the results, Tai-Chi exercise program can be effective nursing intervention for osteoarthritis patient to improve pain, flexibility, perceived health status and Instrumental Activities of Daily Living.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.8
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• pp.269-280
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• 2020

The study investigates Environmental Accounting Information (EAI) as well as factors affecting the environmental accounting implementation by the construction firms listed on the Ho Chi Minh Stock Exchange (HOSE), Vietnam. After eliminating seven enterprises that lacked data, the authors selected a sample of 112 observations from 28 construction businesses listed on the Ho Chi Minh Stock Exchange in the period 2015-2018. This study uses research data extracted from the companies' annual reports. Then, the data are analyzed by Stata 13 software, including descriptive statistics, correlation coefficient analysis, regression analysis of table data using estimation methods (Pooled OLS, REM, FEM), and testing of model defects (heteroskedasticity test, multicollinearity test, autocorrelation test). The results show that construction companies listed on the Ho Chi Minh Stock Exchange have out factors affecting the environmental accounting implementation by these enterprises, including independent audit firm and listed time. While the independent auditor firm has a positive and significant impact, the listed time has a negative influence. In addition, our study has confirmed the role of institutional factors affecting the disclosure level of EAI on the implementation of environmental accounting by construction enterprises listed on the Ho Chi Minh Stock Exchange.

• Journal of muscle and joint health
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• v.13 no.1
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• pp.20-30
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• 2006

Purpose: To determine the effect of Tai Chi exercise program on fatigue, stress, and quality of life in middle aged women. Method: The study was designed as a nonequivalent control group pretest-posttest quasi-experimental study. Thirty subjects were assigned for experimental group and thirty four subjects were assigned for control group. The subjects in the experimental group were participated in Tai Chi exercise program for 60 minutes per session 3 times a week for 8weeks. Tai Chi exercise program consists of 10 minutes warm-up, 45 minutes main, and 5 minutes cooling down exercises. In order to evaluate the effect of Tai Chi exercise program, fatigue, stress, and qualify of life were assessed by measuring the condition of the participants in respect of fatigue, stress, and qualify of life with questionnaire. The data were analyzed by using $x^2-test$, Fisher's exact test, t-test by a SAS-pc+ 8.12 program. Result: After 8 weeks Tai Chi exercise program, there were significant improvement in fatigue, stress, and quality of life in middle aged women. Conclusion: Tai Chi exercise program can be an effective nursing intervention to improve fatigue, stress, and quality of life in middle aged women.

• Journal of Integrative Natural Science
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• v.5 no.4
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• pp.241-245
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• 2012

Categorical data collected based on complex sample design is not proper for the standard Pearson multinomial-based chi-squared test because the observations are not independent and identically distributed. This study investigates effects of bias of point estimator of population proportion and its variance estimator to the standard Pearson chi-squared test statistics when the sample is collected based on complex sampling scheme. This study examines the effect under two population homogeneity test. The standard Pearson test statistic can be partitioned into two parts; the first part is the weighted sum of ${\chi}^2_1$ with eigenvalues of design matrix as their weights, and the additional second part which is added due to the biases of the point estimator and its variance estimator. Our empirical analysis shows that even though the bias of point estimator is small, Pearson test statistic is very much inflated due to underestimate the variance of point estimator. In the connection of design-based variance estimator and its design matrix, the bigger the average of eigenvalues of design matrix is, the larger relative size of which the first component part to Pearson test statistic is taking.

• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.429-440
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• 2006

In statistical computing, it is often for researchers to need the distribution of a weighted sum of noncentral chi-square variables. In this case, it is very limited to know its exact distribution. There are many works to contribute to this topic, e.g. Imhof (1961) and Solomon-Stephens (1977). Imhof's method gives good approximation to the true distribution, but it is not easy to apply even though we consider the development of computer technology Solomon-Stephens's three moment chi-square approximation is relatively easy and accurate to apply. However, they skipped many details, and their simulation is limited to a weighed sum of central chi-square random variables. This paper gives details on Solomon-Stephens's method. We also extend their simulation to the weighted sum of non-central chi-square distribution. We evaluated approximated powers for homogeneous test and compared them with the true powers. Solomon-Stephens's method shows very good approximation for the case.