• Journal of applied mathematics & informatics
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• v.1 no.1
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• pp.43-48
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• 1994

There are some difficulties in applying the Pearson's Chi-Square Test for the continuous distribution. The problems include how to form class intervals for the test of fit how to employ in the test when the estimators of parameters are obtained from the ungrouped sample so on. In order to solve these problems we use the generalized minimum Chi-Square technique which is a test free of the complications associated with the Peason's Chi-Square test. This paper show how to apply the goodness of fit tests based on generalized minimum Chi-Square technique to the extreme values.

• Journal of the Korean Data and Information Science Society
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• v.20 no.3
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• pp.587-592
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• 2009

The most frequent use of the chi-square distribution is in the area of goodness-of-t of a distribution. The likelihood ratio test is a commonly used test statistic as the maximum likelihood estimate in statistical inferences. The recently revised versions of the likelihood ratio test statistics are used in estimating the parameter in the chi-square distribution. The estimates are compared with the commonly used method of moments and the maximum likelihood estimate.

• 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.

• 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.

• 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.

• 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.

• 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 the Institute of Electronics Engineers of Korea CI
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• v.42 no.4 s.304
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• pp.51-58
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• 2005

This paper proposes a robust scene change detection technique that uses the weighted chi-square test and the automated threshold-decision algorithms. The weighted chi-square test can subdivide the difference values of individual color channels by calculating the color intensities according to NTSC standard, and it can detect the scene change by joining the weighted color intensities to the predefined chi-square test which emphasize the comparative color difference values. The automated threshold-decision at algorithm uses the difference values of frame-to-frame that was obtained by the weighted chi-square test. At first, The Average of total difference values is calculated and then, another average value is calculated using the previous average value from the difference values, finally the most appropriate mid-average value is searched and considered the threshold value. Experimental results show that the proposed algorithms are effective and outperform the previous approaches.

• Journal of Information Processing Systems
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• v.4 no.1
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• pp.27-32
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• 2008

Minimum support and confidence have been used as criteria for generating association rules in all association rule mining algorithms. These criteria have their natural appeals, such as simplicity; few researchers have suspected the quality of generated rules. In this paper, we examine the rules from a more rigorous point of view by conducting statistical tests. Specifically, we use contingency tables and chi-square test to analyze the data. Experimental results show that one third of the association rules derived based on the support and confidence criteria are not significant, that is, the antecedent and consequent of the rules are not correlated. It indicates that minimum support and minimum confidence do not provide adequate discovery of meaningful associations. The chi-square test can be considered as an enhancement or an alternative solution.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.5
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• pp.2251-2258
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• 2012

This study compared the unweighted sample design, frequency weighted sample design and complex sample design to using 2009 Korea National Health and Nutrition Examination Survey in an effort to identify whether or not there is any difference in potential risk factors. Pearson chi-square test and Rao-scott chi-square test were applied to the analytic methods. As a result of analyses, all the variables were overestimated as significant risk factors in case of the unweighted sample design to which only the frequency weights were applied. In addition, there were differences in the confidence levels and results from the simple random sampling analysis and complex sample design to which no weight was applied. It is necessary to carry out the complex sample design rather than the analysis to which the frequency weights are applied, in order to ensure the findings to represent the whole population when our national statistics data is used.