• The Korean Journal of Applied Statistics
• /
• v.16 no.2
• /
• pp.455-467
• /
• 2003

There has been a long debate on the applicability of the chi-square approximation to statistics based on small sample size. Extending comparison results among Pearson chi-square Χ$^2$, generalized likelihood .ratio G$^2$, and the power divergence Ι(2/3) statistics suggested by Rudas(1986), recently developed disparity statistics (BWHD(1/9), BWCS(1/3), NED(4/3)) we compared and analyzed in this paper. By Monte Carlo studies about the independence model of two dimension contingency tables, the conditional model and one variable independence model of three dimensional tables, simulated 90 and 95 percentage points and approximate 95% confidence intervals for the true percentage points are obtained. It is found that the Χ$^2$, Ι(2/3), BWHD(1/9) test statistics have very similar behavior and there seem to be applcable for small sample sizes than others.

• Journal of the Korean Data and Information Science Society
• /
• v.24 no.6
• /
• pp.1465-1475
• /
• 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
• /
• v.14 no.3
• /
• pp.123-129
• /
• 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
• /
• v.10 no.1
• /
• pp.135-144
• /
• 2003

This work is concerned with comparison of the recently developed disparity measures for the partial association model in three dimensional categorical data. Data are generated by using simulation on each term in the log-linear model equation based on the partial association model, which is a proposed method in this paper. This alternative Monte Carlo methods are explored to study the behavior of disparity measures such as the power divergence statistic I(λ), the Pearson chi-square statistic X$^2$, the likelihood ratio statistic G$^2$, the blended weight chi-square statistic BWCS(λ), the blended weight Hellinger distance statistic BWHD(λ), and the negative exponential disparity statistic NED(λ) for moderate sample sizes. We find that the power divergence statistic I(2/3) and the blended weight Hellinger distance family BWHD(1/9) are the best tests with respect to size and power.

• 한국데이터정보과학회:학술대회논문집
• /
• 2004.10a
• /
• pp.95-95
• /
• 2004

• The Korean Journal of Applied Statistics
• /
• v.7 no.2
• /
• pp.269-277
• /
• 1994

Bootstrap approximation is compared with ordinary asymptotic method in the context of minimum chi-square estimation through application in a real problem. Fixed interval search method is shown to be superior over a random interval search method or Newton-Raphson method. All the procedures are implemented by S-Plus functions.

• Communications for Statistical Applications and Methods
• /
• v.12 no.2
• /
• pp.463-472
• /
• 2005

In this paper, the problem of estimating a p-variate (p $\ge$4) normal mean vector is considered in decision-theoretic set up. Using a simple property of the noncentral chi-square distribution, a sequence of estimators dominating the Lindley type estimator with the cases of unknown covariance matrices has been produced and each improved estimator is better than previous one.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2005.04a
• /
• pp.403-414
• /
• 2005

Most of the currently used spam-filters are based on a Bayesian classification technique, where some serious problems occur such as a limited precision/recall rate and the false positive error. This paper addresses a solution to the problems using a modified Bayesian classifier based on chi-square statistics. The resulting spam-filter is more accurate and flexible than traditional Bayesian spam-filters and can be a personalized one providing some parameters when the filter is teamed from training data.

• Proceedings of the IEEK Conference
• /
• 2000.06a
• /
• pp.197-200
• /
• 2000

This paper presents a mathematical model of the output of Rake receiver of W-CDMA signals for various outdoor channel environment and different bandwidths. This mathematical model is represented as Rayleigh and noncentral chi distribution with 3 degrees of freedom. Those are obtained from the statistics of numerically generated signals. We employ Chi-square test to show how the mathematical model fits signal statistics, and confirmed that this model is appropriate for representing W-CDMA signals.

• Journal of the Korean Statistical Society
• /
• v.30 no.1
• /
• pp.63-76
• /
• 2001

An adaptive estimation and testing method is proposed for comparing dispersions among several ordered groups. Based upon the large sampling theory for nonparametric quartile estimators, we derive the order restricted estimators and construct a simple test statistic. This test statistic has a mixture of several chi-square distributions as its asymptotic null distribution. The proposed test is illustratively applied to survival time data for the patients with carcinoma of the oropharynx.