• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.543-557
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• 2006

This paper is concerned with the applicability of the chi-square approximation to the six disparity statistics: the Pearson chi-square, the generalized likelihood ratio, the power divergence, the blended weight chi-square, the blended weight Hellinger distance, and the negative exponential disparity statistic. Three dimensional contingency tables of small and moderate sample sizes are generated to be fitted to all possible hierarchical log-linear models: the completely independent model, the conditionally independent model, the partial association models, and the model with one variable independent of the other two. For models with direct solutions of expected cell counts, point estimates and confidence intervals of the 90 and 95 percentage points of six statistics are explored. For model without direct solutions, the empirical significant levels and the empirical powers of six statistics to test the significance of the three factor interaction are computed and compared.

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

• Proceedings of the Safety Management and Science Conference
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• 2012.04a
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• pp.293-300
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• 2012

Reliability measures of questionnaire and ${\chi}^2$ contingency tests of categorized responses are most practical tools to analyze the characteristics of subjects of survey study. This research evaluates the Cronbaha's reliability measures by using Repeated Measure Design (RMD) with illustrated MINITAB examples. In addition, ${\chi}^2$ statistics of each cell of categorized tables can be effectively interpreted with the symmetric plot of correspondence analysis. The practical example is also discussed to provide comprehensive understanding of topic.

• The Korean Journal of Applied Statistics
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• v.23 no.4
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• pp.777-781
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• 2010

Yates' continuity correction of the chi-squared test for testing the homogeneity of two binomial proportions in $2{\times}2$ contingency tables is developed to lower the value of the test statistic slightly. The effect of continuity correction is expected to decrease as the sample size increases. However, in extremely unbalanced $2{\times}2$ contingency tables, we find some cases where the effect of continuity correction is eccentric and is larger than expected. In such cases, we conclude that the chi-squared test with continuity correction should not be employed as a test statistic in both asymptotic tests and exact tests.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.15 no.2
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• pp.423-430
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• 2004

We provide the exact form of a Rao-Robson version of the chi-squared test of multivariate normality suggested by Park(2001). This test is easy to apply in practice since it is easily computed and has a limiting chi-squared distribution under multivariate normality. A self-contained formal argument is provided that it has the limiting chi-squared distribution. A simulation study is provided to study the accuracy, in finite samples, of the limiting distribution. Finally, a simulation study in a nonnormal distribution is conducted in order to compare the power of our test with those of other popular normality tests.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.411-416
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• 1998

A simple nonparametric test of complete or total independence is suggested for continuous multivariate distributions. This procedure first discretizes the original variables based on their order statistics, and then tests the hypothesis of complete independence for the resulting contingency table. Under the hypothesis of independence, the chi-squared test statistic has an asymptotic chi-squared distribution. We present a simulation study to illustrate the accuracy in finite samples of the limiting distribution of the test statistic. We compare our method to another nonparametric test of complete independence via a simulation study. Finally, we apply our method to the residuals from a real data set.

• The KIPS Transactions:PartB
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• v.12B no.2 s.98
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• pp.209-214
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• 2005

The use of protein interaction data is highly reliable for predicting functions to proteins without function in proteomics study. The computational studies on protein function prediction are mostly based on the concept of guilt-by-association and utilize large-scale interaction map from revealed protein-protein interaction data. This study compares graph-based approaches such as neighbor-counting and $\chi^2-statistics$ methods using protein-protein interaction data and proposes an approach that is effective in analyzing large-scale protein interaction data. The proposed approach is also based protein interaction map but sequence similarity and heuristic knowledge to make prediction results more reliable. The test result of the proposed approach is given for KDD Cup 2001 competition data along with those of neighbor-counting and $\chi^2-statistics$ methods.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.135-144
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• 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.

• The Korean Journal of Applied Statistics
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• v.8 no.2
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• pp.109-119
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• 1995

A two sample chi-square test is introduced for testing the equality of the distributions of two populations when observations are subject to random censorship. The statistic is appropriate in testing problems where a two-sided alternative is of interest. Under the null hypothesis, the asymptotic distribution of the statistic is a chi-square distribution. We obtain two types of chi-square statistics ; one as a nonnegative definite quadratic form in difference of observed cell probabilities based on the product-limit estimators, the other one as a summation form. Data pertaining to a cancer chemotheray experiment are examined with these statistics.