• 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.

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

• The Korean Journal of Food & Health Convergence
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• v.5 no.1
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• pp.1-11
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• 2019

Smoking has become one of the public health harzard affecting the world. In the UK, smoking is responsible for around one in five deaths. The illnesses caused by smoking extend beyond the well-reported links with cancer, heart disease and respiratory illnesses. Hence the research to determine the awareness of the predisposing factor to smoking among adults in sokoto metropolis. A cross-sectional form of descriptive survey research design was used for this study. This is because descriptive studies are used when the characteristics of a population are either unknown or partially known (Hennekens & Buring, 2007), and it was used by Ganley and Rosario (2013) in a related research this justified the use of similar design in a study of similar nature.Two hundred and seventy returned questionnaire was collected, analyzed using descriptive statistic of frequency count, normative percentage and grand mean; as well as inferential statistics of chi-square (${\chi}^2$). The level of significant was fixed at 0.05. Appropriate degrees of freedom were worked out. There was statistical significant influence or relationship with marital status on the predisposing factors of smoking chi-square of 19716.516 greater than the critical value 43.77297at df 30 p<0.05. There were statistical significance chi-square =27468.348 which is greater than the critical value 43.77297 at df= 30. These show that there is a relationship on gender awareness of predisposing factors to smoking rejecting the null hypotheses. The respondents across different lever/year higher institution shows that the awareness of predisposing factors of smoking there were a statistical significance difference chi-square =7168.429 (df=88) greater than critical value 102.342 rejecting the null hypotheses. There is consistent evidence that links exposure to depictions of smoking in movies and initiation of smoking in young people. Over the years television shows and films have effectively built up associations between smoking and glamour, sex and risk-taking. Social learning theory describes how we learn by example from others. We are strongly influenced by our parents, and other people we look up to, such as peers, actors and pop stars. This can lead us to emulate their behaviour and try smoking.

• Communications for Statistical Applications and Methods
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• v.5 no.1
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• pp.35-42
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• 1998

Once a contingency table is constructed, the first interest will be the hypotheses of either homogeneity or independence depending on the sampling scheme. The most widely used test statistic in practice is the classical Pearson's $\chi^2$ statistic. When the null hypothesis is rejected, another natural interest becomes which cell contributed to the rejection of the null hypothesis more than others. For this purpose, so called cell $\chi^2$ components are investigated. In this paper, the influence function of a cell to the $\chi^2$ statistic is derived, which can be used for the same purpose. This function measures the effect of each cell to the $\chi$$^2$ statistic. A numerical example is given to demonstrate the role of the new function.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.974-977
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• 2003

The GPS/INS integration system navigation can provide improved navigation performance and has been widely used as a main navigation system for military and commercial vehicles. When two navigation systems are tightly coupled and the structure is complicated, a fault in either the GPS or the INS can lead to a disastrous failure of the whole integration system. This paper proposes a real-time fault detection method for an AGPS/INS integration system. The proposed fault detection method comprises a BIT and a fault detection algorithm based on chi-square test. It is implemented by real-time software modules to apply the AGPS/INS integration system and van test is carried out to evaluate its performance.

• Journal of the Korean Institute of Telematics and Electronics
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• v.21 no.3
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• pp.1-5
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• 1984

It is investigated that Mahalanobis distances are invariant under a proper transformation and interest MDs are distributed as non-central chi-square while it is well known that intraset MDs are distributed as central chi-square. And their moments have been expressed as simple polynomials whose coefficients satisfy straightforward recursive relations.

• The Korean Journal of Applied Statistics
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• v.10 no.2
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• pp.339-352
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• 1997

Chi-square test based on large sample theory is inappropriate for testing the row homogeneity in two-way contingency table with several sparse cells. For that case, exact testing methods has been developed in the literature and implemented in StatXact(1991). However, considerable computing time is inevitable for moderate size tables. So, Monte Carlo approximation is recommended frequently. In this study, we propose a simple algorithm for generating two-way random tables with fixed row and column margins for small sample chi-square test. Also, we develop “Turkey-type” method for multiple between-row comparisons.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.349-365
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• 1994

We develop in this paper the likelihood ratio test (LRT) for testing $H_1 : F_1 \preceq F_2$ against $H_2 - H_1$ where $H_2$ imposes no restriction on $F_1$ and $F_2$ and '$\preceq$' means failure rate ordering. Both one and two-sample problems will be considered. In the one-sample case, one of the two distributions is known, while we assume in the other case both are unknown. We derive the asymptotic null distribution of the LRT statistic which will be of chi-bar-square type. The main issue here is to determine the least favorable distribution which is stochastically largest within the class of null distributions.

• Journal of Food Hygiene and Safety
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• v.6 no.2
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• pp.79-81
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• 1991

On May 23, 1990, an acute self-limited gastrointestinal illness was reported by twenty-seven persons. They were some of the employees and family members who attended a company open house picnic in Bergen County, New Jersey. Food questionnaires implicated that ziti was the vehicle of transmission (chi square 9.05). Median incubation period was 9.0 hours, and the median duration of illness 24 hours Clostridium perfringens organisms and enterotoxin were isolated from stool samples.

• 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.