• The Korean Journal of Applied Statistics
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• v.26 no.3
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• pp.495-509
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• 2013

We study multivariate extension of Kendall's tau and its statistical interpretation. There exist various versions of multivariate Kendall's tau, for example Scarsini (1984), Joe (1990) and Genest et al. (2011); however, few of them mention its lower bounds. For the bivariate case, the Fr$\acute{e}$chet-Hoeffding lower bound can achieve the lower bound of Kendall's tau. However in the multivariate case, the Fr$\acute{e}$chet-Hoeffding lower bound itself does not exist as a distribution, which makes the interpretation of Kendall's tau unclear when it has negative value. In this paper, we explain sufficient conditions to achieve the lower bound of Kendall's tau and provide real data examples that provide further insights into the interpretation for the lower bounds of Kendall's tau.

• Journal of the Korean Statistical Society
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• v.7 no.1
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• pp.17-26
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• 1978

For testing $\beta_i=\beta, i=1,...,k$, in the regression model $Y_{ij} = \alpha_i + \beta_ix_{ij} + e_{ij}, j=1,...,n_i$, a simple and robust test based on Kendall's tau is proposed. Its asymptotic distribution is proved to be chi-square under the null hypthesis and noncentral chi-square under an appropriate sequence of alternatives. For the optimal designs, the asymptotic relative efficiency of the proposed procedure with respect to the least squares procedure is the same as that of the Wilcoxon test with respect to the t-test.

• Journal of the Korean Data and Information Science Society
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• v.16 no.2
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• pp.477-505
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• 2005

This paper gives a computer code that gives p-value's for Kendall's Tau table. The code centers around finding the cumulative frequency of a given Sigma value. Current tables usually give critical values for given cut-off percentages. For small sample sizes the critical values may be inexact, and for large samples the values are not be published. SPSS has a built in function for finding the Kendall rank correlation, but the output does not include the Sigma value. Before the code is given, this paper will concentrate around how to find the Sigma value, and the related tau statistic. The computer code is written in MATLAB, but the ideas can be easily transferred to different languages.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.599-604
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• 2015

Kendall's tau statistic has been applied to test an association of bivariate random variables. However, incomplete bivariate data with a truncation and a censoring results in incomparable or unorderable pairs. With such a partial information, Tsai (1990) suggested a conditional tau statistic and a test procedure for a quasi independence that was extended to more diverse cases such as double truncation and a semi-competing risk data. In this paper, we also employed a conditional tau statistic to estimate an association of bivariate interval censored data. The suggested method shows a better result in simulation studies than Betensky and Finkelstein's multiple imputation method except a case in cases with strong associations. The association of incubation time and infection time from an AIDS cohort study is estimated as a real data example.

• Communications for Statistical Applications and Methods
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• v.30 no.5
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• pp.467-483
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• 2023

In this research, a conversion function and a distortion associated with the conversion function are defined and used to derive a unit power Gompertz distortion. A new family of copulas is built using the global distorted function. Four base copulas, namely Clayton, Gumbel, Frank, and Gaussian, are distorted into the family. Some properties including tail dependence coefficients and tail order are examined. Kendall's tau formula is derived for new copulas when the base copula is Clayton, Gumbel, or Frank. The maximum pseudo-likelihood estimation method is employed, and a simulation study was performed. The log-likelihood and AIC are reported to compare the performance of the fitted copulas. According to the applied data, the results indicate that new distorted copulas with additional parameters improve the fit.

• Journal of Acupuncture Research
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• v.31 no.2
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• pp.99-109
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• 2014

Objectives : The purpose of this study was to analysis the relationship between hours of smartphone use and neck pain in university students. Methods : A survey of 2,353 university students was conducted in Gyeonggi province and Incheon city using a self report questionnaire from April 1 to 11 2013. The questionnaire of questions regarding the hours of using smartphone, mainly used function in participant's smartphone and neck discomfort degree. Neck disability index(NDI) was used to evaluate degree of pain. The collected data were analyzed with the t-test and Kendall's tau test using the SPSS 21.0 program and R 3.1.0, respectively. Results : 1. Almost all of the survey participants(99.07 %) were smartphone users. 66.97 % of them answered that they use their smartphone daily more than 2 hours and 48.18 % of them answered that they use their smartphone 10 to 30 minutes everytime they use it. 2. The overall distribution of NDI scores was 'no disability(0~4 score, 62.92 %)', 'mild disability(5~14 score, 32.85 %)', 'moderate disability(15~24 score, 1.19 %)'. As a result of t-test, we found that the average NDI score for female students was significantly higher than the average NDI score for male students(p<0.05). 3. The Kendall's tau test revealed that total time spent daily using smartphones has a strong positive correlation with 'pain intensity', 'lifting', 'reading' 'headache', 'concentration', and 'driving'(p<0.05) in NDI. Also, time duration of one time smartphone usage has a strong positive correlation with 'pain intensity', 'lifting', 'reading', 'headache', 'concentration', 'work', and 'recreation'(p<0.05). 4. The Kendall's tau test revealed that total NDI scores have a significantly strong positive correlation with both of total time spent daily using smartphones(p<0.05) and time duration for one time smartphone usage(p<0.05). This results imply that long-time use of smartphone has a strong relationship with neck pain. Conclusions : The results of the study would be a good starting point for future studies to reduce the risks of chronic neck pain caused by smartphone usage.

• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.151-159
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• 2021

In this article, our interest is to estimate the association between consecutive gap times which are subject to interval censoring. Such data are referred as doubly interval censored data (Sun, 2006). In a context of serial event, an induced dependent censoring frequently occurs, resulting in biased estimates. In this study, our goal is to propose a Kendall's 𝜏 based association measure for doubly interval censored data. For adjusting the impact of induced dependent censoring, the inverse probability censoring weighting (IPCW) technique is implemented. Furthermore, a multiple imputation technique is applied to recover unknown failure times owing to interval censoring. Simulation studies demonstrate that the suggested association estimator performs well with moderate sample sizes. The proposed method is applied to a dataset of children's dental records.

• The Korean Journal of Applied Statistics
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• v.32 no.5
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• pp.753-761
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• 2019

A test procedure based on a Kendall's τ statistic is proposed for the association of bivariate interval censored data. In particular, a leverage bootstrap technique is applied to replace unknown failure times and a classical adjustment method is applied for treating tied observations. The suggested method shows desirable results in simulation studies. An AIDS dataset is analyzed with the suggested method.

• The Korean Journal of Rehabilitation Nursing
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• v.6 no.1
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• pp.14-25
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• 2003

Purpose: To investigate nutritional status of inpatients by using subjective, and objective evaluation methods and to find the relationship between them. Method: The subjects were 101 inpatients with medical health problems at a university hospital. Nutritional status was evaluated by the Subjective Global Assessment(SGA) and physical assessment including percentage of weight loss, serum albumin, hemogloin, and hematocrit. Data were analyzed using frequency, percentage, mean, Kendall's tau. Results: Grouping by the SGA, 61.4% were classified as severe malnutrition group. When applying the objective methods(physical assessment), 1.9~42.6% were diagnosed as malnutrition each item. The percentage of weight loss during previous 1~6month(${\tau}=.43{\sim}.54$, P=.0001), serum albumin(${\tau}=-.26$, P=.0003), hemoglobin of male(${\tau}=-.38$, P=.0001), and hematocrit of male(${\tau}=-.34$, P=.0001) were significantly correlated with SGA score. The coincidence rate of nutrition evaluation between the objective methods and SGA were 27.7~35.6%, 20.8%, 47.5%, 58.4% in percentage of weight loss, albumin, hemoglobin, and hematocrit. Conclusion: These findings showed a majority of inpatients were exposed to the risk of malnutrition. We recommend to evaluate inpatients' nutritional status periodically and to develop nursing intervention to solve their nutritional problems.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1105-1116
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• 1996

A partial ordering is developed among weakly positive quadrant dependent (WPQD) bivariate random vectors. This permits us to measure the degree of WPQD-ness and to compare pairs of WPQD random vectors. Some properties and closures under certain statistical operations are derived. An application is made to measures of dependence such as Kendall's $\tau$ and Spearman's $\rho$.