• Title/Summary/Keyword: Z-test Statistics

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Testing Goodness-of-Fit for No Effect Models

  • Sungho Lee;Jongtae Kim;GyoungAe Moon
    • Communications for Statistical Applications and Methods
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    • v.5 no.3
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    • pp.935-944
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    • 1998
  • This paper investigates the problem of goodness of fit tests for no effect model. The proposed test statistic $Z_{mn}$ is obtained by multiplying constant on the model free curve estimation techniques. The small and large sample properties of$Z_{mn}$ are investigated and the good results of power studies for the proposed test are illustrated.

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A Study on Mante1-Haenszel Test of Conditional Independence ($2\times2$ 분할표를 이용한 조건부 독립성 검정)

  • 김지현;임현선
    • The Korean Journal of Applied Statistics
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    • v.11 no.2
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    • pp.257-268
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    • 1998
  • Many epidemiological studies investigate whether an association exists between a binary risk factor X and a binary response variable Y. They analyse whether an observed association between X and Y persists when the level of another factor Z that might influence the association is controlled. This involves testing conditional independence of X and Y controlling for Z. The Mantel-Haenszel test is most widely used to test conditional independence for sparse tables. But if the association between X and Y varies along the levels of Z, Mantel-Haenszel test has a low power problem. In this study, we propose an alternative test procedure which overcomes the low power problem in that case. We find out the null distribution of the alternative test statistic and compare its performance with the Mantel-Haenszel test by simulation.

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Goodenss of Fit Test on Density Estimation

  • Kim, J.T.;Yoon, Y.H.;Moon, G.A.
    • Communications for Statistical Applications and Methods
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    • v.4 no.3
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    • pp.891-901
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    • 1997
  • The objective of this research is to investigate the problem of goodness of fit testing based on nonparametric density estimation with a data-driven smoothing parameter. The small and large smaple properties of the proposed test statistic $Z_{mn}$ are investigated with the minimizer $\widehat{m}$ of the estimated mean integrated squared error by the Diggle and Hall (1986) method.

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Comparison Density Representation of Traditional Test Statistics for the Equality of Two Population Proportions

  • Jangsun Baek
    • Communications for Statistical Applications and Methods
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    • v.2 no.1
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    • pp.112-121
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    • 1995
  • Let $p_1$ and $p_2$ be the proportions of two populations. To test the hypothesis $H_0 : p_1 = p_2$, we usually use the $x^2$ statistic, the large sample binomial statistic Z, and the Generalized Likelihood Ratio statistic-2log $\lambda$developed based on different mathematical rationale, respectively. Since testing the above hypothesis is equivalent to testing whether two populations follow the common Bernoulli distribution, one may also test the hypothesis by comparing 1 with the ratio of each density estimate and the hypothesized common density estimate, called comparison density, which was devised by Parzen(1988). We show that the above traditional test statistics ate actually estimating the measure of distance between the true densities and the common density under $H_0$ by representing them with the comparison density.

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Permutation test for a post selection inference of the FLSA (순열검정을 이용한 FLSA의 사후추론)

  • Choi, Jieun;Son, Won
    • The Korean Journal of Applied Statistics
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    • v.34 no.6
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    • pp.863-874
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    • 2021
  • In this paper, we propose a post-selection inference procedure for the fused lasso signal approximator (FLSA). The FLSA finds underlying sparse piecewise constant mean structure by applying total variation (TV) semi-norm as a penalty term. However, it is widely known that this convex relaxation can cause asymptotic inconsistency in change points detection. As a result, there can remain false change points even though we try to find the best subset of change points via a tuning procedure. To remove these false change points, we propose a post-selection inference for the FLSA. The proposed procedure applies a permutation test based on CUSUM statistic. Our post-selection inference procedure is an extension of the permutation test of Antoch and Hušková (2001) which deals with single change point problems, to multiple change points detection problems in combination with the FLSA. Numerical study results show that the proposed procedure is better than naïve z-tests and tests based on the limiting distribution of CUSUM statistics.

A Study on Teaching Method of Two-Sample Test for Population Mean Difference (두 모집단 모평균 비교의 지도에 관한 연구)

  • Kim Yong-Tae;Lee Jang-Taek
    • The Mathematical Education
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    • v.45 no.2 s.113
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    • pp.145-154
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    • 2006
  • The main purpose of this study is to investigate the effect of departures from normality and equal variance on the two-sample test when the variances are unknown. We have found that type I error brought about a little bit change which is ignorable in relation to kurtosis. But the change of type I error was mainly based on the skewness of the parent population. In introductory statistics classes where data analysis includes techniques for detecting skewness of two populations, we recommend the two-sample t-test when maximal skewness of two populations is smalter than the value 4 when the variances seem equal. Furthermore, our simulations reveal that the two-sample t-test appears somewhat more robust than that of z-test if the assumption of equal variance is satisfied. In the case of unequal variance, the two-sample t-test appears somewhat more robust provided the t-statistic using Satterthwaite's approximate degrees of freedom.

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Effects of Balance Taping Therapy on Improving Knee Pain and the Obstacle in Daily Activity in Rural Elderly Women (밸런스 테이핑요법이 농촌 여성노인의 무릎통증과 일상활동장애 개선에 미치는 영향)

  • Kim, Ae-Jung;Park, Hae-Sook
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.20 no.7
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    • pp.218-227
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    • 2019
  • This study examined the effects of balance taping therapy on improving knee pain and the obstacles to daily activity in rural elderly women. The research design was a quasi-experimental research using a non-equivalent control group pre-test and post-test design. The data were collected from January 19th to April 14th, 2017. The research subjects included female elderly over 65 years old who visited 12 senior centers located at Y city in rural areas. The participants were composed of 26 people in the experimental group and 28 people in the control group. Data were collected before and 24 hours after balance taping therapy, and the pain and obstacles to daily activity were measured. The collected data were analyzed using the PASW Statistics 23 Program, which included a $X^2-test$, Shapiro-Wilk test, and Mann-Whitney U test. After the intervention, significant differences were observed in the knee pain (Z=-6.658, p<.001) and obstacles to daily activity (Z=-3.466, p=.001). With regard to lower domain variables of the obstacles to daily activity, significant differences in standing up (Z=-2.860, p=.004), daily activity (Z=-2.629, p=.009), walking (Z=-3.868, p<.001), and dressing up (Z=-2.049, p=.040) were observed between the two groups. On the other hand, there were no significant differences in grip (Z=-.542, p=.588) and arm stretching (Z=-.416, p=.678). In conclusion, applying balance taping to rural elderly women clearly decreases the level of knee pain, reduces the obstacles to daily activity, and improves their quality of life.

The Effects of a Smoking Cessation Program on Nicotine Dependency and Self-Efficacy for Adolescents (금연프로그램이 청소년 흡연자의 니코틴 의존도와 자기효능감에 미치는 영향)

  • Paek, Kyung-Shin
    • Research in Community and Public Health Nursing
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    • v.16 no.3
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    • pp.282-288
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    • 2005
  • Purpose: This study was to verify the effects of a smoking cessation program for adolescents. Method: This study was designed to use one group with one pre-test and two post-tests. One post-test was done immediately after the completion of the program and the other after eight weeks. The subjects were 21 male high school students who were smokers when this study was carried out. The smoking cessation program consisted of 5 sessions with smoking cessation education and e-mail service after the program. Variables in this research were nicotine dependency (using Fagerstrom Tolerance Questionnaire) and self-efficacy. Data were analyzed by descriptive statistics and Wilcoxon signed rank test. Results: Immediately after the program and eight weeks later, nicotine dependency for continuous smokers decreased significantly (after the program: Z=-2.319, p=.020, eight weeks later: Z=-1.999. p=.046) and self-efficacy increased significantly (after program: Z=-3.024. p=.002. eight weeks later: Z=-2.381. p=.017). Conclusions: The smoking cessation program was effective in decreasing nicotine dependency in the continuous adolescent smokers and in increasing their self-efficacy, Further study needs to be made with a lager number of smoking adolescents using control group design.

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Development of a mobile-based self-management health alarm program for obese children in South Korea and a test of its feasibility for metabolic outcomes: A study based on the information-motivation-behavioral skills model

  • Choi, Jihea;Park, Yon Chul;Choi, Sarah
    • Child Health Nursing Research
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    • v.27 no.1
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    • pp.13-23
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    • 2021
  • Purpose: This study aimed to develop a mobile-based self-management health alarm (MSHA) program for modifying obese children's lifestyle based on the information-motivation-behavioral skills (IMB) model and to test its feasibility. Methods: A methodological study for the development of the MSHA program and pilot study with a one-group pretest-posttest design for feasibility testing was conducted. The MSHA program was designed to provide obesity-related information (I), monitor daily diet and exercise, provide motivational text messages (M), and enhance healthy diet and exercise skills (B) via a mobile-based web platform. In the feasibility test, six obese children participated in the 4-week program, and the number of days per week that they achieved their goals and differences in metabolic components were assessed. Data were analyzed using descriptive statistics and the Wilcoxon signed-rank test. Results: Participants successfully achieved their diet and exercise goals≥5 days per week. Body mass index (z=-1.99, p=.046), waist circumference (z=-2.20, p=.028), and triglyceride levels (z=-2.21, p=.027) significantly decreased. Conclusion: The MSHA program showed positive effects on health behaviors and metabolic syndrome risk. The program may be effective in improving metabolic syndrome in obese children by promoting self-health management behaviors.

Closeness of Lindley distribution to Weibull and gamma distributions

  • Raqab, Mohammad Z.;Al-Jarallah, Reem A.;Al-Mutairi, Dhaifallah K.
    • Communications for Statistical Applications and Methods
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    • v.24 no.2
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    • pp.129-142
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    • 2017
  • In this paper we consider the problem of the model selection/discrimination among three different positively skewed lifetime distributions. Lindley, Weibull, and gamma distributions have been used to effectively analyze positively skewed lifetime data. This paper assesses how much closer the Lindley distribution gets to Weibull and gamma distributions. We consider three techniques that involve the likelihood ratio test, asymptotic likelihood ratio test, and minimum Kolmogorov distance as optimality criteria to diagnose the appropriate fitting model among the three distributions for a given data set. Monte Carlo simulation study is performed for computing the probability of correct selection based on the considered optimality criteria among these families of distributions for various choices of sample sizes and shape parameters. It is observed that overall, the Lindley distribution is closer to Weibull distribution in the sense of likelihood ratio and Kolmogorov criteria. A real data set is presented and analyzed for illustrative purposes.