• Title/Summary/Keyword: mean test statistic

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A Moment Inequality for Exponential Better (Worse) Than Used EBU (EWU) Life Distributions with Hypothensis Testing Application

  • Abu-Youssef, S.E.
    • International Journal of Reliability and Applications
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    • v.5 no.4
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    • pp.105-113
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    • 2004
  • The exponential better (worse) than used EBU (EWU) class of life distributions is considered. A moment inequality is derived for EBU (EWU) distributions which demonstrate that if the mean life is finite, then all moments exist. Based on this inequality, a new test statistic for testing exponentiality against EBU (EWU) is introduced. It is shown that the proposed test is simple, enjoys good power and has high relative efficiency for some commonly used alternatives. Critical values are tabulated for sample sizes n = 5(1)40. A set of real data is used as a practical application of the proposed test in the medical science.

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Effective Sample Sizes for the Test of Mean Differences Based on Homogeneity Test

  • Heo, Sunyeong
    • Journal of Integrative Natural Science
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    • v.12 no.3
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    • pp.91-99
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    • 2019
  • Many researchers in various study fields use the two sample t-test to confirm their treatment effects. The two sample t-test is generally used for small samples, and assumes that two independent random samples are selected from normal populations, and the population variances are unknown. Researchers often conduct F-test, the test of equality of variances, before testing the treatment effects, and the test statistic or confidence interval for the two sample t-test has two formats according to whether the variances are equal or not. Researchers using the two sample t-test often want to know how large sample sizes they need to get reliable test results. This research gives some guidelines for sample sizes to them through simulation works. The simulation had run for normal populations with the different ratios of two variances for different sample sizes (${\leq}30$). The simulation results are as follows. First, if one has no idea equality of variances but he/she can assume the difference is moderate, it is safe to use sample size at least 20 in terms of the nominal level of significance. Second, the power of F-test for the equality of variances is very low when the sample sizes are small (<30) even though the ratio of two variances is equal to 2. Third, the sample sizes at least 10 for the two sample t-test are recommendable in terms of the nominal level of significance and the error limit.

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.

Length-biased Rayleigh distribution: reliability analysis, estimation of the parameter, and applications

  • Kayid, M.;Alshingiti, Arwa M.;Aldossary, H.
    • International Journal of Reliability and Applications
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    • v.14 no.1
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    • pp.27-39
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    • 2013
  • In this article, a new model based on the Rayleigh distribution is introduced. This model is useful and practical in physics, reliability, and life testing. The statistical and reliability properties of this model are presented, including moments, the hazard rate, the reversed hazard rate, and mean residual life functions, among others. In addition, it is shown that the distributions of the new model are ordered regarding the strongest likelihood ratio ordering. Four estimating methods, namely, method of moment, maximum likelihood method, Bayes estimation, and uniformly minimum variance unbiased, are used to estimate the parameters of this model. Simulation is used to calculate the estimates and to study their properties. Finally, the appropriateness of this model for real data sets is shown by using the chi-square goodness of fit test and the Kolmogorov-Smirnov statistic.

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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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Quantitative Structure Activity Relationship Prediction of Oral Bioavailabilities Using Support Vector Machine

  • Fatemi, Mohammad Hossein;Fadaei, Fatemeh
    • Journal of the Korean Chemical Society
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    • v.58 no.6
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    • pp.543-552
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    • 2014
  • A quantitative structure activity relationship (QSAR) study is performed for modeling and prediction of oral bioavailabilities of 216 diverse set of drugs. After calculation and screening of molecular descriptors, linear and nonlinear models were developed by using multiple linear regression (MLR), artificial neural network (ANN), support vector machine (SVM) and random forest (RF) techniques. Comparison between statistical parameters of these models indicates the suitability of SVM over other models. The root mean square errors of SVM model were 5.933 and 4.934 for training and test sets, respectively. Robustness and reliability of the developed SVM model was evaluated by performing of leave many out cross validation test, which produces the statistic of $Q^2_{SVM}=0.603$ and SPRESS = 7.902. Moreover, the chemical applicability domains of model were determined via leverage approach. The results of this study revealed the applicability of QSAR approach by using SVM in prediction of oral bioavailability of drugs.

Prevention of Uterine Adhesion by Sodium Carboxymethylcellulose in Dogs (Sodium Carboxymethylcellulose를 이용한 개의 자궁 유착 방지)

  • 강윤호;정종태;연성찬
    • Journal of Veterinary Clinics
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    • v.17 no.2
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    • pp.381-387
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    • 2000
  • Efficacy of a 1% solution of sodium carboxymethylcellulose (SCMC) infu7ed into the peritoneal cavity of dogs was evaluated for prevention of intraperitoneal adhesion, resulting from operations of the reproductive tract. Saline-treated deles (n = 5) were controls that underwent ventral midline celiotomy, and adhesions were cleated by incision and scraping about 5 cm segment of each uterine horn. Saline (7 ml/kg of body weight) was then infused into the peritoneal cavity. Others (n = 5) were treaded similarly to the saline-treated dogs. except that 1% SCMC :solution (7mH/kg of body weight) was infused into the peritoneal cavity. This group was studied to determine whether SCHC would prevent the adhesions in the peritoneal cavity, especially in the uterine horn model. Abdominal adhesions were evaluated and an adhesion severity score was assigned to each dog on the basis of severity of adhesions. At the time of necropsy. the mean adhesion score in the saline treated group was $2.65{\pm}0.22.$ In contrast, adhesion formation in the SCMC treated group was less ($mean score =1.70{\pm}0.26$). Statistic71 analysis was performed using the grouped t-test and paired t-test. A significanlty lower adhesion score was observed in dogs given SCMC than in the saline treated group (P<0.01). In summary, SCMC significantly reduced adhesion formation in the dog uterine horn model. The results of this study suggest that application of 1% SCMC solution, following various reproductive pelvic surgery, will present the adhesions.

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STATISTICAL ALGORITHMS FOR ENGINE KNOCK DETECTION

  • Stotsky, A.
    • International Journal of Automotive Technology
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    • v.8 no.3
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    • pp.259-268
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    • 2007
  • A knock detection circuit that is based on the signal of an accelerometer installed on the engine block of a spark ignition automotive engine has a band-pass filter with a certain frequency as a parameter to be calibrated. A new statistical method for the determination of the frequency which is the most suitable for the knock detection in real-time applications is proposed. The method uses both the cylinder pressure and block vibration signals and is divided into two steps. In both steps, a new recursive trigonometric interpolation method that calculates the frequency contents of the signals is applied. The new trigonometric interpolation method developed in this paper improves the performance of the Discrete Fourier Transformation, allowing a flexible choice of the size of the moving window. In the first step, the frequency contents of the cylinder pressure signal are calculated. The knock is detected in the cylinder of the engine cycle for which at least one value of the maximal amplitudes calculated via the trigonometric interpolation method exceeds a threshold value indicating a considerable amount of oscillations in the pressure signal; this cycle is selected as a knocking cycle. In the second step, the frequency analysis is performed on the block vibration signal for the cycles selected in the previous step. The knock detectability, which is an individual cylinder attribute at a certain frequency, is verified via a statistical hypothesis test for testing the equality of two mean values, i.e. mean values of the amplitudes for knocking and non-knocking cycles. Signal-to-noise ratio is associated in this paper with the value of t-statistic. The frequency with the largest signal-to-noise ratio (the value of t-statistic) is chosen for implementation in the engine knock detection circuit.

Criterion of Test Statistics for Validation in Credit Rating Model (신용평가모형에서 타당성검증 통계량들의 판단기준)

  • Park, Yong-Seok;Hong, Chong-Sun;Lim, Han-Seung
    • Communications for Statistical Applications and Methods
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    • v.16 no.2
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    • pp.239-347
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    • 2009
  • This paper presents Kolmogorov-Smirnov, mean difference, AUROC and AR, four well known statistics that have been widely used for evaluating the discriminatory power of credit rating models. Criteria for these statistics are determined by the value of mean difference under the assumption of normality and equal standard deviation. Alternative criteria are proposed through the simulations according to various sample sizes, type II error rates, and the ratio of bads, also we suggest the meaning of statistic on the basis of discriminatory power. Finally we make a comparative study of the currently used guidelines and simulated results.

Analysis of stage III stomach cancer using the restricted mean survival time (제한된 평균 생존시간을 이용한 위암 3기 자료 분석에 관한 연구)

  • Kim, Bitna;Lee, Minjung
    • The Korean Journal of Applied Statistics
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    • v.34 no.2
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    • pp.255-266
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    • 2021
  • The purpose of this study is to compare the effects of treatment on stage III stomach cancer data obtained from the SEER program of the National Cancer Institute and to identify the significant risk factors for the survival rates of stage III stomach cancer. Since the proportional hazards assumption was violated for treatment, we used the restricted mean survival time as an alternative to the proportional hazards model. The restricted mean survival time was estimated using pseudo-observations, and the effects of treatment were compared using a test statistic based on the estimated restricted mean survival times. We conducted the regression analysis using a generalized linear model to investigate the significant predictors for the restricted mean survival time of patients with stage III stomach cancer. We found that there was a significant difference between the restricted mean survival times of treatment groups. Age at diagnosis, race, substage, grade, tumor size, surgery, and treatment were significant predictors for the restricted mean survival time of patients with stage III stomach cancer. Surgery was the most significant predictor for increasing the restricted mean survival time of patients with stage III stomach cancer.