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31	Item Discrimination, Model-Data Fit, and Type I Error Rates in DIF Detection using Lord's <i>χ<sup>2</sup></i>, the Likelihood Ratio Test, and the Mantel-Haenszel Procedure Price, Emily A. 11 June 2014 (has links) No description available. Educational Tests and Measurements Education Differential Item Functioning Item Discrimination Type I Error Monte Carlo Simulation Lords Chi-Square Likelihood Ratio Test Mantel-Haenszel Procedure Model-Data Fit
32	獨立與非獨立性資料之多重比較李昀叡 Unknown Date (has links) 同時比較多個樣本間的差異，可用ANOVA來檢定，但ANOVA只能得到樣本間有差異的訊息，無法明確指出是哪些樣本間有差異，需要使用多重比較找出樣本間的差異。本文主要探討相關的離散型資料的多重比較，以型I誤差與檢定力兩指標找出最適的多重比較法。本文依序探討獨立的連續型資料、相關的連續型資料、獨立的離散型資料、相關的離散型資料，並針對相關型的資料提出修正法。綜合型I誤差與檢定力兩指標來看，在樣本間的平均差異小時，Shaffer’s first procedure Test (1986)、Procedure 4 by Bergmann and Hommel (1988)為兩兩比較下較佳的修正法，Hochberg Test (1988)為多對ㄧ比較下較佳的修正法；樣本間平均差異大時，Bonferroni 為兩兩比較下較佳的修正法，Hochberg (1988)、Simes (1986)為多對ㄧ比較下較佳的修正法。 / Analysis of variance (ANOVA) is usually applied to check whether there are differences among more than two treatments. However, even there are differences, multiple comparison procedures are still needed to determine which pair(s) of treatments are different. In this study, we use simulation to compare the frequently used multiple comparison procedures, including many-to-one and pair-wise, and type-I error and power are used to measure the performance of procedures. Two types of data were considered, independently and correlated distributed data. If the differences among treatments are small, Shaffer’s first procedure test (1986) and Procedure 4 by Bergmann and Hommel (1988) are the best in pair-wise case, and Hochberg test (1988) is the best in many-to-one case. If the differences among treatments are large, the Bonferroni procedure is the best in pair-wise case, and the procedures by Hochberg (1988) and Simes (1986) are the best in many-to-one case. 多重比較電腦模擬變異數分析型I誤差檢定力 Bonferroni Multiple comparison computer simulation ANOVA Type-I error power
33	Essays on categorical and universal welfare provision : design, optimal taxation and enforcement issues Slack, Sean Edward January 2016 (has links) Part I comprises three chapters (2-4) that analyse the optimal combination of a universal benefit (B≥0) and categorical benefit (C≥0) for an economy where individuals differ in both their ability to work and, if able to work, their productivity. C is ex-ante conditioned on applicants being unable to work, and ex-post conditioned on recipients not working. In Chapter 2 the benefit budget is fixed but the test awarding C makes Type I and Type II errors. Type I errors guarantee B > 0 at the optimum to ensure all unable individuals have positive consumption. The analysis with Type II errors depends on the enforcement of the ex-post condition. Under No Enforcement C > 0 at the optimum conditional on the awards test having some discriminatory power; whilst maximum welfare falls with both error propensities. Under Full Enforcement C > 0 at the optimum always; and whilst maximum welfare falls with the Type I error propensity it may increase with the Type II error propensity. Chapters 3 and 4 generalise the analysis to a linear-income tax framework. In Chapter 3 categorical status is perfectly observable. Optimal linear and piecewise-linear tax expressions are written more generally to capture cases where it is suboptimal to finance categorical transfers to eliminate inequality in the average social marginal value of income. Chapter 4 then derives the optimal linear income tax for the case with classification errors and Full Enforcement. Both equity and efficiency considerations capture the incentives an increase in the tax rate generates for able individuals to apply for C. Part II (Chapter 5) focuses on the decisions of individuals to work when receiving C, given a risk of being detected and fined proportional to C. Under CARA preferences the risk premium associated with the variance in benefit income is convex-increasing in C, thus giving C a role in enforcement.
34	L’intelligence artificielle pour analyser des protocoles avec alternance de traitements Heng, Emily 08 1900 (has links) Les protocoles avec alternance de traitements sont des protocoles expérimentaux à cas uniques utiles pour évaluer et pour comparer l’efficacité d’interventions. Pour l’analyse de ces protocoles, les meilleures pratiques suggèrent aux chercheurs et aux professionnels d’utiliser conjointement les analyses statistiques et visuelles, mais ces méthodes produisent des taux d’erreurs insatisfaisants sous certaines conditions. Dans le but de considérer cet enjeu, notre étude a examiné l’utilisation de réseaux de neurones artificiels pour analyser les protocoles avec alternance de traitements et a comparé leurs performances à trois autres approches récentes. Plus précisément, nous avons examiné leur précision, leur puissance statistique et leurs erreurs de type I sous différentes conditions. Bien qu’il ne soit pas parfait, le modèle de réseaux de neurones artificiels présentait en général de meilleurs résultats et une plus grande stabilité à travers les analyses. Nos résultats suggèrent que les réseaux de neurones artificiels puissent être des solutions prometteuses pour analyser des protocoles avec alternance de traitements. / Alternating-treatment designs are useful single-case experimental designs for the evaluation and comparison of intervention effectiveness. Most guidelines suggest that researchers and practitioners use a combination of statistical and visual analyses to analyze these designs, but current methods still produce inadequate levels of errors under certain conditions. In an attempt to address this issue, our study examined the use of artificial neural networks to analyze alternating-treatment designs and compared their performances to three other recent approaches. Specifically, we examined accuracy, statistical power, and type I error rates under various conditions. Albeit not perfect, the artificial neural networks model generally provided better and more stable results across analyses. Our results suggest that artificial neural networks are promising alternatives to analyze alternating-treatment designs. apprentissage automatique erreurs de type I protocole à cas uniques protocole avec alternance de traitements réseaux de neurones artificiels alternating-treatment design artificial neural networks machine learning N-of-1 trials type I error
35	A Monte Carlo Study to Determine Sample Size for Multiple Comparison Procedures in ANOVA Senteney, Michael H. January 2020 (has links) No description available. Educational Evaluation Statistics One-way ANOVA t-test Multiple Comparison Procedures Post-Hoc Tests Sample Size Estimation Statistical Power Analysis Monte Carlo Simulation Effect Size Type I Error Robust Tests
36	Hur påverkar avrundningar tillförlitligheten hos parameterskattningar i en linjär blandad modell? Stoorhöök, Li, Artursson, Sara January 2016 (has links) Tidigare studier visar på att blodtrycket hos gravida sjunker under andra trimestern och sedanökar i ett senare skede av graviditeten. Högt blodtryck hos gravida kan medföra hälsorisker, vilket gör mätningar av blodtryck relevanta. Dock uppstår det osäkerhet då olika personer inom vården hanterar blodtrycksmätningarna på olika sätt. Delar av vårdpersonalen avrundarmätvärden och andra gör det inte, vilket kan leda till svårigheter att tolkablodtrycksutvecklingen. I uppsatsen behandlas ett dataset innehållandes blodtrycksvärden hos gravida genom att skatta nio olika linjära regressionsmodeller med blandade effekter. Därefter genomförs en simuleringsstudie med syfte att undersöka hur mätproblem orsakat av avrundningar påverkar parameterskattningar och modellval i en linjär blandad modell. Slutsatsen är att blodtrycksavrundningarna inte påverkar typ 1-felet men påverkar styrkan. Dock innebär inte detta något problem vid fortsatt analys av blodtrycksvärdena i det verkliga datasetet. Coarsening Heaping Likelihood ratio test (LRT) Linear Mixed Models Mean square error (MSE) Measurement error Power Reliability Rounding Type I-error Validity Avrundning Förgrovning Hopning Likelihood ratio test (LRT) Linjär blandad modell Medelkvadratfel (MSE) Mätfel Reliabilitet Styrka Typ 1-fel Validitet
37	基因晶片實驗其樣本數之研究 / Sample Size Determination in a Microarray Experiment 黃東溪, Huang, Dong-Si Unknown Date (has links) 微陣列晶片是發展及應用較為成熟的生物晶片技術。由於微陣列實驗程序複雜，故資料常包含多種不同來源的實驗誤差，為了適當的區分實驗中來自處理、晶片及基因的效應，我們提出混合效應變異數分析模型來調整系統誤差。針對各基因在不同實驗環境的差異性假設檢定問題，利用最小平方法推導出點估計以及對應的檢定統計量。本研究介紹多重檢定問題中的族型一誤差，並證明在此模型下，Sidak調整法為適當的多重檢定方法。在給定族型一誤差率的顯著水準，利用檢定力的公式，運算出在預設檢定力的最低水準下所需最小樣本（晶片）數。最後我們透過電腦模擬，以蒙地卡羅法來估計檢定力與族型一誤差率，由模擬結果發現，採用此最小樣本數結果，其檢定力可達到預期的水準以上，並且其族型一誤差率皆適當地控制在顯著水準以內。混合效應變異數分析模型最小平方法族型一誤差檢定力蒙地卡羅法顯著水準 Mix Model Least Square Method Familywise Type I Error Power Monte Carlo Methods Significant Level
38	An Assessment of the Performances of Several Univariate Tests of Normality Adefisoye, James Olusegun 24 March 2015 (has links) The importance of checking the normality assumption in most statistical procedures especially parametric tests cannot be over emphasized as the validity of the inferences drawn from such procedures usually depend on the validity of this assumption. Numerous methods have been proposed by different authors over the years, some popular and frequently used, others, not so much. This study addresses the performance of eighteen of the available tests for different sample sizes, significance levels, and for a number of symmetric and asymmetric distributions by conducting a Monte-Carlo simulation. The results showed that considerable power is not achieved for symmetric distributions when sample size is less than one hundred and for such distributions, the kurtosis test is most powerful provided the distribution is leptokurtic or platykurtic. The Shapiro-Wilk test remains the most powerful test for asymmetric distributions. We conclude that different tests are suitable under different characteristics of alternative distributions. Normality test Goodness-of-fit Power Type I error Shapiro-Wilk Kolmogorov Analysis Applied Mathematics Applied Statistics Insurance Numerical Analysis and Computation Other Statistics and Probability Risk Analysis Science and Mathematics Education Statistics and Probability
39	複迴歸係數排列檢定方法探討 / Methods for testing significance of partial regression coefficients in regression model 闕靖元, Chueh, Ching Yuan Unknown Date (has links) 在傳統的迴歸模型架構下，統計推論的進行需要假設誤差項之間相互獨立，且來自於常態分配。當理論模型假設條件無法達成的時候，排列檢定（permutation tests）這種無母數的統計方法通常會是可行的替代方法。在以往的文獻中，應用於複迴歸模型（multiple regression）之係數排列檢定方法主要以樞紐統計量（pivotal quantity）作為檢定統計量，進而探討不同排列檢定方式的差異。本文除了採用t統計量這一個樞紐統計量作為檢定統計量的排列檢定方式外，亦納入以非樞紐統計量的迴歸係數估計量b22所建構而成的排列檢定方式，藉由蒙地卡羅模擬方法，比較以此兩類檢定方式之型一誤差（type I error）機率以及檢定力（power），並觀察其可行性以及適用時機。模擬結果顯示，在解釋變數間不相關且誤差分配較不偏斜的情形下，Freedman and Lane (1983)、Levin and Robbins (1983)、Kennedy (1995)之排列方法在樣本數大時適用b2統計量，且其檢定力較使用t2統計量高，但差異程度不大；若解釋變數間呈現高度相關，則不論誤差的偏斜狀態，Freedman and Lane (1983)、Kennedy (1995) 之排列方法於樣本數大時適用b2統計量，其檢定力結果也較使用t2統計量高，而且兩者的差異程度比起解釋變數間不相關時更加明顯。整體而言，使用t2統計量適用的場合較廣；相反的，使用b2的模擬結果則常需視樣本數大小以及解釋變數間相關性而定。 / In traditional linear models, error term are usually assumed to be independently, identically, normally distributed with mean zero and a constant variance. When the assumptions cannot meet, permutation tests can be an alternative method. Several permutation tests have been proposed to test the significance of a partial regression coefficient in a multiple regression model. t=b⁄(se(b)), an asymptotically pivotal quantity, is usually preferred and suggested as the test statistic. In this study, we take not only t statistics, but also the estimates of the partial regression coefficient as our test statistics. Their performance are compared in terms of the probability of committing a type I error and the power through the use of Monte Carlo simulation method. Situations where estimates of the partial regression coefficients may outperform t statistics are discussed. 排列檢定複迴歸模型樞紐統計量蒙地卡羅模擬型一誤差檢定力 Permutation test Multiple regression model Pivotal quantity Monte Carlo simulation Type I error Power
40	Statistical Inference Chou, Pei-Hsin 26 June 2008 (has links) In this paper, we will investigate the important properties of three major parts of statistical inference: point estimation, interval estimation and hypothesis testing. For point estimation, we consider the two methods of finding estimators: moment estimators and maximum likelihood estimators, and three methods of evaluating estimators: mean squared error, best unbiased estimators and sufficiency and unbiasedness. For interval estimation, we consider the the general confidence interval, confidence interval in one sample, confidence interval in two samples, sample sizes and finite population correction factors. In hypothesis testing, we consider the theory of testing of hypotheses, testing in one sample, testing in two samples, and the three methods of finding tests: uniformly most powerful test, likelihood ratio test and goodness of fit test. Many examples are used to illustrate their applications. finite population correction factor statistical hypothesis type I error composite hypothesis power Central limit theorem Basu theorem critical value goodness of fit test likelihood ratio test Lehmann-Scheffe theorem complete statistic ancillary statistic P-value type II error Rao-Blackwell theorem simple hypothesis one-sided test two-sided test significance level sufficient statistic alternative hypothesis testing hypothesis null hypothesis rejection region confidence interval confidence level minimum variance unbiased estimator interval estimation uniformly most powerful test Cramer-Rao inequality likelihood function mean square error moment estimator error of estimation point estimation maximum likelihood estimator bias consistent estimator minimal sufficient statistic factorization theorem unbiased estimator statistic most powerful test test statistics Neyman-Pearson lemma decision rule

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