本研究主要目的是探討複式評量融入數學教學對不同學習風格的高二學生在圓與球面課程的學習成效。研究採用不等組前後測準實驗研究設計，以桃園縣一所完全中學高中部二年級社會組兩班共80名學生為研究對象，教師為研究者，非隨機分派一班為實驗組，進行「複式評量融入數學教學」之實驗教學，另一班為控制組，實施「傳統數學科教學」。學生學習風格採用Kolb學習風格量表區分為「主動驗證」及「被動觀察」兩類型。為探究不同學習風格的學生接受不同教學方法後，在數學學習態度、成就及保留三方面的差異性，採用二因子共變數分析之統計方法檢定研究假設，並於實驗教學後以實驗教學回饋單調查其對複式評量之看法及態度，檢定分析及調查結果整理後得如下結論。 一、排除前測影響後，學生在數學學習態度上的表現： （一）學習風格因子與教學方法因子之間沒有交互作用。 （二）學習風格因子不會造成顯著差異。 （三）教學方法因子會造成顯著差異；複式評量教學優於傳統教學。 二、排除前測影響後，學生在數學學習成就上的表現： （一）學習風格因子與教學方法因子之間有交互作用。 （二）以傳統教學法而言，學習風格因子會造成顯著差異；主動驗證風格優於被動觀察風格。 （三）以被動觀察風格而言，教學方法因子會造成顯著差異；複式評量教學法優於傳統教學法。 （四）以被動觀察風格接受傳統教學法後為最差。 三、排除前測影響後，學生在數學學習保留上的表現： （一）學習風格因子與教學方法因子之間有交互作用。 （二）以複式評量教學法而言，學習風格因子會造成顯著差異；主動驗證風格優於被動觀察風格。 （三）以主動驗證風格而言，教學方法因子會造成顯著差異；複式評量教學法優於傳統教學法。 （四）以主動驗證風格接受複式評量教學法後為最佳。 四、實驗組學生在圓與球面課程實施「複試評量融入數學教學」後，絕大多數的學生喜歡此教學方法，而對未來數學課程實施「複試評量融入數學教學」則絕大多數抱持贊成的看法。 最後針對研究結果提出數點建議，以供教師教學及後續研究之參考。 / The purpose of this study is to explore the effects on learning performance of 11th graders based on two factors – teaching methods and learning styles. This study was conducted as a quasi-experimental design. Two classes,which have a total of 80 students, were sampled from a high school in Taoyuan County. One was assigned as an experimental group and the other one as a control group. The first one took a “composite assessment embedded in mathematics teaching” method learning, while the second one took a “traditional mathematics teaching” method learning respectively. This study used the learning styles inventory (LSI) of Kolb to classify learners into two groups – “active experimentation (AE)” and “Reflective Observation (RO)”. Two-way ANCOVA was conducted to test all hypotheses in order to find variations of mathematical learning attitudes, mathematical learning achievements, and mathematical learning retention. The study also investigated the views of points of the students in control group after the experiment. According to the analysis, we reach the following conclusions︰ 1. In mathematical learning attitudes: (1) Teaching methods and learning styles don’t interact significantly. (2) There is no significant difference between two learning styles. (3) There is a significant difference between two teaching methods. The effect on experimental group is better than that on control group significantly. 2. In mathematical learning achievements: (1) Teaching methods and learning styles interact significantly. (2) For the control group, there is a significant difference between two learning styles. The effect on style AE is better than that on style RO significantly. (3) For the style RO, there is a significant difference between two teaching methods. The effect on experimental group is better than that on control group significantly. (4) The effect on control group with the style RO is the worst. 3. In mathematical learning retention: (1) Teaching methods and learning styles interact significantly. (2) For the experimental group, there is a significant difference between two learning styles. The effect on style AE is better than that on style RO significantly. (3) For the style AE, there is a significant difference between two teaching methods. The effect on experimental group was better than that on control group significantly. (4) The effect on experimental group with the style AE is the best. 4. After the experiment, most of the students in the experimental group like “composite assessment embedded in mathematics teaching” method. They also agree that “composite assessment embedded in mathematics teaching” should be conducted in the future. Finally, suggestions for the teachers and future researches are also discussed.

Eee PC的低價小筆記型電腦的銷售成功，小筆記型電腦衍然己被筆記型電腦廠商視為下一個藍海市場，以產品生命週期來看，Eee PC由萌芽期進入成長期，而早期辨出消費者中的創新使用者及早期採用者，在新產品發展階段有策略上的重要意義，本研究目的在進一步辨識出消費者及其使用習慣，讓市場行銷人員能選定目標市場及制定適當的行銷策略。 本研究以消費者決策歷程(Consumer Decision Process, CDP)為基礎，在配合科技接受理論TAM (Technology Acceptable Model)當中的有用知覺(Perceived Usefuless, PU) 及易用知覺 (Perceived Eas of Use, PEOU) 發展成本研究的研究架構，並以線上問卷便利取樣己購買Eee PC的消費者，以AIO生活型態做為Eee PC消費者使用者行為的市場區隔基礎，以市場區隔理論(Segmentation)及創新擴散理論將消費者予以區隔，利用因素分析、集群分析、變異數分析、卡方檢定及區別分析等統計方法做為分析方法的工具，試圖分辨出購買Eee PC的使用者並了解Eee PC購買者的使用習慣。 本研究經由實證分析得到了以下的發現: (1)Eee PC消費者具有創新者與早期使用者的特性 (2)依Eee PC消費者之購買行為資料分析，消費者最重視的產品屬性 為小巧方便攜帶及重量輕盈而非價格低廉。 (3)Eee PC消費者資訊搜尋對象以網站為主，但購買仍以實體通路為 主。 (4)Eee PC消費者購買用途以休閒娛樂及工作課業需要為主，不同族 群之間有有顯著差異。 (5)依人口統計變數來看，各族群在特徵上有所不同。 (6)依知覺程度來看，各族群在知覺程度上有所不同。 / The success of selling of ASUS’s Eee PC, the low-priced laptop, led Eee PC be taken as the next blue ocean for notebook manufactures. In the product life cycle of Eee PC, it has been changed from the introduction stage to growth stage. Early identification of the innovators and early adoptors is a strategical important meaning for new product development. The research is to identify the the consumers and their consuming habits, so that the marketing departments can select an ideal market segment and to employ effective marketing tactics. The research is based on the conceptual framework for the consumer decision process proposed by Kolter & Keller (2007) and combines the perspective from the Technology Acceptance Model proposed by Davis(1989) to identify the consumer of Eee PC and explores their satisfacation and how they use Eee PC. Finally, the research uses the traditional stastics tool to differentiate Eee PC buyers based on Psychology variables from AIO theory proposed by Plummer(1974) and segmentation theory proposed by Wind(1978). The research obtains the following findings: (1) Eee PC buyers can be distinguished as innovator and rearly adoptor. (2) According to the data analysis from Eee PC, the features that consumers highly concerned are easy and light for hand-carry instead of cheap price. (3) Eee PC buyers use internet to search information, but they buy Eee PC via the physical channel or stores (4) Eee PC buyers use Eee PC for entertainment and academic or job purpose. (5) As the point of view in demographic, two clusters are significance different. (6) As the point of view in perspective, two clusters are significance different.

在本論文中，根據所建立的100,000筆模擬資料作為抽樣的母體，利用簡單隨機抽樣法（simple random sampling；SRS）從此模擬的資料中共抽出1068筆成功樣本，分別考慮了當個案訪問失敗（unit nonresponse）情形發生時是『隨機性』及『非隨機性』兩種情況下比較(1)事後分層加權（poststratification approach）；(2)多個變數反覆加權（raking or raking ratio）；及(3)估計成功率加權等三種加權方法之效果如何。 當訪問失敗具完全隨機性的情況之下所抽出之樣本，由於原始樣本的代表性過於『完美』，即使是經過事後分層加權或是raking加權後，均無顯著的效果。因此，對於樣本的改善程度實在是微不足道！而在訪問失敗是非隨機性的情況時，事後分層加權對於變數間具較強相關性時，則具有較佳的加權效果；raking加權方式的加權效果普遍上均不錯的表現，值得廣泛地採用；而估計成功率加權的效果則必須取決於估計準確與否，否則可能由於估計的偏差而導致加權效果不彰。 最後，本文亦提供了事後分層加權及raking加權的適用時機及建議，以作為日後從事抽樣調查工作者的參考意見。

本研究的目的為研究台灣省在1990年之15-17歲的在學率，在找出可能影響因素並蒐集好相關的資料後，我們將蒐集到的資料分成兩個部份，一個部份用來建造模型，而另一個部份則用來測試所建立出來的模型。主要的過程是：先利用簡單迴歸模型了解各個可能的因素對於15-17歲的在學率的影響程度，經過許多分析及了解後再對這些變數採取可能的變數轉換(variable transformations)，而後再利用三種常用的統計迴歸方法﹝包含有逐步迴歸(stepwise regression)方法、前進選擇(forward selection)方法以及後退消除(backward elimination)方法﹞去發展出一個適當的複迴歸模型(multiple regression model)。對於這個模型，以實際的台灣在學情況來看，我們看不出它有任何的不合理；同時也利用圖形及檢定去驗證模型的假設，其次還做有關迴歸參數的推論(inferences about regression parameters)。再其次，我們運用變異數分析的結果(analysis of variance results)以及新觀察值的預測情形(predictions of new observations)來評估模型的預測能力。最後並利用所得到的最適當的模型，對如何提昇15-17歲青少年的在學率給予適當的建議。 / The objective of this research is to study what factors may affect the schooling rates of 15-17 years old in Taiwan province in 1990. After finding out some possible factors and collecting those data regarding those factors, we separate the data (by stratified random sampling) into two sets. One set is used to construct the model, and the other set shall be used to test the model. The main process to build a regression model is as follows. First, we shall use simple linear regression models to help us to see if each factor may have relation with the schooling rates. With the analysis of residuals and so on, we then make appropriate transformations on each of these factors. Finally, we use three common statistical regression techniques (including stepwise regression, forward selection, and backward elimination methods) to develop a suitable multiple regression model. It seems that, by our understanding of schooling rates in Taiwan, this model is not unreasonable. In addition, we verify the assumptions of the model by graphical methods and statistical tests. We also do the inferences about regression parameters. Furthermore, ye use the results of the analysis of variance and predictions of new observations to evaluate the prediction ability of the model. Finally, we use the most appropriate multiple regression model to give some suggestions to improve (or keep) the schooling rates of 15-17 years old.

迴歸分析通常被用來描述兩個或兩個以上變數間的關係，或藉由一群自變數來預測某一應變數的相關資訊。然而，通常我們只知道自變數會對應變數造成影響，至於兩者間真正的函數型態為何，卻不得而知。因此，本文試圖介紹不同型式的殘差圖，諸如：簡單殘差圖(simple residual plot)、加變數解釋圖(added-variable plot)、部份殘差圖（partial residual plot或component-plus-residual plot）、增加部份殘差圖(augmented partial residual plot)，藉由圖形所提供的資訊，希望能更有效率地找出適當的函數關係，將資料作轉換，使線性迴歸模式適用於轉換後的資料。 / The primary goal in a regression analysis is to understand how a response variable depends on one or more predictors, and to predict the value of response variable according to the predictors. However, most of the time, we only know that the predictors will have effect on the response variable, but not the true function of them. Therefore, some different forms of residual plot are considered in the study, including simple residual plot, added-variable plot, partial residual plot (or component-plus-residual plot), and augmented partial residual plot. In view of these residual plots, we can visualize easily the dependence of a response on predictors. Hence, after transforming the data using an appreciate function suggested by the plots, the data can be better fitted.

The use of transformation can usually simplify the analysis of data, especiallywhen the original observations deviate from the underlying assumption of linearmodel. Box-Cox transformation receives much more attention than others. Inthis dissertation, we will review the theory about the estimation, hypotheses test on transformation parameter and about the sensitivity of the linear model parameters. Monte Carlo simulation is used to study the performance of the transformation. We also display whether Box-Cox transformation makes the transformed observations satisfy the assumption of linear model actually.

線性結構關係模式是一種考慮以多個直線方程式來分析處理變數間因果關 係的統計方法，其結合了因徑分析及因素分析之優點並將之融合於整體模 式中。線性結構關係模式經過參數估計後，需評估整個模式之好壞，因此 許多學者嘗試提出一些評估模式好壞的適合度指標，如一般常用的卡方檢 定、殘差均方根、適合度指標、調整後適合度指標以及基準指標等。這些 指標中有的指標會受到樣本數大小或樣本分布的影響，有些指標受模式隱 藏變數多寡或因素指標多寡的影響，有些指標需有嚴格的條件（如樣本需 服從常態分布）及前提方可適用，且有些指標的分布是未知的，因此欲對 這些指標進行區間估計、假設檢定、或顯著性差異比較是不可能的。基於 上述各種適合度指標的缺點，本論文利用拔靴法進行重抽樣求得拔靴分布 來解決上述各種問題。然而傳統的拔靴法在線性結構關係模式上是不適用 的，因此，再提出一改良拔靴法程序，求得拔靴分布來做為評估模式好壞 的依據，並利用改良拔靴法來做巢狀模式之顯著性差異比較及利用抽樣誤 差和非抽樣誤差觀念來評估模式適合度。

使用母數統計方法（Parametric Tests）分析資料時，常需滿足常態假設，但實際得到的資料卻少有常態，因此研究違反常態假設對統計量所造成影響的強韌性研究（Robustness Research）在應用統計方法上是重要的研究主題。在進行此類研究時，常使用蒙地卡羅法（Monte Carlo Method）產生非常態之資料進一步進行研究，目前雖已有多個可產生非常態連續資料的方法被提出，但心理學研究之資 料卻多為間斷資料。而在產生非常態間斷資料時，除難以產生指定參數之間斷分配外，亦有無限多組具同樣參數之間斷分配可供選擇。針對以上兩困難，本研究提出可使用最大資訊熵程序估計符合指定參數之單變數間斷分配，用以產生對應之單變數間斷資料。最大資訊熵方法可所估出之間斷最大資訊熵分配除為符合指定參數時最常出現之分配以外，同時具有平滑、非必要無0 機率等特性。本研究呈現指定4 參數（平均數、變異數、偏態及峰度）與指定2 參數（偏態及峰度） 之最大資訊熵方法，及相對應之R 套件，並以R 套件對此2 方法進行探討評估。結果發現本研究所提出之二方法，在要求指定參數與估計參數之誤差均不超過 .001 時，均可估計出符合指定參數之可能組合之分配，顯示此二方法可精確產生指定參數之間斷分配。而本研究所提供之R 套件，除可在輸入點數、指定參數後產生間斷分配，亦可輸入指定樣本數目及樣本數於此間斷分配中抽取樣本，使此二方法於使用蒙地卡羅法進行間斷資料之強韌性研究時，更易於使用。 / When conducting the robustness researches about normality assumption with Monte Carlo method, a procedure for simulating non-normal data is needed. Some procedures for simulating the non-normal continuous data have been proposed, but the discrete data of ordered categorized variables (e.g., Likert-Type scale) are what we met mostly in practice. To estimate the discrete probability distribution precisely and choose one from infinite discrete probability distributions with the same constraints are 2 difficulties encountered on discrete data simulating process. Therefore, the research purposed a procedure called Maximum Entropy Procedure (MEP) which simulates the univariate discrete maximum entropy distribution with the specified parameters. The distribution is the one with greatest number with the specified parameters, most unlikely probability distribution with 0 probability and smoothest. The characteristics make the MEP a reasonable and considerable choice on simulating univariate discrete data with specified parameters. The MEP-4 (constraints on mean, variance, skewness and kurtosis), the MEP-2 (constraints on skewness and kurtosis) and the corresponding R packages which could estimate the univariate discrete distributions with the specified parameters are presented, evaluated and discussed in this research. It shows that the MEP-4 and MEP-2 are able to estimate the discrete probability distributions precisely with possible combinations of specified parameters with all differences are smaller than .001 and thus useful for robustness researches. The R packages presented in this study are easily to estimate the discrete probability distributions with specified parameters and generate data from these distributions with specified number of samples and sample size. Therefore the MEP-4 and MEP-2 could be easily implemented for generating discrete data with the specified parameters through the corresponding R package and thus useful for Monte Carlo method of robustness researches.

本研究之樣本取自1991年7月1日至2010年3月之月資料，探討各總體經濟變數包括：利率、匯率(美元對新台幣)、M1B、出口、GDP、領先指標綜合指數與大陸及美國兩股市，對台股指數之影響。實證結果顯示，道瓊工業指數為影響台股加權指數最具代表性與領先的指標，大陸股市則非如一般所預期對台股指數變動有重要解釋能力。且道瓊工業指數、利率、M1b、GDP對台股具有領先的單向因果關係。 在衝擊反應函數及變異數分解中，除了道瓊工業指數為判斷台股指數變動最重要因素外，利率與貨幣供給則扮演著解釋台股變動另一重要的角色，利率調升對台股指數之影響為先正後負，當利率調升前，投資者會事先反應，但調升後便會開始調節，反而對台股造成負向影響；而GDP及出口在變異數分解中占台股變異數比例是相對次高的比重，說明台股的變動反應了經濟的基本面因素，台股的變動亦會受其影響，惟此二項變數屬於落後指標，只能用在事後分析。而(美元兌新台幣)匯率及領先指標綜合指數則對台股變動無顯著解釋能力。

在現今生物醫學領域中，一重要課題為透過基因實驗所獲得的量化資料，來研究與分析基因與外顯表型變數(phenotype)的相關性。已知多數已發展的方法皆屬於單基因分析法，無法適當的考慮基因之間的相關性。本研究主要針對基因組分析(gene set analysis)問題，提出統計檢定方法來驗證特定基因組的顯著性。為了能盡其所能的捕捉整體基因組與外顯表型變數的關係，我們結合了傳統的檢定方法與分類方法，提出以隨機森林分類方法(Random Forests)的測試組分類誤差值(test error)作為檢定統計量(test statistic)，並以其排列顯著值(permutation-based p-value)來獲得統計結論。我們透過模擬研究將本研究方法和其他七種基因組分析方法做比較，可發現本方法在型一誤差率(type I error rate)和檢定力(power)上皆有優異表現。最後，我們運用本方法在數個實際基因資料組的分析上，並深入探討所獲得結果。 / Nowadays microarray data analysis has become an important issue in biomedical research. One major goal is to explore the relationship between gene expressions and some specific phenotypes. So far in literatures many developed methods are single gene-based methods, which use solely the information of individual genes and cannot appropriately take into account the relationship among genes. This research focuses on the gene set analysis, which carries out the statistical test for the significance of a set of genes to a phenotype. In order to capture the relationship between a gene set and the phenotype, we propose the use of performance of a complex classifier in the statistical test: The test error rate of a Random Forests classification is adopted as the test statistic, and the statistical conclusion is drawn according to its permutation-based p-value. We compare our test with other seven existing gene set analyses through simulation studies. It’s found that our method has leading performance in terms of having a controlled type I error rate and a high power. Finally, this method is applied in several real examples and brief discussions on the results are provided.