摘 要 在基因微陣列(DNA microarrays)的技術中，可同時得到數以千筆的資料，為了找出具有顯著差異的基因，一般會考慮控制整體誤差率(familywise error rate,FWE) 的多重比較方法(multiple comparison procedures,MCP)。但當基因數或假設檢定個數過多時，其檢定會產生不易拒絕虛無假設的結果，使得結論過於保守。為解決此一問題，Benjamini & Hochberg(1995)建議採用控制錯誤發現率(false discovery rate,FDR)的方法來替代整體誤差率FWE。且Tusher et al.(2001)在DNA微陣列顯著分析(significance analysis of microarrays,SAM)的文章中提出利用排列分佈(permutations)估計錯誤發現率FDR的方法。本篇論文將介紹Tusher et al.(2001)所提出的SAM估計錯誤發現率FDR的方法，且提出一修正SAM方法：SAMM。另外介紹兩種控制顯著水準的統計方法：SAME和SAMT(t檢定)。透過電腦模擬驗證四種方法其錯誤發現率FDR的表現。 / Abstract DNA microarray technology provides tools enable to simultaneously study thousands of genes. A conservative multiple comparison procedure (MCP) controlling the familywise type I error rate (FWE) is considered. However, the conservativeness of a MCP becomes more and more severe as the number of comparisons (genes) increases. Instead of FWE, another error rate, the false discovery rate (FDR), is suggested. Tusher et al.(2001) proposed a statistical procedure, the Significance Analysis of Microarrays (SAM), to analyze a microarray data set. In which, the conclusion is drawn at a specific threshold and the false discovery rate (FDR) of the conclusion is estimated by permutations. In this paper, inspired by the SAM, three other methods are proposed. The performances of these methods are investigated and compared through simulations.

房地產業在整個國民經濟體系中有舉足輕重的作用。伴隨著房地產業的飛速發展，房仲業也應運而生。而在目前的房地產市場上，一方面有為數眾多的房仲企業，其服務品質參差不齊，行業整體服務滿意度令人堪憂，另一方面在互聯網的浪潮下，各種新興模式的房仲企業層出不窮，著實令公眾難以甄別。因此，無論是整體性或區域性的房仲企業績效排名，對於消費者、房仲經紀人與資本市場都具有重要的參考意義，此外還可作為房仲企業之間相互比較的可靠依據，是一個值得深入探討的課題。 本研究將利用上海市房地產交易中心的交易資料，其中交易資料包含交易時間、交易次數、交易金額、房屋類型、房屋面積、交易區域等資料，透過RFM分析及平均數檢定等方法的應用，以2014年上海市房地產交易市場作為研究對象，首先對於上海市的房地產交易狀況進行概述，其次研究分析上海的房仲企業在不同交易區域與房屋類型上的表現，進而結合優質房仲企業的經營特點做出建議，其研究發現概述如下： 一、公寓的交易次數約有逾八成的比例； 二、上海市次級核心地區房屋交易占交易總量的50%； 三、上海市核心地區平均房屋交易單價較偏遠地區高出約1.8萬； 四、中原物業、我愛我家房屋、德佑房地產與太平洋房屋的經營績效最佳。

在DNA微陣列基因的實驗中資料包括數千個cDNA 序列，為了要篩選出有差異表現基因，同時針對大量基因個數作假設檢定。若無適當地調整個別檢定問題中的誤差率，則將會膨脹整體的誤差率。在多重假設檢定中為了讓整體誤差率(familywise error rate, FWE)控制在設定水準下，必須調整個別假設檢定之個別型一誤差率CWE的檢定準則，此為多重比較方法(multiple comparison procedures：MCP)。然而當多重比較的個數增加時，控制整體誤差率FWE之傳統的多重比較方法會是過於嚴格的標準，不容易推翻虛無假設，使得檢定的結果太過保守。為了解決此現象，Benjamini and Hochberg(1995) 建議另一種錯誤率：錯誤發現率(false discovery rate：FDR)。錯誤發現率定義為在被拒絕之虛無假設中錯誤拒絕的比例之期望值。而Benjamini and Hochberg(1995)也在文中提出一個得以控制錯誤發現率的多重比較方法，稱為BH方法。本篇論文將詳盡地介紹CWE、FWE和FDR三種誤差率，並提出－修正BH的方法，稱為BH( )。我們將透過電腦模擬驗證出新的修正BH方法之表現比原BH方法有較高的檢定力，且從實例的結果中發現BH( )比原BH方法能檢測出更多的顯著個數。 關鍵字：個別型一誤差率(CWE)；整體誤差率(FWE)；多重比較方法(MCP)； 錯誤發現率(FDR)。 / cDNA microarray technology provides tools to study thousands of genes simultaneously. Since a large number of genes are compared, using a conventional significant test leads to the increase of the type I error rate. To avoid the inflation, the adjustment for multiplicity should be considered and a multiple comparison procedure (MCP) that controls the familywise error rate (FWE) is recommended. However, the conservativeness of a MCP that controls FWE becomes more and more severe as the number of comparisons (genes) increases. Instead of FWE, Benjamini and Hochberg (1995) recommended to control the expected proportion of falsely rejecting hypotheses—the false discovery rate (FDR)—and developed a MCP, which has its FDR under control. In this paper, the error rates CWE, FWE and FDR are fully introduced. A new MCP with FDR controlled is developed and its performance is investigated through intensive simulations. KEY WORDS：Comparison-wise error rate (CWE)；Familywise error rate (FWE)；Multiple comparison procedure (MCP)；False discovery rate (FDR).

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.