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1、 畢 業(yè) 設 計（論文） 外 文 文 獻 翻 譯 題 目：What is Hypothesis Testing 學 院： 專業(yè)名稱： 學 號： 學生姓名： 指導教師： 2012 年 2 月 1 日 假設檢驗的概念 Enrico Borriello 1、引言 統(tǒng)計假設是指關(guān)于總體參數(shù)的一種假設。這個假設可為真也可以為假。假設檢驗則指統(tǒng)計員運用正式程序來檢驗該假設并確定其真假度，檢測為真則接受結(jié)果，反之則拒絕接受 2、統(tǒng)計假設 檢驗統(tǒng)計假設的最

2、好方法是檢驗整體參數(shù)，但由于其可行性較低故很難運用到實際操作中。因此，研究人員經(jīng)常選擇從整體參數(shù)中隨機抽樣檢測的方法。如果樣本參數(shù)與統(tǒng)計假設的結(jié)果不一致，那原假設便不成立。 這里有2種統(tǒng)計假設。 零假設 零假設，表示為，通常是假設樣本觀測結(jié)果從純粹的機會。 對立假設 對立假設，表示為 或是，是假設樣本中由一些非隨機的原因決定的觀測值的指標。 例如，假設我們想確定一個硬幣的投擲問題是否是公平和合理。一個零假設則可以為，硬幣的投擲結(jié)果為，一半為正一半為反。對立假設則可以設定為，出現(xiàn)正面和出現(xiàn)反面的次數(shù)大不相同。象征性而言，以上假設可以有如下表達方式 H0: P = 0.5 Ha:

3、P ≠ 0.5 假設我們投擲硬幣50次，結(jié)果為40次正面，10次背面，基于該結(jié)果，原先的零假設可以被拒絕。因此得出結(jié)論，由實驗證據(jù)表明，扔硬幣的結(jié)果不會是正反完全一致。 那么原來的零假設應該是：投擲出正面和反面的次數(shù)一致。即一半幾率為正，一半幾率為背。 零假設能否被“接受”？ 一些研究學者認為一個零假設檢驗無外乎兩種結(jié)果，要么接受零假設，要么拒絕之。然后更多的統(tǒng)計學家對于“接受”零假設依然持保留態(tài)度。相反，他們認為正確的表述應該是，對于零假設，要么拒絕，要么拒絕失敗。為什么要區(qū)分“接受”和“拒絕失敗”？因為“接受”即意味著原零假設為真，“拒絕失敗”則指原數(shù)據(jù)不足以支持對立假設要優(yōu)于零假

4、設。 3、假設檢驗 在樣本數(shù)據(jù)的基礎上，統(tǒng)計員遵照一定程序來檢驗是否能夠拒絕零假設。該程序被稱為假設檢驗，總共有四個步驟。 1.陳述假設。該步驟包括陳述零假設和對立假設，兩者在表述過程中互相排斥，即一方若為真，則另一方必須為假。 2.設計分析計劃。分析計劃描述了樣本數(shù)據(jù)將如何被分析，并用來評估零假設。評估通常會重點分析一個單獨的檢測數(shù)據(jù) 3.分析樣本數(shù)據(jù)。找出被檢測的各項數(shù)值（例如平均數(shù)，比例數(shù)，t-score，z-score等等），此類數(shù)據(jù)在分析計劃中已被列出。 4.說明結(jié)果。運用在分析計劃中所列出的決策規(guī)則，如果檢測數(shù)據(jù)與原假設不相符，基于零假設的定義，則可以拒絕之。

5、 4、決策失誤 在一個假設檢測里，會出現(xiàn)的錯誤主要有兩種 錯誤種類1，當計算員在零假設為真的情況下，采用了拒絕假設。犯該類錯誤的可能性被稱為顯著水平。通常也被稱為alpha，以α表示。 錯誤種類2，當零假設為假時，計算員拒絕零假設失敗。犯該類錯誤的可能性被稱為beta，由字母β表示。不犯該類錯誤的可能性則稱之為檢測能力。 本文研究模糊評判法在教學管理系統(tǒng)中的學生評價的應用，通過對影響學生評價的各種因素的分析而對其賦予不同的權(quán)重，利用模糊評判法對學生做出一個綜合的評判。由于本人水平有限，再加上本文是針對特定地區(qū)的個別教學管理系統(tǒng)的評判，在文中的權(quán)重通過專家調(diào)查分析而來，帶有一定的

6、主觀色彩。 5、判斷法則 分析計劃的規(guī)則就是分析零假設域。在實踐操作中，統(tǒng)計學家描述這些決策規(guī)則的方法，就是參考p值或參考該接受區(qū)。 p值。作為零假設是測量值的強有力的證據(jù)。假設檢驗統(tǒng)計等于S值的概率是觀察一個檢驗統(tǒng)計量作為極端的假設是正確的，假設零假設是成立的。如果值小于平均值，便接受假設，反之則拒絕假設。 接受域。該區(qū)域的區(qū)間是一個范圍值。如果檢驗結(jié)果落在檢驗統(tǒng)計區(qū)域內(nèi)，該零假設成立。該地區(qū)接受的判斷標準時，使第一類誤差的值等于平均值。 拒絕域的定義是，集值以外的地區(qū)。如果判斷標準不被接受，則零假設被拒絕。在這種情況下，我們說，假設被拒絕在α的區(qū)域外。 這兩種方法是等效

7、的。一些統(tǒng)計文本用P值法；其他的文本使用該區(qū)域檢驗該方法。在具體的實例中，不同的方法有不同的應用 。 What is Hypothesis Testing? Enrico Borriello 1、preface A statistical hypothesis is an assumption about a population parameter. This assumption may or may not be true. Hypothesis testing refers to the formal procedures us

8、ed by statisticians to accept or reject statistical hypotheses. 2、Statistical Hypotheses The best way to determine whether a statistical hypothesis is true would be to examine the entire population. Since that is often impractical, researchers typically examine a random sample from the populatio

9、n. If sample data are not consistent with the statistical hypothesis, the hypothesis is rejected. There are two types of statistical hypotheses. Null hypothesis. The null hypothesis, denoted by H0, is usually the hypothesis that sample observations result purely from chance. Alternative hypothesi

10、s. The alternative hypothesis, denoted by H1 or Ha, is the hypothesis that sample observations are influenced by some non-random cause. Because For example, suppose we wanted to determine whether a coin was fair and balanced. A null hypothesis might be that half the flips would result in Heads

11、 and half, in Tails. The alternative hypothesis might be that the number of Heads and Tails would be very different. Symbolically, these hypotheses would be expressed as H0: P = 0.5 Ha: P ≠ 0.5 Suppose we flipped the coin 50 times, resulting in 40 Heads and 10 Tails. Given this result, we wou

12、ld be inclined to reject the null hypothesis. We would conclude, based on the evidence, that the coin was probably not fair and balanced. Can we accept the null hypothesis ? Some researchers say that a hypotheis test can have one of two outcomes: you accept the null hypothesis or you reject the nul

13、l hypothesis. Many statisticians, however, take issue with the notion of “accepting the null hypothesis.” Instead, the say: you reject the null hypothesis or you fail to reject the null hypothesis. Why the distinction between “acceptance” and “failure to reject?” Acceptance implies that the null hy

14、pothesis is true. Failure to reject implies that the data are not sufficiently persuasive for us to prefer the alternative hypothesis over the null hypothesis. 3、Hypothesis Tests Statisticians follow a formal process to determine whether to reject a null hypothesis, based on sample data. This proc

15、ess, called hypothesis testing, consists of four steps. (1) State the hypotheses. This involves stating the null and alternative hypotheses. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false. (2) Formulate an analysis plan. T

16、he analysis plan describes how to use sample data to evaluate the null hypothesis. The evaluation often focuses around a single test statistic. (3) Analyze sample data. Find the value of the test statistic (mean score, proportion, t-score, z-score, etc.) described in the analysis plan. (4) Interpr

17、et results. Apply the decision rule described in the analysis plan. If the value of the test statistic is unlikely, based on the null hypothesis, reject the null hypothesis. 4、Decision Errors Two types of errors can result from a hypothesis test. Type I error. A Type I error occurs when the res

18、earcher rejects a null hypothesis when it is true. The probability of committing a Type I error is called the significance level. This probability is also called alpha , and is often denoted by α. Type II error. A Type II error occurs when the researcher fails to reject a null hypothesis that is f

19、alse. The probability of committing a Type II error is called beta, and is often denoted by β. The probability of not committing a Type II error is called the power of the test. 5、Decision Rules The analysis plan includes decision rules for rejecting the null hypothesis. In practice, statistician

20、s describe these decision rules in two ways - with reference to a P-value or with reference to a region of acceptance. P-value. The strength of evidence in support of a null hypothesis is measured by the P-value. Suppose the test statistic is equal to S. The P-value is the probability of observing

21、a test statistic as extreme as S, assuming the null hypothesis is true. If the P-value is less than the significance level, we reject the null hypothesis. Region of acceptance. The region of acceprance is a range of values. If the test statistic falls within the region of acceptance, the null hypot

22、hesis is not rejected. The region of acceptance is defined so that the chance of making a Type I error is equal to the significance level. The set of values outside the region of acceptance is called the region of rejection . If the test statistic falls within the region of rejection, the null hypo

23、thesis is rejected. In such cases, we say that the hypothesis has been rejected at the α level of significance. These approaches are equivalent. Some statistics texts use the P-value approach; others use the region of acceptance approach. In subsequent lessons, this tutorial will present examples t

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