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1、 毕 业 设 计（论文）外 文 文 献 翻 译题 目：What is Hypothesis Testing学 院： 专业名称： 学 号： 学生姓名： 指导教师： 2012 年 2 月 1 日假设检验的概念Enrico Borriello1、引言统计假设是指关于总体参数的一种假设。这个假设可为真也可以为假。假设检验则指统计员运用正式程序来检验该假设并确定其真假度，检测为真则接受结果，反之则拒绝接受2、统计假设检验统计假设的最好方法是检验整体参数，但由于其可行性较低故很难运用到实际操作中。因此，研究人员经常选择从整体参数中随机抽样检测的方法。如果样本参数与统计假设的结果不一致，那原假设便不成立。这
2、里有2种统计假设。 零假设 零假设，表示为，通常是假设样本观测结果从纯粹的机会。 对立假设 对立假设，表示为 或是，是假设样本中由一些非随机的原因决定的观测值的指标。例如，假设我们想确定一个硬币的投掷问题是否是公平和合理。一个零假设则可以为，硬币的投掷结果为，一半为正一半为反。对立假设则可以设定为，出现正面和出现反面的次数大不相同。象征性而言，以上假设可以有如下表达方式H0: P = 0.5Ha: P 0.5假设我们投掷硬币50次，结果为40次正面，10次背面，基于该结果，原先的零假设可以被拒绝。因此得出结论，由实验证据表明，扔硬币的结果不会是正反完全一致。那么原来的零假设应该是：投掷出正面和
3、反面的次数一致。即一半几率为正，一半几率为背。零假设能否被“接受”？一些研究学者认为一个零假设检验无外乎两种结果，要么接受零假设，要么拒绝之。然后更多的统计学家对于“接受”零假设依然持保留态度。相反，他们认为正确的表述应该是，对于零假设，要么拒绝，要么拒绝失败。为什么要区分“接受”和“拒绝失败”？因为“接受”即意味着原零假设为真，“拒绝失败”则指原数据不足以支持对立假设要优于零假设。3、假设检验在样本数据的基础上，统计员遵照一定程序来检验是否能够拒绝零假设。该程序被称为假设检验，总共有四个步骤。1.陈述假设。该步骤包括陈述零假设和对立假设，两者在表述过程中互相排斥，即一方若为真，则另一方必须为
4、假。2.设计分析计划。分析计划描述了样本数据将如何被分析，并用来评估零假设。评估通常会重点分析一个单独的检测数据3.分析样本数据。找出被检测的各项数值（例如平均数，比例数，t-score，z-score等等），此类数据在分析计划中已被列出。4.说明结果。运用在分析计划中所列出的决策规则，如果检测数据与原假设不相符，基于零假设的定义，则可以拒绝之。4、决策失误在一个假设检测里，会出现的错误主要有两种错误种类1，当计算员在零假设为真的情况下，采用了拒绝假设。犯该类错误的可能性被称为显著水平。通常也被称为alpha，以表示。错误种类2，当零假设为假时，计算员拒绝零假设失败。犯该类错误的可能性被称为b
5、eta，由字母表示。不犯该类错误的可能性则称之为检测能力。本文研究模糊评判法在教学管理系统中的学生评价的应用，通过对影响学生评价的各种因素的分析而对其赋予不同的权重，利用模糊评判法对学生做出一个综合的评判。由于本人水平有限，再加上本文是针对特定地区的个别教学管理系统的评判，在文中的权重通过专家调查分析而来，带有一定的主观色彩。5、判断法则分析计划的规则就是分析零假设域。在实践操作中，统计学家描述这些决策规则的方法，就是参考p值或参考该接受区。 p值。作为零假设是测量值的强有力的证据。假设检验统计等于S值的概率是观察一个检验统计量作为极端的假设是正确的，假设零假设是成立的。如果值小于平均值，便接
6、受假设，反之则拒绝假设。 接受域。该区域的区间是一个范围值。如果检验结果落在检验统计区域内，该零假设成立。该地区接受的判断标准时，使第一类误差的值等于平均值。 拒绝域的定义是，集值以外的地区。如果判断标准不被接受，则零假设被拒绝。在这种情况下，我们说，假设被拒绝在的区域外。 这两种方法是等效的。一些统计文本用P值法；其他的文本使用该区域检验该方法。在具体的实例中，不同的方法有不同的应用 。What is Hypothesis Testing?Enrico Borriello1、preface A statistical hypothesis is an assumption about a p
7、opulation parameter. This assumption may or may not be true. Hypothesis testing refers to the formal procedures used by statisticians to accept or reject statistical hypotheses.2、Statistical HypothesesThe best way to determine whether a statistical hypothesis is true would be to examine the entire p
8、opulation. Since that is often impractical, researchers typically examine a random sample from the population. If sample data are not consistent with the statistical hypothesis, the hypothesis is rejected.待添加的隐藏文字内容1There are two types of statistical hypotheses.Null hypothesis. The null hypothesis,
9、denoted by H0, is usually the hypothesis that sample observations result purely from chance.Alternative hypothesis. 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
10、 whether a coin was fair and balanced. A null hypothesis might be that half the flips would result in Heads 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 asH0: P = 0.5 Ha: P 0.5Sup
11、pose we flipped the coin 50 times, resulting in 40 Heads and 10 Tails. Given this result, we would 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 hyp
12、otheis test can have one of two outcomes: you accept the null hypothesis or you reject the null 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 d
13、istinction between “acceptance” and “failure to reject?” Acceptance implies that the null hypothesis 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 TestsStatisticians follow a formal p
14、rocess to determine whether to reject a null hypothesis, based on sample data. This process, 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
15、. That is, if one is true, the other must be false.(2) Formulate an analysis plan. The 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
16、, proportion, t-score, z-score, etc.) described in the analysis plan.(4) Interpret 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 ErrorsTwo types of errors can result
17、 from a hypothesis test.Type I error. A Type I error occurs when the researcher 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 .Type II error. A Type II error oc
18、curs when the researcher fails to reject a null hypothesis that is false. The probability of committing a Type II error is called beta, and is often denoted by . The probability of not committing a Type II error is called the power of the test.5、Decision RulesThe analysis plan includes decision rule
19、s for rejecting the null hypothesis. In practice, statisticians 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
20、 is equal to S. The P-value is the probability of observing 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 stati
21、stic falls within the region of acceptance, the null hypothesis 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 stati
22、stic falls within the region of rejection, the null hypothesis is rejected. In such cases, we say that the hypothesis has been rejected at the 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 that illustrate each approach.
