Chapter 2 Experimental error and data process

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计算机体系结构量化研究方法英文版第四版教学设计 (3)

Teaching Design for Quantitative Research Methods in Computer Architecture, 4th Edition IntroductionComputer architecture is the study of the design and organization of computer systems. As the field has evolved, so too have the tools and techniques used for research in computer architecture. This document outlines a teaching design for the fourth edition of the book Quantitative Research Methods in Computer Architecture, which provides an overview of the quantitative research methods most commonly used in the field.ObjectivesThe objectives of this teaching design are:1.To provide an overview of the fundamental concepts andprinciples of quantitative research methods in computerarchitecture.2.To enable students to design and perform experiments usingappropriate research methods.3.To help students develop critical thinking skills toevaluate research findings.Course OutlineThe course is divided into the following chapters:1.Introduction to Quantitative Research Methods in ComputerArchitecture2.Research Design and Experimental Design3.Sampling4.Measurement5.Data Analysis and Statistics6.Reporting Research FindingsChapter 1: Introduction to Quantitative Research Methods in Computer ArchitectureThis chapter provides an introduction to the course. It introduces the terminology and concepts commonly used in quantitative research, and the reasons for using quantitative research methods in computer architecture. It also reviews the different kinds of research questions that can be addressed using quantitative methods.Chapter 2: Research Design and Experimental DesignIn this chapter, students will learn about research design and experimental design. This chapter will cover topics such as identifying research questions, choosing experimental units, selecting the appropriate type of design, and choosing an experimental group and control group.Chapter 3: SamplingThis chapter covers the topic of sampling. Students will learn about different types of sampling methods, including random, stratified, and systematic sampling, and how to choose the appropriate sampling method based on their research questions.Chapter 4: MeasurementIn this chapter, students will learn about measurement and the different types of measurement scales used in quantitative research. They will also learn about the criteria for selecting appropriate measures and techniques for measuring different aspects of computer architecture.Chapter 5: Data Analysis and StatisticsIn this chapter, students will learn about data analysis and statistics. They will learn how to use statistical software to analyze data, conduct descriptive statistics, and use inferential statistics to test hypotheses.Chapter 6: Reporting Research FindingsThe final chapter of the course focuses on reporting research findings. Students will learn how to prepare reports, present findings to different audiences, and deal with ethical issues related to reporting research.Course RequirementsStudents will need to:1.Attend all lectures and participate in class discussions.plete all assigned readings before class.3.Participate in group discussions and group assignments.4.Write a final research paper on a topic related to thecourse.ConclusionThis teaching design provides a comprehensive overview of the quantitative research methods commonly used in computer architecture. Through this course, students will learn the theory and practical skills necessary to design and perform experiments using appropriate research methods. By the end of the course, students will be able to interpret, analyze, and report on research findings in a clear and concise manner.。

APES_Chapter_2_Science_Matter_Energy_and_Systems_2010-09

• Based on the assumption that events in the natural
Science
world follow orderly cause-and-effect patterns that can be understood through careful observation, measurements, experimentation, and modeling.
Concept
2-1 Scientists collect data and develop theories, models, and laws about how nature works. – endeavor to discover how nature works and to use that knowledge to make predictions about what is likely to happen in nature.
• Studies how climate systems work, document past
climate changes, and project future changes.
The 4th IPCC report, 2007 • Very likely (90-99% probability) that the
story
• Polynesians arrived about 800 years ago
• Population may have reached 3000
• Used trees in an unsustainable manner, but rats
may have multiplied and eaten the seeds of the trees

伍德里奇计量经济学英文各章总结

CHAPTER 1TEACHING NOTESYou have substantial latitude about what to emphasize in Chapter 1.I find it useful to talk about the economics of crime example (Example and the wage example (Example so that students see, at the outset, that econometrics is linked to economic reasoning, even if the economics is not complicated theory.I like to familiarize students with the important data structures that empirical economists use, focusing primarily on cross-sectional and time series data sets, as these are what I cover in a first-semester course. It is probably a good idea to mention the growing importance of data sets that have both a cross-sectional and time dimension.I spend almost an entire lecture talking about the problems inherent in drawing causal inferences in the social sciences. I do this mostly through the agricultural yield, return to education, and crime examples. These examples also contrast experimental and nonexperimental (observational) data. Students studying business and finance tend to find the term structure of interest rates example more relevant, although the issue there is testing the implication of a simple theory, as opposed to inferring causality. I have found that spending time talking about these examples, in place of a formal review of probability and statistics, is more successful (and more enjoyable for the students and me).CHAPTER 2TEACHING NOTESThis is the chapter where I expect students to follow most, if not all, of the algebraic derivations. In class I like to derive at least the unbiasedness of the OLS slope coefficient, and usually I derive the variance. At a minimum, I talk about the factors affecting the variance. To simplify the notation, after I emphasize the assumptions in the population model, and assume random sampling, I just condition on the values of the explanatory variables in the sample. Technically, this is justified by random sampling because, for example, E(u i|x1,x2,…,x n) =E(u i|x i) by independent sampling. I find that students are able to focus on the key assumption and subsequently take my word about how conditioning on the independent variables in the sample is harmless. (If you prefer, the appendix to Chapter 3 does the conditioning argument carefully.) Because statistical inference is no more difficult in multiple regression than in simple regression, I postpone inference until Chapter 4. (This reduces redundancy and allows you to focus on the interpretive differences between simple and multiple regression.)You might notice how, compared with most other texts, I use relatively few assumptions to derive the unbiasedness of the OLS slope estimator, followed by the formula for its variance. This is because I do not introduce redundant or unnecessary assumptions. For example,once is assumed, nothing further about the relationship between u and x is needed to obtain the unbiasedness of OLS under random sampling.CHAPTER 3TEACHING NOTESFor undergraduates, I do not work through most of the derivations in this chapter, at least not in detail. Rather, I focus on interpreting the assumptions, which mostly concern the population. Other than random sampling, the only assumption that involves more than population considerations is the assumption about no perfect collinearity, where the possibility of perfect collinearity in the sample (even if it does not occur in the population) should be touched on. The more important issue is perfect collinearity in the population, but this is fairly easy to dispense with via examples. These come from my experiences with the kinds of model specification issues that beginners have trouble with.The comparison of simple and multiple regression estimates – based on the particular sample at hand, as opposed to their statistical properties – usually makes a strong impression. Sometimes I do not bother with the “partialling out” interpretation of multiple regression.As far as statistical properties, notice how I treat the problem of including an irrelevant variable: no separate derivation is needed, as the result follows form Theorem .I do like to derive the omitted variable bias in the simple case. This is not much more difficult than showing unbiasedness of OLS in the simple regression case under the first four Gauss-Markov assumptions. It is important to get the students thinking about this problem early on, and before too many additional (unnecessary) assumptions have been introduced.I have intentionally kept the discussion of multicollinearity to a minimum. This partly indicates my bias, but it also reflects reality. It is, of course, very important for students to understand the potential consequences of having highly correlated independent variables. But this is often beyond our control, except that we can ask less of our multiple regression analysis. If two or more explanatory variables are highly correlated in the sample, we should not expect to precisely estimate their ceteris paribus effects in the population.I find extensive treatments of multicollinearity, where one “tests” or somehow “solves” t he multicollinearity problem, to be misleading, at best. Even the organization of some texts gives the impression that imperfect multicollinearity is somehow a violation of the Gauss-Markov assumptions: they include multicollinearity in a chapter or part of the book devoted to “violation of the basic assumptions,” or something like that. I have noticed that master’s students who have had some undergraduate econometrics are often confused on the multicollinearityissue. It is very important that students not confuse multicollinearity among the included explanatory variables in a regression model with the bias caused by omitting an important variable.I do not prove the Gauss-Markov theorem. Instead, I emphasize its implications. Sometimes, and certainly for advanced beginners, I put a special case of Problem on a midterm exam, where I make a particular choice for the function g(x). Rather than have the students directly compare the variances, they should appeal to the Gauss-Markov theorem for the superiority of OLS over any other linear, unbiased estimator.CHAPTER 4TEACHING NOTESAt the start of this chapter is good time to remind students that a specific error distribution played no role in the results of Chapter 3. That is because only the first two moments were derived under the full set of Gauss-Markov assumptions. Nevertheless, normality is needed to obtain exact normal sampling distributions (conditional on the explanatory variables). I emphasize that the full set of CLM assumptions are used in this chapter, but that in Chapter 5 we relax the normality assumption and still perform approximately valid inference. One could argue that the classical linear model results could be skipped entirely, and that only large-sample analysis is needed. But, from a practicalperspective, students still need to know where the t distribution comes from because virtually all regression packages report t statistics and obtain p-values off of the t distribution. I then find it very easy to cover Chapter 5 quickly, by just saying we can drop normality and still use t statistics and the associated p-values as being approximately valid. Besides, occasionally students will have to analyze smaller data sets, especially if they do their own small surveys for a term project.It is crucial to emphasize that we test hypotheses about unknown population parameters. I tell my students that they will be punished ifˆ = 0 on an exam or, even worse, H0: .632 they write something like H0:1= 0.One useful feature of Chapter 4 is its illustration of how to rewrite a population model so that it contains the parameter of interest in testing a single restriction. I find this is easier, both theoretically and practically, than computing variances that can, in some cases, depend on numerous covariance terms. The example of testing equality of the return to two- and four-year colleges illustrates the basic method, and shows that the respecified model can have a useful interpretation. Of course, some statistical packages now provide a standard error for linear combinations of estimates with a simple command, and that should be taught, too.One can use an F test for single linear restrictions on multiple parameters, but this is less transparent than a t test and does notimmediately produce the standard error needed for a confidence interval or for testing a one-sided alternative. The trick of rewriting the population model is useful in several instances, including obtaining confidence intervals for predictions in Chapter 6, as well as for obtaining confidence intervals for marginal effects in models with interactions (also in Chapter 6).The major league baseball player salary example illustrates the difference between individual and joint significance when explanatory variables (rbisyr and hrunsyr in this case) are highly correlated. I tend to emphasize the R-squared form of the F statistic because, in practice, it is applicable a large percentage of the time, and it is much more readily computed. I do regret that this example is biased toward students in countries where baseball is played. Still, it is one of the better examples of multicollinearity that I have come across, and students of all backgrounds seem to get the point.CHAPTER 5TEACHING NOTESChapter 5 is short, but it is conceptually more difficult than the earlier chapters, primarily because it requires some knowledge of asymptotic properties of estimators. In class, I give a brief, heuristic description of consistency and asymptotic normality before stating the consistency and asymptotic normality of OLS. (Conveniently, the sameassumptions that work for finite sample analysis work for asymptotic analysis.) More advanced students can follow the proof of consistency of the slope coefficient in the bivariate regression case. Section contains a full matrix treatment of asymptotic analysis appropriate for a master’s level course.An explicit illustration of what happens to standard errors as the sample size grows emphasizes the importance of having a larger sample.I do not usually cover the LM statistic in a first-semester course, and I only briefly mention the asymptotic efficiency result. Without full use of matrix algebra combined with limit theorems for vectors and matrices, it is very difficult to prove asymptotic efficiency of OLS.I think the conclusions of this chapter are important for students to know, even though they may not fully grasp the details. On exams I usually include true-false type questions, with explanation, to test the stud ents’ understanding of asymptotics. [For example: “In large samples we do not have to worry about omitted variable bias.” (False). Or “Even if the error term is not normally distributed, in large samples we can still compute approximately valid confidence intervals under the Gauss-Markov assumptions.” (True).]CHAPTER6TEACHING NOTESI cover most of Chapter 6, but not all of the material in great detail.I use the example in Table to quickly run through the effects of data scaling on the important OLS statistics. (Students should already have a feel for the effects of data scaling on the coefficients, fitting values, and R-squared because it is covered in Chapter 2.) At most, I briefly mention beta coefficients; if students have a need for them, they can read this subsection.The functional form material is important, and I spend some time on more complicated models involving logarithms, quadratics, and interactions. An important point for models with quadratics, and especially interactions, is that we need to evaluate the partial effect at interesting values of the explanatory variables. Often, zero is not an interesting value for an explanatory variable and is well outside the range in the sample. Using the methods from Chapter 4, it is easy to obtain confidence intervals for the effects at interesting x values.As far as goodness-of-fit, I only introduce the adjusted R-squared, as I think using a slew of goodness-of-fit measures to choose a model can be confusing to novices (and does not reflect empirical practice). It is important to discuss how, if we fixate on a high R-squared, we may wind up with a model that has no interesting ceteris paribus interpretation.I often have students and colleagues ask if there is a simple way to predict y when log(y) has been used as the dependent variable, and to obtain a goodness-of-fit measure for the log(y) model that can be compared with the usual R-squared obtained when y is the dependent variable. The methods described in Section are easy to implement and, unlike other approaches, do not require normality.The section on prediction and residual analysis contains several important topics, including constructing prediction intervals. It is useful to see how much wider the prediction intervals are than the confidence interval for the conditional mean. I usually discuss some of the residual-analysis examples, as they have real-world applicability.CHAPTER 7TEACHING NOTESThis is a fairly standard chapter on using qualitative information in regression analysis, although I try to emphasize examples with policy relevance (and only cross-sectional applications are included.).In allowing for different slopes, it is important, as in Chapter 6, to appropriately interpret the parameters and to decide whether they are of direct interest. For example, in the wage equation where the return to education is allowed to depend on gender, the coefficient on the female dummy variable is the wage differential between women and men at zero years of education. It is not surprising that we cannot estimatethis very well, nor should we want to. In this particular example we would drop the interaction term because it is insignificant, but the issue of interpreting the parameters can arise in models where the interaction term is significant.In discussing the Chow test, I think it is important to discuss testing for differences in slope coefficients after allowing for an intercept difference. In many applications, a significant Chow statistic simply indicates intercept differences. (See the example in Section on student-athlete GPAs in the text.) From a practical perspective, it is important to know whether the partial effects differ across groups or whether a constant differential is sufficient.I admit that an unconventional feature of this chapter is its introduction of the linear probability model. I cover the LPM here for several reasons. First, the LPM is being used more and more because it is easier to interpret than probit or logit models. Plus, once the proper parameter scalings are done for probit and logit, the estimated effects are often similar to the LPM partial effects near the mean or median values of the explanatory variables. The theoretical drawbacks of the LPM are often of secondary importance in practice. Computer Exercise is a good one to illustrate that, even with over 9,000 observations, the LPM can deliver fitted values strictly between zero and one for all observations.If the LPM is not covered, many students will never know about using econometrics to explain qualitative outcomes. This would be especially unfortunate for students who might need to read an article where an LPM is used, or who might want to estimate an LPM for a term paper or senior thesis. Once they are introduced to purpose and interpretation of the LPM, along with its shortcomings, they can tackle nonlinear models on their own or in a subsequent course.A useful modification of the LPM estimated in equation is to drop kidsge6 (because it is not significant) and then define two dummy variables, one for kidslt6 equal to one and the other for kidslt6 at least two. These can be included in place of kidslt6 (with no young children being the base group). This allows a diminishing marginal effect in an LPM. I was a bit surprised when a diminishing effect did not materialize.CHAPTER 8TEACHING NOTESThis is a good place to remind students that homoskedasticity played no role in showing that OLS is unbiased for the parameters in the regression equation. In addition, you probably should mention that there is nothing wrong with the R-squared or adjusted R-squared as goodness-of-fit measures. The key is that these are estimates of the population R-squared, 1 – [Var(u)/Var(y)], where the variances are the unconditional variances in the population. The usual R-squared, andthe adjusted version, consistently estimate the population R-squared whether or not Var(u|x) = Var(y|x) depends on x. Of course, heteroskedasticity causes the usual standard errors, t statistics, and F statistics to be invalid, even in large samples, with or without normality.By explicitly stating the homoskedasticity assumption as conditional on the explanatory variables that appear in the conditional mean, it is clear that only heteroskedasticity that depends on the explanatory variables in the model affects the validity of standard errors and test statistics. The version of the Breusch-Pagan test in the text, and the White test, are ideally suited for detecting forms of heteroskedasticity that invalidate inference obtained under homoskedasticity. If heteroskedasticity depends on an exogenous variable that does not also appear in the mean equation, this can be exploited in weighted least squares for efficiency, but only rarely is such a variable available. One case where such a variable is available is when an individual-level equation has been aggregated. I discuss this case in the text but I rarely have time to teach it.As I mention in the text, other traditional tests for heteroskedasticity, such as the Park and Glejser tests, do not directly test what we want, or add too many assumptions under the null. The Goldfeld-Quandt test only works when there is a natural way to order thedata based on one independent variable. This is rare in practice, especially for cross-sectional applications.Some argue that weighted least squares estimation is a relic, and is no longer necessary given the availability of heteroskedasticity-robust standard errors and test statistics. While I am sympathetic to this argument, it presumes that we do not care much about efficiency. Even in large samples, the OLS estimates may not be precise enough to learn much about the population parameters. With substantial heteroskedasticity we might do better with weighted least squares, even if the weighting function is misspecified. As discussed in the text on pages 288-289, one can, and probably should, compute robust standard errors after weighted least squares. For asymptotic efficiency comparisons, these would be directly comparable to the heteroskedasiticity-robust standard errors for OLS.Weighted least squares estimation of the LPM is a nice example of feasible GLS, at least when all fitted values are in the unit interval. Interestingly, in the LPM examples in the text and the LPM computer exercises, the heteroskedasticity-robust standard errors often differ by only small amounts from the usual standard errors. However, in a couple of cases the differences are notable, as in Computer Exercise .CHAPTER 9TEACHING NOTESThe coverage of RESET in this chapter recognizes that it is a test for neglected nonlinearities, and it should not be expected to be more than that. (Formally, it can be shown that if an omitted variable has a conditional mean that is linear in the included explanatory variables, RESET has no ability to detect the omitted variable. Interested readers may consult my chapter in Companion to Theoretical Econometrics, 2001, edited by Badi Baltagi.) I just teach students the F statistic version of the test.The Davidson-MacKinnon test can be useful for detecting functional form misspecification, especially when one has in mind a specific alternative, nonnested model. It has the advantage of always being a one degree of freedom test.I think the proxy variable material is important, but the main points can be made with Examples and . The first shows that controlling for IQ can substantially change the estimated return to education, and the omitted ability bias is in the expected direction. Interestingly, education and ability do not appear to have an interactive effect. Example is a nice example of how controlling for a previous value of the dependent variable – something that is often possible with survey and nonsurvey data – can greatly affect a policy conclusion. Computer Exercise is also a good illustration of this method.I rarely get to teach the measurement error material, although the attenuation bias result for classical errors-in-variables is worth mentioning.The result on exogenous sample selection is easy to discuss, with more details given in Chapter 17. The effects of outliers can be illustrated using the examples. I think the infant mortality example, Example , is useful for illustrating how a single influential observation can have a large effect on the OLS estimates.With the growing importance of least absolute deviations, it makes sense to at least discuss the merits of LAD, at least in more advanced courses. Computer Exercise is a good example to show how mean and median effects can be very different, even though there may not be “outliers” in the usual sense.CHAPTER 10TEACHING NOTESBecause of its realism and its care in stating assumptions, this chapter puts a somewhat heavier burden on the instructor and student than traditional treatments of time series regression. Nevertheless, I think it is worth it. It is important that students learn that there are potential pitfalls inherent in using regression with time series data that are not present for cross-sectional applications. Trends, seasonality, and high persistence are ubiquitous in time series data. By this time,students should have a firm grasp of multiple regression mechanics and inference, and so you can focus on those features that make time series applications different from cross-sectional ones.I think it is useful to discuss static and finite distributed lag models at the same time, as these at least have a shot at satisfying theGauss-Markov assumptions. Many interesting examples have distributed lag dynamics. In discussing the time series versions of the CLM assumptions, I rely mostly on intuition. The notion of strict exogeneity is easy to discuss in terms of feedback. It is also pretty apparent that, in many applications, there are likely to be some explanatory variables that are not strictly exogenous. What the student should know is that, to conclude that OLS is unbiased – as opposed to consistent – we need to assume a very strong form of exogeneity of the regressors. Chapter 11 shows that only contemporaneous exogeneity is needed for consistency.Although the text is careful in stating the assumptions, in class, after discussing strict exogeneity, I leave the conditioning on X implicit, especially when I discuss the no serial correlation assumption. As this is a new assumption I spend some time on it. (I also discuss why we did not need it for random sampling.)Once the unbiasedness of OLS, the Gauss-Markov theorem, and the sampling distributions under the classical linear model assumptions havebeen covered – which can be done rather quickly – I focus on applications. Fortunately, the students already know about logarithms and dummy variables. I treat index numbers in this chapter because they arise in many time series examples.A novel feature of the text is the discussion of how to compute goodness-of-fit measures with a trending or seasonal dependent variable. While detrending or deseasonalizing y is hardly perfect (and does not work with integrated processes), it is better than simply reporting the very high R-squareds that often come with time series regressions with trending variables.CHAPTER 11TEACHING NOTESMuch of the material in this chapter is usually postponed, or not covered at all, in an introductory course. However, as Chapter 10 indicates, the set of time series applications that satisfy all of the classical linear model assumptions might be very small. In my experience, spurious time series regressions are the hallmark of many student projects that use time series data. Therefore, students need to be alerted to the dangers of using highly persistent processes in time series regression equations. (Spurious regression problem and the notion of cointegration are covered in detail in Chapter 18.)It is fairly easy to heuristically describe the difference between a weakly dependent process and an integrated process. Using the MA(1) and the stable AR(1) examples is usually sufficient.When the data are weakly dependent and the explanatory variables are contemporaneously exogenous, OLS is consistent. This result has many applications, including the stable AR(1) regression model. When we add the appropriate homoskedasticity and no serial correlation assumptions, the usual test statistics are asymptotically valid.The random walk process is a good example of a unit root (highly persistent) process. In a one-semester course, the issue comes down to whether or not to first difference the data before specifying the linear model. While unit root tests are covered in Chapter 18, just computing the first-order autocorrelation is often sufficient, perhaps after detrending. The examples in Section illustrate how differentfirst-difference results can be from estimating equations in levels.Section is novel in an introductory text, and simply points out that, if a model is dynamically complete in a well-defined sense, it should not have serial correlation. Therefore, we need not worry about serial correlation when, say, we test the efficient market hypothesis. Section further investigates the homoskedasticity assumption, and, in a time series context, emphasizes that what is contained in the explanatory variables determines what kind of heteroskedasticity is ruled out by theusual OLS inference. These two sections could be skipped without loss of continuity.CHAPTER 12TEACHING NOTESMost of this chapter deals with serial correlation, but it also explicitly considers heteroskedasticity in time series regressions. The first section allows a review of what assumptions were needed to obtain both finite sample and asymptotic results. Just as with heteroskedasticity, serial correlation itself does not invalidate R-squared. In fact, if the data are stationary and weakly dependent, R-squared and adjusted R-squared consistently estimate the population R-squared (which is well-defined under stationarity).Equation is useful for explaining why the usual OLS standard errors are not generally valid with AR(1) serial correlation. It also provides a good starting point for discussing serial correlation-robust standard errors in Section . The subsection on serial correlation with lagged dependent variables is included to debunk the myth that OLS is always inconsistent with lagged dependent variables and serial correlation. I do not teach it to undergraduates, but I do to master’s students.Section is somewhat untraditional in that it begins with an asymptotic t test for AR(1) serial correlation (under strict exogeneity of the regressors). It may seem heretical not to give the Durbin-Watsonstatistic its usual prominence, but I do believe the DW test is less useful than the t test. With nonstrictly exogenous regressors I cover only the regression form of Durbin’s test, as the h statistic is asymptotically equivalent and not always computable.Section , on GLS and FGLS estimation, is fairly standard, although I try to show how comparing OLS estimates and FGLS estimates is not so straightforward. Unfortunately, at the beginning level (and even beyond), it is difficult to choose a course of action when they are very different.I do not usually cover Section in a first-semester course, but, because some econometrics packages routinely compute fully robust standard errors, students can be pointed to Section if they need to learn something about what the corrections do. I do cover Section for a master’s level course in applied econometrics (after the first-semester course).I also do not cover Section in class; again, this is more to serve as a reference for more advanced students, particularly those with interests in finance. One important point is that ARCH is heteroskedasticity and not serial correlation, something that is confusing in many texts. If a model contains no serial correlation, the usual heteroskedasticity-robust statistics are valid. I have a brief subsection on correcting for a known。

初一英语科学实验设计巧妙构思单选题40题

初一英语科学实验设计巧妙构思单选题40题1. In a science experiment, what should you do first?A. Record the results.B. Prepare the materials.C. Analyze the data.D. Draw a conclusion.答案：B。

解析：在科学实验中，首先应该准备材料，A 选项“记录结果”应在实验结束时进行，C 选项“分析数据”是实验后期的步骤，D 选项“得出结论”也是在实验完成后进行。

2. When doing a science experiment, which step comes after observing the phenomenon?A. Making a hypothesis.B. Designing the experiment.C. Collecting data.D. Sharing the results.答案：A。

解析：观察现象之后应提出假设，B 选项“设计实验”在提出假设之后，C 选项“收集数据”是实验过程中的步骤，D 选项“分享结果”是实验的最后一步。

3. In a chemical experiment, you need to mix two substances. What should you do next?A. Clean the equipment.B. Wait for a reaction.C. Measure the temperature.D. Write down your observations.答案：B。

解析：混合两种物质后应该等待反应发生，A 选项“清洁设备”是实验结束后的工作，C 选项“测量温度”可能在反应过程中进行，D 选项“写下观察结果”不是紧接着的步骤。

4. Before starting a physics experiment, what is very important to do?A. Check the safety rules.B. Guess the outcome.C. Borrow tools from others.D. Choose a partner.答案：A。

1-1UNCERTAINTIES and ERRORS

Errors of Measurement
There are two main types of error (uncertainty) of -

-
measurement or observation: systematic random A systematic error will result in all readings being either above or below the accepted value it cannot be eliminated by repeating measurements can be reduced by improving experimental techniques Random error results in readings being scattered around the accepted value can be reduced
Accuracy
Accuracy is concerned with how close a reading
is to true value If there is a large instrumental error, then the readings would not be accurate
measurement approaches the “true value” Accuracy depends on - the equipment used - the skill of the experimenter - the techniques involved Precision is that part of the accuracy which is within the control of the experimenter

计量经济学中英文词汇对照

Common variance Common variation Communality variance Comparability Comparison of bathes Comparison value Compartment model Compassion Complement of an event Complete association Complete dissociation Complete statistics Completely randomized design Composite event Composite events Concavity Conditional expectation Conditional likelihood Conditional probability Conditionally linear Confidence interval Confidence limit Confidence lower limit Confidence upper limit Confirmatory Factor Analysis Confirmatory research Confounding factor Conjoint Consistency Consistency check Consistent asymptotically normal estimate Consistent estimate Constrained nonlinear regression Constraint Contaminated distribution Contaminated Gausssian Contaminated normal distribution Contamination Contamination model Contingency table Contour Contribution rate Control

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检验超标(OOS)、超趋势(OOT)实验室调查管理规程

1. 制订/日期QC/主管2. 审核/日期QC/部长3. 批准/日期质量副总经理分发部门：质保部（QA）、质控部（QC）修订历史：版本号修订日期修订概述01 2020.07.02 首次制订1.0 目的本规程用于建立实验室检验结果超标及超趋势的实验室调查处理程序，指导实验室发现实验过程缺陷，进行整改并采取相应预防措施，保证检验结果的客观和准确。

2.0 范围适用于质控部（QC）检验过程中出现的检验结果超出质量标准规定（OOS）、超出正常趋势（OOT）的实验室调查处理。

不适用于以下情况：（1）GMP相关的检验室新仪器设备批准使用前的仪器和系统的验证，此阶段出现的超标及超趋势状况应在验证报告中讨论；（2）用于调整工艺参数的中间控制，如工艺控制的测试结果表明某工艺步骤没有完成，从而继续该步骤，属正常操作，不是异常测试结果；（3）稳定性研究中的强制降解实验（比如影响因素实验中的强光照射、高温、高湿实验）；（4）不适用于检验方法或药典规定已有复验/重新取样规则的检验，如：溶出度或含量均匀度的测定；但适用于按照复验规则完成复验的结果。

3.0 职责3.1 本文件由质控部（QC）负责起草，质控部（QC）部长审核，质量副总经理批准。

3.2 质保部（QA）、质控部（QC）负责本规程的贯彻实施。

3.3 QC检验员职责3.3.1检验员应确认只使用符合性能要求并经过正确校正的仪器，某些检验项目要求做系统适用性，若试验结果不符合要求，则该系统不得用于该项目检验。

3.3.2 检验员有责任注意所得到的数据，得到准确的检验结果；应明白检验过程中可能会产生的问题，对可能会导致不准确结果的问题应特别注意。

一旦发现异常的或不符合规格标准的测试结果应保留供试液，立即向QC主管/负责人报告，并在调查过程中，本着实事求是的原则同QC负责人共同执行实验室调查，并执行与实验室相关的预防及整改措施。

3.3.3如果错误是明显的，例如样品溶液溅出或样品转移不完全，检验员应立即如实记录所发生的事情，停止继续检验。

误差和分析数据处理(2)

Analytical chemistryErrors and data treatment(2)二、有效数字及运算法则2非测量所得的自然数测量次数、样品份数计算中的倍数反应中的化学计量关系各类常数测量所得的数字测量值数据计算的结果3数字位数应与分析方法的准确度及仪器测量的精度相适应4有效数字: 分析工作中实际能测得的数字1. 有效数字(significant figure)☐在记录测量数据时，只保留一位可疑数（欠准数）☐只有数据的末尾数欠准，误差是末位数的±1个单位☐有效数字位数反映了测量和结果的准确程度，决不能随意增加或减少5m ◇分析天平(称至0.1mg):12.8228g (6),0.2348g (4) , 0.0600g (3)◇千分之一天平(称至0.001g): 0.235g (3)◇1%天平(称至0.01g): 4.03g (3), 0.23g (2)◇台秤(称至0.1g): 4.0g (2), 0.2g (1)V ☆滴定管(量至0.01mL):26.32mL (4), 3.97mL (3)☆容量瓶:100.0mL (4),250.0mL (4)☆移液管:25.00mL (4);☆量筒(量至1mL或0.1mL):25mL (2), 4.0mL (2)重量分析和滴定分析允许的误差一般在±0.2%之内，各测量数据应保留四位有效数字，注意计算结果的有效数字位数6☐数字1~9均为有效数字☐数字前0不是有效数字,其他数字之间的0计入有效数字: 0.0304(3)☐数字后的0，在小数中，计入有效数字位数：0.03400(4)☐数字后的0，在整数中，含义不清楚时, 最好用指数形式表示: 1000 (1.0×103, 1.00×103, 1.000 ×103)☐很小的数字，也可以用指数形式表示，但有效数字位数需保持不变:0.000018 → 1.8 ×10-5☐变换单位时，有效数字位数需保持不变：0.0038g→3.8mg ☐数据的第一位数≥8的,可多计一位有效数字，如9.35×104(4), 95.2%(4), 8.65(4)☐对数的有效数字位数按小数部分数字的位数计,其整数部分的数字只代表原值的幂次，如pH=10.28(2), 则[H +]=5.2×10-11有效数字位数72. 有效数字运算中的修约规则尾数≤4时舍; 尾数≥6时入尾数＝5时, 若后面无数，或后面数为0, 舍5成双;若5后面还有不是0的任何数皆入四舍六入五成双例下列值修约为四位有效数字0.3247 40.3247 6 0.3247 50.3248 50.3248 500.3248 510.32470.32480.32480.32480.32480.32498禁止分次修约0.57490.570.5750.58×9运算时可多保留一位有效数字进行5.3527+2.3+0.054+3.355.35+2.3+0.05+3.35=11.0511.010标准限度值0.03%测定值0.033%修约标准偏差对标准偏差的修约，应使准确度降低统计检验时，标准偏差可多保留1-2位数参与运算表示标准偏差和RSD时，一般取两位有效数字与标准限度值比较时不修约×不合格0.03%0.2130.2211加减法:结果的绝对误差应不小于各项中绝对误差最大的数。

monocle2结果解读 -回复

monocle2结果解读-回复Monocle 2 is a well-known assessment tool used to measure various aspects of individuals' personalities, including their strengths, weaknesses, and overall potential. In this article, we will delve into the results obtained from Monocle 2 and provide a comprehensive analysis of each theme that emerged.Firstly, let's explore the theme of "Leadership Skills." Monocle 2 evaluates an individual's ability to lead and influence others towards a common goal. Results indicated that you possess strong leadership qualities, showcasing your ability to inspire and motivate others. Your charisma and excellent communication skills enable you to effectively convey your ideas and visions, gaining the trust and support of your team. Building on these strengths, you have the potential to excel in leadership roles, driving teams towards success.Next, we examine the theme of "Analytical Thinking." Monocle 2 measures one's problem-solving and critical thinking skills. The results suggest that you possess remarkable analytical abilities. With a keen eye for detail and a systematic approach, you excel in identifying patterns, understanding complex information, andformulating effective solutions. This skill set makes you an invaluable asset in fields that require logical reasoning and data analysis.Moving on to the theme of "Creativity and Innovation," Monocle 2 assesses an individual's ability to think outside the box and generate new ideas. The results indicate that you possess a high level of creativity, constantly seeking innovative solutions to challenges. Your ability to look beyond conventional methods and come up with fresh perspectives allows you to bring unique insights to projects. Leveraging this creativity, you can drive innovation and inspire others with your imaginative ideas.The theme of "Collaboration and Teamwork" evaluates one's ability to work effectively with others. Monocle 2 shows that you excel in collaborating with colleagues, valuing their input and fostering a harmonious team dynamic. Your open-mindedness and adaptability enable you to integrate varied perspectives, resulting in better outcomes. Your strong interpersonal skills and empathy make you a valuable team member, contributing to a positive work environment.Lastly, we explore the theme of "Resilience and Adaptability." Monocle 2 assesses an individual's ability to cope with stress and adapt to changing circumstances. The results indicate that you demonstrate great resilience in the face of adversity. You remain composed and composed under pressure, allowing you to find effective solutions even in challenging situations. Additionally, you showcase impressive adaptability, quickly adjusting to new environments and embracing change.In conclusion, the Monocle 2 assessment provides valuable insights into an individual's personality traits, strengths, and areas for improvement. Your leadership skills, analytical thinking, creativity, collaboration, and resilience all contribute to a well-rounded and high-potential individual. By leveraging these strengths and continuing to develop your areas of improvement, you are poised for success in various professional arenas.。

分析化学英文课件02误差与数据处理 Errors and Data Treatment

§2.4 Ways of Expressing Precision §2.5 The Confidence Limit §2.6 Rejection of a Result §2.7 Significant Figures and
Computation Rules
§2.1 Errors in Quantitative Analysis §2.1.1 Systematic Errors
CV% = S / X Standard deviation is more accurate and scientific than average deviation.
Example: two sets of experimental data
1． X-X： 0.11, -0.73, 0.24, 0.51,
2. Precision──the degree of agreement between the
replicate measurements of the same quantity Precision is expressed by deviation
Deviation is the difference between the individual measurement and the mean of the measurement
lim X n
2. When the measurement time is finite
Standard deviation：
s X X 2 /n 1
The standard deviation is sometimes expressed as the relative standard deviation, which is often called the coefficient of variation(CV)

机械工程学专业词汇英语翻译(E)2

机械工程学专业词汇英语翻译(E)2energy line 能量线energy loss 能量损耗energy metabolism 能量代谢energy migration 能量迂移energy momentum flux 能量动量通量energy momentum tensor 能量动量张量energy of absorption 吸收能energy of attachment 附着能energy of combustion 燃烧能energy of interaction 相互酌能energy of thermal motion 热运动能量energy of turbulence 湍淋energy of vibration 振动能量energy operator 能量算符energy oscillation 能量振荡energy output 能量输出energy principle 能量原理energy relaxation 能量弛豫energy resolution 能量分辨率energy source 能源energy spectrum 能谱energy spectrum equation of turbulence 湍淋谱方程energy storage 蓄能energy surface 能面energy transfer 能量传输energy unit 能单位engine power 发动机功率engine speed 发动机转速engineering fluid mechanics 工程铃力学engineering system of units 工程单位制engineering unit 工程单位engler degree 恶勒度engler viscosimeter 断粘度计enlargement 放大enlargement of pipe 管扩张enlargement scale 放大标度enrichment 浓缩entering 入射enthalpy 焓enthalpy of combustion 燃烧焓enthalpy of mixing 混合焓entrainment 卷入entrance loss 进口损失entrance pressure 进口压力entrance velocity 进口速度entropic efficiency 熵效率entropic wave 熵波entropy 熵entropy balance equation 熵平衡方程entropy elasticity 熵弹性entropy equation 熵方程entropy flow 熵流entropy increase 熵增加entropy inequality 熵不等式entropy layer 熵层entropy of evaporation 汽化熵entropy of formation 形成熵entropy of melting 熔融熵entropy of mixing 混合熵entropy wave 熵波envelope surface 包络面envelope velocity 包络速度environment 环境environment temperature 周围温度environmental aerodynamics 环境空气动力学environmental conditions 环境条件epicenter 震中epicycloidal motion 外摆线运动equal armed lever 等臂杠杆equal energy source 等能源equalization 均衡equalization of concentration 浓度均衡equalization of potential 位势均衡equally distributed 均匀分布的equating 均衡equation of compatibility 协到程equation of continuity 连续性原理equation of equilibrium 平衡方程equation of five moments 五力矩方程equation of heat balance 热平衡方程equation of hydrodynamics 铃动力学方程equation of hydrostatics 铃静力学方程equation of motion 运动方程equation of radiative transfer 辐射传递方程equation of the vibrating string 弦振动方程equations of gravitational field 引力场方程equations of gyroscopic motion 陀螺仪运动方程equatorial moment of inertia 轴惯性矩equiangular 等角的equiangular spiral 等角螺线equidensity 等密度equidimensional 等量纲的equidistribution 等分布equilbrium state 平衡态equilibrant force 补偿力equilibrating force system 平衡力系equilibrium 平衡equilibrium conditions 平衡条件equilibrium constant 平衡常数equilibrium criterion 平衡判据equilibrium diagram 平衡状态图equilibrium flow 平衡流equilibrium form 平衡形式equilibrium gradient 平衡梯度equilibrium momentum 平衡动量equilibrium of couples 力偶平衡equilibrium of forces 力平衡equilibrium partial pressure 平衡分压力equilibrium point 平衡点equilibrium process 平衡过程equilibrium state 平衡态equilibrium structure 平衡结构equilibrium surface 平衡面equilibrium surface tension 平衡表面张力equilibrium system 平衡系equilibrium tide 平衡潮equilibrium time 平衡时间equilibrium value 平衡值equilibrium vapor pressure 平衡蒸气压equipartition law 均分定律equipartition of energy 能量均分equiphase surface 等相面equipollent vectors 等效矢量equipotential line 等位线equipotential surface 等位面equivalence of mass and energy 质能等效equivalence principle 等效原理equivalence relation 等价关系equivalent bonds 等效结合equivalent couple 等值力偶equivalent damping 等价阻尼equivalent diameter 等效直径equivalent force systems 等效力系equivalent load 等效负载equivalent mass 等效质量equivalent permeability 当量渗透性equivalent roughness 等效粗度equivalent stopping power 等效阻止本领equivalent stress 等效应力equivalent system 等效系统equivalent thickness 等效厚度equivalent turbulence 等效湍寥equivalent twisting moment 等量扭矩equivoluminal wave 等容波erection load 装配负载erection stress 架设应力erg 尔格ergodic hypothesis 脯历经假说ergodic property 脯历经性ergodic random process 脯历经随机过程ergodic theorem 脯历经定理ergodic theory 脯历经理论erosion corrosion 侵蚀性腐蚀error function 误差函数error limit 误差限度error of division 分度误差error of graduation 分度误差error of mean square 均方误差error of measurement 测量误差escape velocity 脱离速度escape velocity from galaxy 脱离银河系的速度escape velocity from solar system 脱离太阳系的速度essential boundary condition 本质边界条件estimation 估计etalon 标准euler angle 欧拉角euler d'alembert principle 欧拉达朗伯原理euler dynamical equations 欧拉动力学方程euler equation 欧拉方程euler equation for turbomachine 欧拉涡轮机方程euler equations of hydrokinetics 欧拉铃运动方程euler gas dynamical equations 欧拉气体动力学方程euler lagrange equation 欧拉拉格朗日方程euler number 欧拉数euler static balance equation 欧拉静平衡方程euler stress tensor 欧拉应力张量euler stretching tensor 欧拉伸长张量euler theorem 欧拉定理euler turbine formula 欧拉涡轮机公式euler variable 欧拉变量eulerian coordinates 欧拉坐标eulerian correlation 欧拉相关eulerian derivative 欧拉导数eulerian difference method 欧拉差分法eulerian free period 欧拉自由周期evacuation 抽真空evanescent mode 衰减模式evanescent wave 衰减波evaporation 汽化evaporation coefficient 蒸发系数evaporation heat 蒸发热evaporation loss 蒸发损失evaporative cooling 蒸发冷却evection 出差evection tide 出差潮汐even fracture 平坦断口evolute 渐开线exact solution 精确解exactitude 精确exceptional plane 特战面excess air 过剩空气excess entropy 过剩熵excess head 超压水头excess heat 过剩热excess load 过负荷excess noise factor 过量噪声因数excess pressure of sound 声超压excess velocity 超速excessive pressure 超压exchange 交换exchange coefficient 交换系数exchange collision 交换碰撞exchange deformation 交换形变exchange diffusion 交换扩散exchange energy 交换能exchange energy density 交换能密度exchange force 交换力exchange frequency 交换频率exchange potential 交换势exchange rate 交换速率exchange resonance 交换共振exchange tensor 交换张量excitation 激发excitation energy 激发能量excitation level 激发级excitation of boundary layer 边界层激发excitation spectrum 激发谱excitation state 激发态excitation wave 激发波excited atom 受激原子excited state 激发态exciter 激振器exciting force 激发力executive device 执行机构exhaust nozzle 排气喷嘴exhaust pipe 排气管exhaust port 排出口exhaust pressure 排气压力exhaustion 排气exit 出口exit angle 出口角exit boundary point 出口边界点exit flow 出射流exit loss 出口损失exit momentum 出口动量exit pressure 出口压力exit temperature 出口温度exit track 出口轨道exit turn 出口转弯exit velocity 出口速度exosphere 外大气层exothermic 发热的expand 展开expansibility 膨胀性expansion 膨胀expansion coefficient 膨胀系数expansion crack 膨胀裂缝expansion curve 膨胀曲线expansion mach wave 膨胀马赫波expansion orbit 扩展轨道expansion parameter 展开参数expansion ratio 膨胀比expansion tank 膨胀水箱expansion vessel 膨胀水箱expansion wave 膨胀波expansion work 膨胀功expansive force 膨胀力expectation 期望值expected life 预期寿命expected value 期望值expected wind speed 期望风速experiment 实验experimental aerodynamics 实验空气动力学experimental check 实验检验experimental condition 实验条件experimental data 实验数据experimental error 实验误差experimental facility 实验装置experimental material 检验材料experimental method 实验法experimental point 实验点experimental result 实验结果experimental section 实验段experimental set up 实验装置experimental tests 实验检验experimental value 实验值explosion 爆炸explosion center 爆炸中心explosion chamber 燃烧室explosion equivalent 爆炸当量explosion forming 爆炸成形explosion heat 爆炸热explosion index 爆炸指数explosion limit 爆炸极限explosion line 爆破线explosion pressure 爆发压力explosion product 爆炸产物explosion theory 爆炸理论explosion wave 爆炸波explosion work 爆发功explosive 炸药explosive compaction 爆炸压实explosive force 爆炸力explosive gas 爆炸气explosive material 爆炸材料explosive power 爆炸力explosive reaction 爆炸反应explosive sintering 爆炸烧结explosive theory 爆炸理论explosive welding 爆炸焊接explosive working 爆炸加工explosiveness 爆炸性exponential curve 指数曲线expulsion 排出expulsive force 斥力extended tip 伸展翼梢extensibility 可延展性extension 延伸extension fissure 膨胀裂缝extensional oscillation 纵向振荡extensional vibration 纵向振荡extensional wave 膨胀波extensometer 伸长计exterior 外部exterior ballistics 膛外弹道学exterior pressure 外压力external constraint 外部约束external crack 外表裂纹external damping 外阻尼external effect 外效应external energy 外能external excitation 外加激发external force 外力external gravitational field 外引力场external heat of evaporation 外蒸发热external load 外加载external potential energy 外势能external power 外功率external pressure 外部压力external radiation 外辐射external resistance 外阻力external rotation 外转动external virtual work 外虚功external work 外功extinction 消光extra high pressure 超高压extract 提出物extraction of gas 放气extraction turbine 抽汽式涡轮机extraordinary wave 异常波extrapolation method 外推法extreme 极值extreme fiber stress 最外纤维应力extremity 端extremum 极值extremum conditions 极值条件extrinsic load 外加载extrusion 挤压。

exampleReport

AN EXAMPLE REPORTbyCecil Dybowski, dybowski@Here you list all names of people involved, along with emailaddresses.CHEMISTRY 446Here you enter the section and group numbers.EXPERIMENT 6Here you insert the date that the report is submitted.Executive SummaryThe general format of a laboratory report is explained and illustrated. Each section is illustrated. Common errors and problems are discussed. Data analogous to those of experiment 6 are used to demonstrate a typical report structure. [NOTE: THE EXECUTIVE SUMMARY SHOULD ALWAYS BE THE LAST SECTION ONE WRITES. IT IS A SUMMARY, WHICH CANNOT BE DONE UNTIL ALL OF THE WORK OF THE EXPERIMENT AND THE WRITING OF OTHER SECTIONS IS FINISHED.] The title information and Executive Summary should not exceed one page.Text in blue font indicates text that is part of the report. Text is black is commentary on how to write the report.IntroductionWriting a laboratory report is as important as taking data. When I say “writing,” that includes the careful analysis of data and attention to the details of how the information is formatted for the ultimate reader. Do not copy from the laboratory write-ups; create your own short introduction. The introduction should be concise. It should explain the outlines of the experiment, what results have been determined, and salient points about the experiment. It should be about how your experiment worked, not some reprise of the general statements in the write-ups. Remember that an introduction “tells the reader what he/she is going to be reading.” Here is an example of a concise introduction:The infrared (IR) spectrum of CO has been analyzed to determine the fundamental constants of the molecule. The results can be expressed in terms of the rotation constant, B e , the rotation-vibration constant, αe , and the vibrational frequency. By IR spectroscopy on ground state molecules, it is not possible to determine the zeroth-order vibrational frequency, so we report the vibrational frequency, 002ννe x −. The results are consistent with data in the literature, within experimental error.The object of the introduction is to give the reader a sense of what you are doing, why you are doing it in the way you are doing the experiment, and what results you have determined. Since scientific results are considered to be independent of the observer, it is appropriate to state any differences between one’s work and that of others. It may be appropriate to give numbers at this point (as well as in a section labeled “Conclusions”, but it is not always necessary.ExperimentalThe section entitled “Experimental” generally contains information on the physical properties of the experiment, such as the type of instrumentation used, the variables controlled and those that are not controlled, and any unusual conditions. Here is an example of a section of that type.The experiment was carried out with a Nicolet Fourier transform infrared (FTIR) spectrometer. The resolution of the spectrometer was set at 1 cm -1 for all spectra. The experiment involved the accumulation of background spectra which were subtracted from the spectra of the sample to provide the response of the sample. The detector was a nitrogen-cooled cadmium-telluride detector. Each experiment resulted from the average 64 transient responses coadded, with the background spectrum being the accumulation of 64 spectra without the sample present. The data were analyzed by Fourier transformation using the software of the instrument. The data were saved to disk, and were subsequently analyzed with a spreadsheet program, in this case, Microsoft EXCEL.The section need not be long, but it should include everything about the experimental setup that the author thinks is important. While the data are usually gathered with an infrared spectrometer, the data discussed below are taken from Noggle’s book.1In a real report, one would include such things as calibration of instruments and special features. In addition, in some cases it is appropriate to discuss features such as how well the temperature was controlled (if it was or if it was necessary), barometric pressure or other pertinent experimental details such as concentrations of solutions (with an indication of calculations).Anything important in defining the experimental conditions should be stated. One should also report safety concerns in this section.Results and DiscussionTo start this section one has to refer to data. I do not write an example paragraph, but the student should be able to write out a simple explanation. In the case of the infrared spectrum, the data are the positions of absorptions read off the spectrum. In other experiments, there may not be a table of data. In some cases there may be plots of data. Note the format of a table. There is a title. Generally there is a heading for each column describing what is contained in the column (including the appropriate units), and there are entries below that. If you are using WORD or some similar word processing program, you may be able to format the table in different ways. Don’t get carried away with this sort of thing; the important thing is to convey to the reader as precisely as possible what the data are. Do not allow the word processor to split a table unless there are so many entries that is absolutely necessary.In writing each report, you have to make judgments about what things to include in the text of the report, sometimes original data, sometimes partially reduced data. Data must be accompanied by some estimate of the uncertainty. The exact form of the reported uncertainty depends on the data source. In this case, I assumed that the data were uncertain to 1 unit in the last reported digit. A difference, such as the second column, has a larger uncertainty by virtue of the rules for determining uncertainty. I show a footnote way and an in-line way; use only one. TABLE 1. PARTIAL LIST OF LINE POSITIONS IN THE SPECTRUM OF 12C16OLine Position (cm-1)a Line Position Difference (cm-1)b J J’ 2115.632 7 6 2119.681 4.049 ± 0.002 6 5 2123.700 4.019 ± 0.002 5 4 2127.684 3.984 ± 0.002 4 3 2131.633 3.949 ± 0.002 3 2 2135.548 3.915 ± 0.002 2 1 2139.427 3.879 ± 0.002 1 0 2147.084 7.657 ± 0.002 0 1 2150.858 3.774 ± 0.002 1 2 2154.599 3.741 ± 0.002 2 3 2158.301 3.702 ± 0.002 3 4 2161.971 3.670 ± 0.002 4 5 2165.602 3.631 ± 0.002 5 6a The uncertainty in the line position is ± 0.001 cm-1.b The uncertainty in the difference is ± 0.002 cm-1.Determining Associated Quantum Numbers. [NOTE THAT I CREATED A HEADING FOR THIS SUBSECTION TO MAKE IT CLEAR TO THE READER THAT I AM DISCUSSING SOMETHING SPECIAL. I DID NOT NUMBER THE SUBSECTION. Sometimes there are special considerations of data reduction. You should explain these clearly and concisely in a section of the results and discussion, as shown below.] Onedifficulty in resolving the data in the vibration-rotation spectroscopy experiment is determining the quantum numbers associated with each transition. For diatomic molecules, the J=0 ↔ J=0 transition is forbidden and will be absent from the spectrum. This makes the separation of the first transition of the R branch from the first transition of the P branch approximately twice the spacing of the other transitions (which are otherwise roughly equally spaced). Examination of the difference between the line positions (second column of Table I) reveals that the lines are not exactly equally spaced. In particular, the two transitions at 2139.427 cm -1 and 2147.084 cm -1 have a much wider separation than the others. It is reasonable to assign these two transitions to J=1→J’=0 and J=0→J’=1, one from the P branch and one from the R branch. Once that assignment is made, assigning J and J’ for each of the other transitions is straightforward, since each transition corresponds to the rd and fourth rows of Table 1.Analyzing the Branches to Obtain Parameters . [NOTE THAT A NEW SUBSECTION IS STARTED BECAUSE THIS IS ANOTHER PHASE OF THE ANALYSIS.] The energies of transition are expected to follow equations (1), where m is either J or J’, depending on the branch:)1()1()1()1(010010+−−+=∆−−++=∆m m B m m B E m m B m m B E P R ωω. (1) In this equation, the definitions of the parameters are as follows: B n is the rotational constant for the vibrational state with quantum number n and ω0 = ωe – 2x e ωe . Expansion of the first of these equations gives equation (2), a second-order equation in m :201010)()(m B B m B B E R −+++=∆ω.(2) A similar equation can be found by expanding the second equation. From a plot of ∆E R versus m , one determines the values of B 1, B 0, and ω0 from the best-fit coefficients. An EXCEL graph of the data is given in Figure 1, showing plots for the R and P branches.In EXCEL, one may arrange to show the best-fit equation on the graph, and this is done in Figure1. Note the correlation coefficient, which shows that these are excellent fits to the data. [NOTE: ALL FIGURES SHOULD BE NUMBERED CONSECUTIVELY THROUGHOUT THE REPORT. EACH FIGURE SHOULD HAVE A CAPTION BELOW IT THAT SHOULD CLEARLY STATE THE NATURE OF THE INFORMAITON IN THE FIGURE.]The coefficients in these fits give values for the rotational and vibrational parameters of carbon monoxide by a simple algebraic transformation. The results for the R branch are given below: R Branch:ω0 = 2143.3 (±0.1) cm -1B 1 + B 0 = 3.829 (±0.001) cm -1B 1 – B 0 = -0.018 (±0.001) cm -1These result in simultaneous equations for the parameters. Solving these gives:B 1 = 1.905 (± 0.0014) cm -1B 0 = 1.924 (± 0.0014) cm -1Note that uncertainties are reported for each of these values. With these numbers, the equilibrium rotational constant and the rotation-vibration coupling constant are determined:αe = B 0 – B 1 = 0.0179 (± 0.002) cm -1 (3) B e = ½ (3B 0 – B 1) = ½ (3(1.924 cm -1) – 1.905 cm -1) = 1.933 (± 0.008) cm -1. (4)The data are summarized in Table 2, along with values from the literature.TABLE 2. SUMMARY OF RESULTS FROM INFRARED SPECTROSCOPY OF 12C 16O Parameter Experimental Value Literature Value aωe – 2x e ωe 2142.2 ± 0.1 cm -12143.3 cm -1 B e 1.933 ± 0.008 cm -11.9313 cm -1 αe 0.018 ± 0.002 cm -10.01748 cm -1 R e 0.1128 ± 0.0007 nm 0.11281 nm a From Gordy, W.; Smith, W. V.; Trambarulo, R. F. Microwave Spectroscopy ; DoverPublications: New York, 1953.The Bond Length. From knowledge of B e , the parameter R e can be calculated from the definition of the equilibrium rotation constant:Ich B e 28π=, (5) where I is the moment of inertia, c is the speed of light in a vacuum, and h is Planck’s constant. Rearranging this equation, one calculates the moment of inertia of CO:2468123410*4489.1sec/10*99792458.2*3.193**8sec 10*6260755.6m kg m m joule I −=−=−−−π Since the uncertainty in the constants is much smaller than the uncertainty in the measured value of B e , only the uncertainty in this latter quantity makes a significant contribution to theuncertainty in I . One may estimate this by percentage (about 1.3%), so the result for the moment of inertia is:I = 1.4489 (± 0.019) × 10-46 kg-m 2.To determine R e requires knowledge of the reduced mass of 12C 16O. The exact masses of the two atoms can be found from standard references.2 The values arem C = 0.012000000 kg, exactlym O = 0.0159949146 kg,with an assumed uncertainty of 1 in the last digit. From these, one obtains the reduced mass: kg kg 262310*1385009.110*0221367.6*)0159949146.0012.0(0159949146.0*012.0−=+=µ Finally, the value of R e can be calculated as:m kg m kg R e 1026246101281.1101385009.1104489038.1−−−×=×−×=One may show, if the uncertainty arises only from the determination of the moment of inertia, that:I I R R ee ∆=∆21. (6) so the percentage error is one half that for the moment of inertia, or 0.7%. So, the value of the interatomic distance is:R e = 0.1128 (± 0.0007) nm.This compares favorably to the reported value of 0.11282 nm in Table 2.Theoretical Predictions of Parameters. The values of the various parameters were calculated using GAUSSIAN-98.3 The calculation was carried out in a restricted Hartree-Fock model, using the 6-31G(d) basis set. First, the bond distance was optimized. From the data generated, a plot of energy versus bond length was constructed. [At this point you may wish to insert a figure that shows the variation of energy with bond length. Do not forget to reference the figure in the text.] From the variation of energy with bond distance, the optimal distance is found to be 0.11138 nm, not too different from the experimentally determined value. The program also predicts the rotational constant for this configuration, which in this case it gave as 59.4205597 GHz. Converting this number to the standard units used throughout this report, B e = 1.982 cm -1. Again, this is a little high, compared to the value determined experimentally. TABLE 3. COMPARISON OF CALCULATED AND EXPERIMENTAL PARAMETERS FOR CARBON MONOXIDEParameter Calculated with GAUSSIAN Experimental aR e 0.1114 nm 0.1128 nm B e 1.982 cm -1 1.933 cm -1ωe2439.0 cm -1 ωe – 2x e ωe 2141.4 cm -1 a Note that I have not included uncertainties in these data. You would be expected to reportuncertainties in any experimental data that you report.In a second calculation, the harmonic frequency for this geometry was determined to be 2439.0288 cm-1. In Table 3, the experimental and theoretical results are summarized. One cannot experimentally determine the harmonic frequency from this experiment alone, so the experimental band center is given for comparison.You may include a paragraph or two with your concluding observations and comments. It is often convenient to reiterate the results in text form. Summarizing the laboratory experiment, including any problems that may have arisen, is a good practice.Discussion QuestionsIn this section, you write each of the discussion questions in order, immediately following each question by a brief answer. The length of the answer varies from question to question, and the length of this section varies from experiment to experiment.You may include references in a section at the end of the report. All references must be in the style of the ACS Style Guide. Do not put in references to Internet sites; use original books or articles as the primary reference, even if the information is gotten through the Internet. AppendicesFrom report to report, it may be necessary to append various data and/or calculations to the end of the report. As an appendix to my example report, I present some points about a report that you should consider:1.Be consistent about the style of capitalization of titles of figures, tables, and sections of areport.e the ACS Style Guide (parts of which are available on line) for the proper format ofreferences. Note that the style3.Do not use jargon or shortened forms of words in a formal report. Words like “lab” and“LN2” should not appear in a report.4.If you use abbreviations, you must use the full word the first time, followed by theabbreviation in parentheses. Subsequently you may use only the abbreviation.5.Do not “overwrite”. By that I mean that you should state results simply, in words, themeanings of which you understand clearly. Do not write a long explanation of the experimental theory or technique when a single sentence will do. Above all, do not try to use a complex word unless you are sure of the meaning. Check a dictionary to be sure of the meanings of words.6.Uncertainty is a part of the report of any measurement or calculation. Determine theuncertainty and report it as part of any parameter.7.Number figures and tables consecutively through the report.8.Tables and figures should be placed adjacent to the place of first mention. However, theymay be moved a slight distance away if that keeps one from wasting space at the bottom of a page. In general, do NOT put figures and tables into appendices. [An exception is a table of raw data that must be reported.]9.All units should be written in a table, either in each entry or as part of the title of acolumn. The first kind of entry is appropriate if you are making a table of different parameters, such as Table III of this report. For tables of numbers that are all the same, itis more appropriate to include the label as part of the title, and only put numbers as entries in the cells. An appropriate title for a column of equivalent conductivities might be Λ/(S*m2eq-1), for example.10.Data in tables should be expressed as simple numbers (1.732) or in scientific notation(1.732×1016), not in calculator notation.11.Report data only to the appropriate number of significant figures, depending on yourdata. Remember that EXCEL sometimes truncates numbers to fewer figures than appropriate, and you must correct for that truncation if you are writing a table with EXCEL into your report.12.Handwritten parts of a report are not acceptable.13.Take sufficient time to make sure that your report prints out appropriately. You cannotjust print out the report and turn it in; you should have read it over after printing to make sure that the formatting and symbols have not changed in the printing (something that does happen).14.Check for “widows,” lines such as titles that stand alone at the bottom of a page, and“orphans”, a single line of a paragraph that stands alone at the top of a page. Rearrange your report to make sure you have no widows or orphans.15.Do not let tables be broken onto two pages. This may necessitate moving the table a bitfrom its first mention. What I frequently do, if this happens, is put it either so the last line of the table is at the bottom of one page or so that that the table starts at the very top of a page. This can be done in WORD by moving the table relative to the text.References1Noggle, J. H. Physical Chemistry, 3rd Edition; Harper-Collins: New York, 1996, p. 835. [NOTE THE FORMAT OF ENDNOTES; THIS FORMAT SHOULD BE USED AT ALL TIMES.]2 For example, see Table 13.2 in Noggle, J. H. Physical Chemistry, 3rd Edition; Harper-Collins: New York, 1996.3Gaussian 98, Revision A.7, M. J. Frisch, G. W. Trucks, . B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrewski, H. A. Montgomery, Jr., R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A.D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A.D. Rabuck, K. Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, A. G. Baboul, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L . Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P. M. W. Gill, B, Johnson, W. Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-Gordon,E. S. Replogle, and J. A. Pople, Gaussian, Inc., Pittsburgh, PA, 1998.。

大学物理实验的英语教材

大学物理实验的英语教材University Physics Laboratory: English TextbookIntroduction:The aim of this English textbook is to provide comprehensive guidance and instructions for university physics laboratory experiments. The textbook covers a wide range of topics, including fundamental laws and principles, experimental techniques, data analysis, and safety precautions. By following this textbook, students will enhance their laboratory skills, develop a deeper understanding of physics concepts, and improve their English proficiency.Chapter 1: Introduction to Laboratory Equipment1.1 Laboratory Safety1.2 Basic Laboratory Equipment1.2.1 Glassware and Containers1.2.2 Measuring Instruments1.2.3 Electrical Equipment1.2.4 Advanced EquipmentChapter 2: Measurement Techniques2.1 Units and Dimensions2.2 Uncertainty and Error Analysis2.3 Measurement Tools and Techniques2.3.1 Length Measurement2.3.2 Time Measurement2.3.3 Mass Measurement2.3.4 Temperature Measurement2.3.5 Other Important MeasurementsChapter 3: Experiments on Mechanics3.1 Introduction to Mechanics3.2 Experimental Procedures for Newton's Laws3.2.1 Experiment 1: Force and Motion3.2.2 Experiment 2: Frictional Forces3.3 Experiment on Gravitation3.3.1 Experiment 3: Gravitational Force and Acceleration due to Gravity 3.4 Experiment on Simple Harmonic Motion3.4.1 Experiment 4: Pendulum MotionChapter 4: Experiments on Optics4.1 Introduction to Optics4.2 Experiments on Geometrical Optics4.2.1 Experiment 5: Reflection4.2.2 Experiment 6: Refraction4.3 Experiments on Wave Optics4.3.1 Experiment 7: Interference of Light4.3.2 Experiment 8: Diffraction of LightChapter 5: Experiments on Electricity and Magnetism 5.1 Introduction to Electricity and Magnetism5.2 Experiments on DC Circuits5.2.1 Experiment 9: Ohm's Law and Resistors5.2.2 Experiment 10: Kirchhoff's Laws and DC Circuits 5.3 Experiments on Magnetism and Electromagnetism 5.3.1 Experiment 11: Magnetic Fields and Forces5.3.2 Experiment 12: Electromagnetic Induction Chapter 6: Experiments on Modern Physics6.1 Introduction to Modern Physics6.2 Experiments on Atomic and Nuclear Physics6.2.1 Experiment 13: Radioactivity and Half-Life6.2.2 Experiment 14: Atomic Spectra and Energy Levels 6.3 Experiments on Quantum Mechanics6.3.1 Experiment 15: Wave-Particle Duality6.3.2 Experiment 16: Photoelectric EffectChapter 7: Data Analysis and Error Propagation7.1 Data Collection and Recording7.2 Data Analysis Techniques7.3 Graphing and Curve Fitting7.4 Error Propagation and ReportingChapter 8: Laboratory Reports and Presentation8.1 Structure of a Laboratory Report8.2 Writing Style and Language8.3 Presenting Experimental Results8.4 Peer Review and FeedbackConclusion:This English textbook for university physics laboratory experiments offers a comprehensive guide for students to conduct practical experiments effectively. With a strong emphasis on safety, accurate measurements, data analysis, and clear reporting, the textbook equips students with the necessary skills to excel in the laboratory. By using this textbook, students will enhance their understanding of physics concepts, improve their English proficiency, and become adept researchers in the field of physics.。

实验计划数据收集工具及实验步骤

实验计划数据收集工具及实验步骤As a researcher, one of the most important aspects of conducting experiments is the collection of data. Without accurate and reliable data, the results of an experiment may be skewed or even meaningless. In order to collect data effectively, it is essential to have a well-thought-out experimental plan and the right tools for data collection.作为一名研究者，进行实验的最重要方面之一是数据的收集。

如果没有准确可靠的数据，实验的结果可能会被歪曲甚至毫无意义。

为了有效地收集数据，需要有深思熟虑的实验计划以及正确的数据收集工具。

The first step in creating an experimental plan is to clearly define the research question or hypothesis. This will help guide the rest of the experimental design, including the selection of variables, the choiceof experimental methods, and the identification of potential sources of error. By clearly defining the research question, researchers can ensure that their experiments are focused and purposeful.创建实验计划的第一步是明确定义研究问题或假设。

生物统计学-Biostatistics

1.Make a more reasonable hypotheses about life sciences.
2.Make reasonable investigation and experimental design in order to verify the hypothesis.
3.Have ability to use correct statistical methods to process data from surveys and experiments.
• Chapter 3 Basic Knowledge of Probability and Probability Distribution
• Chapter 4 Principles and Methods of Statistical Inference
• Chapter 5 Principles and methods of χ^2 test
Syllabus ofBiotechnologyat Haide College
Biostatistics
Description
This course is a compulsory course for all majors of Life College. It provides a broad introduction of principles and methods to reveale the intrinsic characteristics and laws of things under incomplete information conditions, including parameter estimation, hypothesis testing, correlation and regression analysis, half-validity, investigation and experimental design.

涵道风扇矢量推进系统气动特性研究

南京航空航天大学硕士学位论文涵道风扇矢量推进系统气动特性研究姓名：张德先申请学位级别：硕士专业：飞行器设计指导教师：陈仁良20070601南京航空航天大学硕士学位论文摘要涵道风扇矢量推进系统可以有效地提升复合式直升机的最大飞行速度，改善直升机的操纵性能，在复合式高速直升机中具有广泛的应用前景。

然而由于其空气动力学特性极为复杂，目前尚没有完善的理论计算方法。

本文通过试验和计算流体力学(CFD)技术对涵道风扇矢量推进系统的气动特性进行详细的研究。

第二章介绍了涵道风扇矢量推进系统气动特性试验研究，利用涵道风扇矢量推进系统试验模型对涵道风扇矢量推进系统在悬停（无风）状态下的气动力和力矩进行了详细的测量，研究了几何设计参数对涵道风扇矢量推进系统气动特性的影响，获得了一些涵道风扇矢量推进系统特有的气动现象。

第三章首先建立了涵道风扇系统气动特性的数值模拟计算方法，并通过试验结果和数值计算结果的对比验证数值计算方法的有效性。

然后在此基础上建立了涵道风扇矢量推进系统气动特性的数值分析计算模型，并通过数值计算结果和第二章试验结果的对比验证了该模型的合理性。

最后将该方法推广到斜流情况下涵道风扇矢量推进系统的气动力数值计算，并对其各部件间的相互作用机理进行了深入的研究。

关键词：复合式高速直升机，涵道风扇矢量推进，CFD，动量源方法，气动特性ABSTRACTVectored Thrust Ducted Propeller (VTDP) has been promising to be equipped on compound helicopters because it is proved to be an effective way in enhancing the maximum velocity and handling performance of the compound helicopters. However, due to the complexity of the aerodynamics of the VTDP, the theory of the VTDP is far from complete. This thesis is aimed to resolving the aerodynamic problem of the VTDP by both experimental investigation and CFD (Computational Fluid Dynamics) technique.In chapter 2, the experiment on aerodynamics of the model VTDP and the important results are presented in detail. A test VTDP model was developed and the aerodynamics forces and moments were measured in axial flow condition to investigate the aerodynamic characteristics and the influences of design parameters.In chapter 3，a numerical simulation model is developed firstly for the ducted fan system which is the key step for further research into the VTDP. The capability of this numerical model is validated by the comparison between the calculation results and available experimental data. Based on the CFD model of ducted fan developed, a numerical model of the model VTDP is developed and the capability of this numerical model is demonstrated by the comparison between the calculation and the experimental data in chapter 2. Finally, the numerical model of the VTDP is extended to analysis the aerodynamic characteristics of VTDP in the oblique flow condition as well as the interactions among the components of the VTDP.Keywords: compound helicopter, vectored thrust ducted propeller, CFD, momentum-source method, aerodynamic characteristics图表清单图1.1 SH-60复合式高速直升机 (1)图2.1 试验装置 (9)图2.2 试验模型各个部件分解及装配情况 (10)图2.3 修改前后的涵道翼型形状 (11)图2.4 孤立风扇和涵道风扇及涵道风扇矢量推进系统推力的对比 (12)图2.5 系统推力随垂直舵面偏角的变化 (14)图2.6 系统侧向力随垂直舵面偏角的变化 (16)图2.7 系统偏航力矩随垂直舵面偏角的变化 (17)图2.8 系统俯仰力矩随垂直舵面偏角的变化 (19)图2.9 系统推力随水平舵面偏角的变化 (20)图2.10 系统侧向力随水平舵面偏角的变化 (21)图2.11 系统滚转力矩随水平舵面偏角的变化 (22)图2.12 系统偏航力矩随水平舵面偏角的变化 (23)图2.13 系统俯仰力矩随水平舵面偏角的变化 (25)图2.14 风扇轴向位置对系统气动力的影响 (29)图2.15 不同涵道唇口形状对系统推力的影响 (30)图3.1 CFD求解的一般步骤 (34)图3.2 示意输运方程离散方法的控制体 (36)图3.3 桨叶剖面来流图 (39)图3.4 FAN边界条件 (41)图3.5 涵道风扇数值计算模型 (42)图3.6 涵道风扇数值计算模型的网格划分 (43)图3.7 涵道风扇系统的风轴系和体轴系及方位角的定义 (45)图3.8 涵道风扇升力系数随迎角的变化 (46)图3.9 涵道风扇推力系数随迎角的变化 (46)图3.10 涵道风扇俯仰力矩系数随迎角的变化 (47)图3.11 风扇推力与总推力之比随迎角的变化 (48)图3.12 风扇功率系数随迎角的变化 (48)图3.13 涵道壁面静压分布（V=30m/s） (49)图3.14 桨叶几何参数 (51)南京航空航天大学硕士学位论文图3.15 涵道风扇矢量推进系统的数值计算模型 (52)图3.16系统迎角和方位角及体轴系中作用力方向的定义（俯视图） (52)图3.17 涵道风扇矢量推进系统数值计算模型的网格划分 (56)图3.18 系统推力随垂直舵面偏角的变化（V=0m/s） (58)图3.19 系统侧向力随垂直舵面偏角的变化（V=0m/s） (58)图3.20 系统滚转力矩随垂直舵面偏角的变化（V=0m/s） (59)图3.21 系统偏航力矩随垂直舵面偏角的变化（V=0m/s） (59)图3.22 系统俯仰力矩随垂直舵面偏角的变化（V=0m/s） (60)图3.23 轴向力随垂直舵面偏角的变化（V=0m/s） (61)图3.24 侧向力随垂直舵面偏角的变化（V=0m/s） (61)图3.25垂直舵面偏转对涵道壁面静压分布的影响(V=0m/s) (63)图3.26悬停状态垂直舵面偏转时涵道内的静压分布（Pa，水平剖面）..63 图3.27 风扇转速对系统推力的影响（舵面不偏转） (64)图3.28 涵道推力与风扇推力的关系 (64)图3.29 轴向力随垂直舵面偏角的变化关系（V=10m/s,α=0o） (65)图3.30 轴向来流对涵道壁面静压的影响（φ＝90o,舵面不偏转） (66)图3.31 侧向力随垂直舵面偏角的变化关系（V=10m/s,α=0o） (66)图3.32 轴向力随垂直舵面偏角的变化关系（V=10m/s,α=30o） (67)图3.33 侧向力随垂直舵面偏角的变化关系（V=10m/s,α=30o） (68)图3.34 V=10m/s,α=0o时的尾流流场（m/s，舵面不偏转） (68)图3.35 V=10m/s,α=30o时的尾流流场(m/s，舵面不偏转） (69)表2.1 试验模型主要参数尺寸 (10)表2.2 主要试验状态 (11)表3.1 算例涵道风扇模型的主要参数尺寸 (42)表3.2 涵道风扇矢量推进系统的数值计算状态 (57)承诺书本人郑重声明：所呈交的学位论文，是本人在导师指导下，独立进行研究工作所取得的成果。

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2.1 Experimental Error in analytical chemistry
1.Error（误差）：（误差）：difference between measured ）： value to the true value
E=x-xT (absolute), Er=E/xT (relative)
2.2 Significant figures p45 2.2.1 what is significant figures? The number of significant figures is the minimum number of digits needed to write a given value in scientific notation(符号，记号）without loss of accuracy. How many significant figures are there in the following numbers? 25.20, 1.4207 × 102 , 0.0106, 92500
The power 10 has no influence on the number of figures that should be retained pH, pM, logK 等对数值，有效数字取决于尾数（小数部分）的位数，整数部分只代表方次。
2.3 propagation of uncertainty(random error) Suppose that you determine the density of a mineral by measuring its mass (4.635±0.002g) and volume (1.13±0.05mL). Density is mass per unit volume: 4.635g/1.13mL=4.1018g/mL. The uncertainties in measured mass and volume are ±0.002g and ±0.05mL, but what is the uncertainty in computed density?? The following discussion applies only to random error. (we assume systematic error has been detected and corrected).
Percent relative uncertainty=0.041÷3.06×100=1.3% 3.06(±0.04) absolute uncertainty 3.06(±1%) relative uncertainty
2.3 propagation of uncertainty (continued) Multiplication and division First, convert all uncertainties to percent relative uncertainties; then, calculate the error of product as follows
2.Deviation（偏差）:difference between measured （偏差） value to mean value
d = x−x
平均偏差
∑ d=
x−x n
相对平均偏差
d d r = × 100% x
Definition（continued）
3. standard deviation标准偏差标准偏差
Chapter 2 Experimental Error and Statistics (Key points)
1. Experimental Error in analytical chemistry 2. Significant figures 3. Propagation of uncertainty Propagation of uncertainty 4. Gaussian distribution 5. Confidence interval 6. Comparison of means with student’s t test 7. Comparison of standard deviation with the F test 8. Some tests for bad data 9. Calibration methods
1.76 (± 0.03) ← e1 ＋ 1.89 (± 0.02) ← e2 － 0.59 (± 0.02) ← e3 ± 3.06 (± e4) Uncertainty equation (add/sub):
2 2 e4 = e12 + e2 + e3
e4 = 0.032 + 0.022 + 0.022 = 0.041
Chapter 2 Experimental Error and Statistics (误差及其数据处理) Every measurement has some uncertainty— there is no way to measure the “true value” of anythingБайду номын сангаас Conclusions can be expressed with a high or a low degree of confidence, but never with complete certainty.
The analytical chemist as an expert archer….
Definition（continued）
5. Systematic error and random error p49－50 系统误差和随机误差 Systemetic error: arises from a flaw in a equipment or the design of an experiment Classification-method, instrument, operation, subjective error Key feature: reproducible; one-dimensional, can be discovered and corrected. Ways to detect systemetic error: p 50
Definition（continued）
5. Systematic error and random error p49－50 系统误差和随机误差 Random error: arises from effects of uncontrolled variables in the measurements Random error results from: reading a scale; random electronic noise in an instrument Key feature: positive and negative fluctuation occur with approximately equal frequency and can not be completely eliminated.
2.3 propagation of uncertainty(continued) Addition and subtraction The uncertainty in the answer is obtained from the absolute uncertainties of the individual terms. Relative uncertainty can be found at the end of the calculation.
The first uncertainty figure of the answer is the last significant figure - the real rule for significant figures!!
2.2 Significant figures (continued) 2.2.2 significant figures in arithmetic(算术） Addition and subtraction： Express all numbers with the same exponent(指数） and align all the numbers with respect to the decimal point. Round off the answer according to the number of decimal place in the number with the fewest decimal places.
2.2 Significant figures (continued)
Multiplication and division We are normally limited to the number of digits contained in the number with the fewest significant figures.以有效数字位数最少的那个数据为准。 4.3179×1012 ×3.6 ×10-19 1.6 ×10-6 34.60 ÷2.46287 14.05
s= ( x − x) 2 ∑ n −1
s2 =
( x − x) 2 ∑ n −1
，variance方差
4. Precision and accuracy 精密度和准确度精密度和准确度p51 Precision: describes the reproducibility of a result. Accuracy: describes how close a measured value to a “true” value
Look at the text in p 46- Fig 3-1, what’s the values of absorbance and transmittance in the position of needle? There is uncertainty in any measured quantity, even if the measuring instrument has a digital readout that does not fluctuate Some numbers are exact – with an infinite number of significant digits.