Evidence Based Reasoning / Statistical Literacy Teaching Statistics and Econometrics

Contents

I. Introduction
1.1 Purpose of the Paper

II. Main Part
2.1 Main Problems in Teaching Statistics and Econometrics
2.2 New Initiatives in Teaching Statistics and Econometrics
2.3 Models of Teaching Statistics and Econometrics
2.3.1 Traditional Instruction
2.3.2 Hybrid Internet-Based Instruction
2.3.3 Internet-Based Instruction
2.3.4 Comparison of the Three Models

III. Conclusion

Bibliography

I. Introduction

Outdated education models, technological advances and increasing enrollment of students have led to involve Web-based education in some economics classes of various universities. The options range from Web-based applications in traditional classes to complete online courses without any face-to-face contact. Two facts are stressed with special regard to statistics and econometrics classes in this paper. These are, firstly, the problems tutors^[1] have to teach students the essential contents of the courses (this refers also to many aspects of economic undergraduate courses) and, secondly, the problems tutors face to find the right way to teach by using the possibilities the technological advance offers to education methods.

1.1 Purpose of the Paper

Given that only a few written sources on teaching statistics and econometrics exist (Becker and Greene 2001) and having in mind that econometrics is part of the economics education, articles regarding research in overall economic education will also be analyzed in this paper. Due to the latest articles the aim of the paper is to compare and combine the findings of different studies carried out in order to find the best way of teaching econometrics and statistics. After this short introduction the main part of the paper gives an overview of the conventional way of teaching statistics and econometrics and indicates the problems involved. This is followed by a section on new initiatives in the education of econometrics and statistics. Thereinafter, three forms of teaching – traditional (off-line) instruction, hybrid Internet-based instruction and Internet-based instruction – will be dealt with to see in how far the proposed initiatives already have been applied on the subjects. In the last part a conclusion is drawn to summarize the main findings and to show the direction of future teaching in this field. As it already became clear in the headline subject matter of this paper is the aspect of teaching and not learning (which will be analyzed by a fellow student). Thus, all aspects of learning statistics and econometrics, such as the Ten Principles of Learning Statistics developed by Garfield (1995) or the study of Johnson (2005), are omitted; the work deals exclusively with the perspectives of the teaching institutions and not of those on the receiving end of the instruction.

II. Main Part

2.1 Main Problems in Teaching Statistics and Econometrics

Sowey (1983, p. 257) defined econometrics as “[…] the discipline in which one studies theoretical and practical aspects of applying statistical methods to economic data for the purpose of testing economic theories (represented by carefully structured models) and of forecasting and controlling the future path of economic variables.” Thus, it is not enough to provide the students with the theoretical knowledge, it is also necessary to give them appropriate practical examples so that they can use the theoretical key concepts for quantitative analyses on their own. In opposition to that stands the fact that Principles instructors in economics spent most time in class lecturing, leaving insufficient time for practical activities (Becker and Watts 2001). Becker and Greene (2001) analyzed the essential topics to be taught to undergraduates in statistics and econometrics and additionally point out the problems in the traditional instruction. Next to problems related directly to specific statistical topics, there are also general problems: (i) abstract and dry textbooks and (ii) use of problem sets^[2] of made up data and unrealistic numerical examples. Although an immense supply of statistic textbooks exists, there is little attention paid on the applications of concepts and procedures. To engage students more in class it is necessary to use real-world examples, which can be obtained from history, news, popular culture, the classroom itself and the students’ lives. Especially current events in the news can be used to show the importance of economics and statistics in real situations (compare also Hansen et al. 2002 and Hamermesh 2002). Articles on active learning techniques, as published in the Journal of Statistics Education and the Journal of Economic Education (JEE), can also help to teach more actively in classroom. The high importance of mathematics in statistics and econometrics in comparison to other economics classes may deter some students from signing up because instructors view students’ skills in numerical calculations and algebra as extremely important, in graphs as important and in calculus as to some extent important (Becker and Watts 2001). Becker and Greene go on with a detailed description of the necessary undergraduate concepts and skills to be taught, which seem to be difficult to many students. These are probability, sampling and sampling distributions, hypothesis testing, regression to the mean, motivating the least squares estimator and alternatives to least squares. Nonetheless, basic subject in any statistics and econometrics undergraduate course has to be calculation and use of descriptive statistics (mean, median, standard deviation, etc.), as well as teaching of basic skills related to data management, computation and graphing. The more difficult concepts will be introduced here in shortform separately. Concerning probability many students are able to repeat basic formulas and rules but the distinction between marginal, joint and conditional probabilities in applications are from time to time difficult, even for instructors. Here the authors recommend sources of examples for such cases, such as Marilyn vos Savant’s weekly Parade magazine column and a book by Paulos (1995). Regarding sampling students often have problems to understand that from sample data calculated statistics used to estimate corresponding population parameters are themselves random, with in the sampling distribution of the statistic, which is a histogram, represented values. Due to the importance of this concept, it is inappropriate to let the students work with an imaginable construct while they could develop a histogram of possible values of a sample statistic themselves through group experiments in computer labs. One important thing they would learn by experimenting on their own, is the difference between the law of large numbers^[3] and the central limit theorem^[4]. Thus, students could see how a standard normal random variable (with mean of zero and standard deviation of one) that does not degenerate to a single value, as the sample size increases infinitely, is created through the standardization of a sample mean. For the students in the computer lab bootstrapping is a natural real-world extension of their work with sample distributions. Here from the original sample repeated samples are taken (with replacement) and from these the distribution of the desired descriptive statistic is deduced. Without requiring further assumptions about the underlying distribution of the population or the context of the considered real-world problem this sampling distribution is used to construct an interval estimate of the population parameters of interest. Consequently, the use of bootstrap as a teaching tool provides students with early and practical experience to a strong research tool. Regarding hypothesis testing many students have problems with the understanding of the tradeoffs between Type I^[5] and Type II^[6] errors. Also the debate over the application of statistical significance in opposition to magnitude and practical importance of an effect is ignored. Most econometrics textbooks recommend stress on statistical significance and minimum concentration on the size of the estimated effect. Confidence intervals could be used to stress the importance of sign, size and significance, thus, avoiding the use of a formal null hypothesis. Especially the conditional nature of a Type II error is difficult to understand: hence, here again, the practical use of computers could show the students the changing size of the Type II error by increasing the sample size. On the subject of regression to the mean a fallacy is that relatively high values are expected to fall toward the average while relatively low values are expected to rise to the average. This often occurs when analyzing high-value and low-value points of a splitted sample separately. If regression to the mean in fact exists, the variance of the distribution as a whole should decline and all values should cluster continually closer to the mean. Looking at averages of subgroups does not give an idea about whether the variance of the entire distribution has declined. About motivating the least squares estimator scatterplots usually have provided the means for introducing linear least squares regression. Nonetheless, it does not remain unquestioned that the suggestion of minimizing the sum of the squares of the residuals should be the correct instrument to estimate a mean value of a dependent variable conditional on the values of the independent variables. Although there are some approaches to motivating the least squares estimator, many students still do not see an obvious reason why it should estimate the relevant population parameter. Thus, the authors suggest estimation on the method-of-moments, which is the norm in advanced statistical treatments. This method is based on the understanding that a population parameter estimator comes from the corresponding feature of the sample, in other words, estimators of population parameter must have sample properties that mimic similar properties of the population model. Thus, within the method-of-moments method the starting point is not the data but the properties from the population. The approach states that from the population model generated sample data must have the same properties, as forced on the data due to selection of the intercept and slope of the sample regression line. At last, traditional econometrics course primarily emphasize the algebra of least squares estimation of parameters in well structured models. Due to advances of incorporating computer labs in econometrics education nonlinear modeling and nonparametric regression techniques should be applied because it is important to show the students alternatives, although they must be able to handle least squares. Students now can use these tools without learning difficult programming syntax or mathematical specialties.

Sometimes ideas at the frontier of research (e.g. topics the teacher is temporarily working on) presented in class can reveal the excitement of the subject and can attract the students who consider become majors (Hamermesh 2002) but it should be considered that most of the students will not take any other courses than Elemtary and Principles in these subjects and that many of them have very limited analytical abilities (compare Case 2002). Altogether, not too many and too advanced contents should be taught and these carefully and real-life oriented. Finally, Hamermesh (2002) introduced some general hints on teaching all kinds of economics courses of which the most important ones will be presented shortly. Besides the lecture notes the instructor should have detailed notes with illustrations and examples worked out that should all be ready several classes ahead of schedule to avoid last minute preparations. It also should be noticed that with Power Point, although the complete lecture is ready-made for presentation, passive learning is encouraged by giving the students an incentive to avoid active engagement with the material as they will certainly rely on the printed notes of the lecture. Despite the vast amount of content included in each lecture, there are typically only three or four main points, each briefly expressible. These should be listed for the students at the end of the lecture to provide them with a good overview. A detailed syllabus can be seen as a contract between instructor and students and eliminates possible misunderstandings. Finally, two midterms and a final exam should be enough and students should be offered a question-and-answer session outside the normal class time before each exam. There are also some other important and interesting hints for teaching economics but as these are more general it is recommended (especially for teachers) to directly read the article of Hamermesh (2002).

2.2 New Initiatives in Teaching Statistics and Econometrics

The previous part demonstrated the necessary contents for econometrics classes while in the following sections the focus will be set on how to teach econometrics and statistics classes independent of the subject’s theoretical contents. To sum up once again, the lack of real world topics for applications in the textbooks as well as in classes is a problem that has to be dealt with intensively. The theoretical concepts shown above and their application must be focused by the instructors. Although nowadays it is possible to integrate the use of computer labs in education, in teaching business, econometrics and economic statistics the “chalk-and-talk” mode still dominates; thus, modes should be developed to incorporate computer technology in the most efficient way into classes. Nonetheless, changes can only be expected if students, instructors and education institutes are open to it (Becker and Greene 2001). This starting points go along with the initiatives for improving economic education in general. Salemi et al. (2001) introduced five new initiatives for research in economic education initiated by the Committee on Economic Education (CEE) of the American Economic Association (compare also the improvement suggestions by Hansen et al. 2002). These are Teaching Methods and Incentives for College Level Economics Instruction, Ph.D. Education in Economics in the United States, Improving the Assessment of Student Learning in College Economics Courses, Long-Term Effects of Learning Economics and Efficiency in the Use of Technology in Economic Education. Each initiative should be executed by a project group of scientists. The initiatives could be divided up into three categories. The first category deals with the direct in-class improvement through more efficiency. For that the task of the project of assessment is the development of test instruments to examine if students really learn more effective when tutors use an active learning method as a substitute for standard lecturing. The technology project should show the effects of use of information technologies in class because an evaluation of the costs and benefits of electronic technologies is important since there is still little evidence on the learning- and cost-effectiveness of recent changes in technology and the lasting-effects project should recommend strategies for ensuring that the students are able to use their knowledge learnt in the economics classes even years after course completion. The second category deals with different ways to encourage the changes in teaching. The teaching-methods project should establish a certificate of achievement in economic education, as well as workshops to initiate a more active learning concept. Furthermore, a new section of the Journal of Economic Education should be initialized through which the assessment project tries to find out if tutors will improve the quality of their tests and assessment practices when they get a publication opportunity. In the last category the graduate-training project should help to determine the reasons and effects of the upcoming decrease in economics Ph.D. recipients. Here, in this paper, the fist category is being focused. Thus, the next part shows the different offerings in statistics and econometrics teaching models.

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^[1] A survey by Becker and Watts (2001) shows the dominant picture of the US undergraduate economics teacher in higher education institutions (without doctorate universities). This teacher is male, Caucasian, has a Ph.D. degree and lectures to his class by using the chalkboard and a standard textbook. He spends 40 percent of his time on teaching and the same amount of time on research.

^[2] Although teachers mostly develop their own problem sets these are rarely based on press readings or on scholary publications (Becker and Watts 2001).

^[3] The law of large numbers means that by increasing the size of the sample, the sample mean coverges to the true mean.

^[4] The central limit theorem states that for many samples of like and sufficiently large size, the histogram of these sample means appears to be a normal distribution.

^[5] A Type I error arises when the the null hypothesis is incorrectly rejected.

^[6] A Type II error arises when the null hypothesis is not rejected when it is in fact false.