Evidence Based Reasoning / Statistical Literacy Teaching Statistics and Econometrics

I  Introduction  1

1.1  Purpose of the Paper  1

II  Main Part  2

2.1  Main Problems in Teaching Statistics and Econometrics  2

2.2  New Initiatives in Teaching Statistics and Econometrics  5

2.3  Models of Teaching Statistics and Econometrics  7

2.1  Traditional Instruction  7

2.2  Hybrid Internet Based Instruction  8

2.3  Internet Based Instruction  9

2.4  Comparison of the Three Models  10

III  Conclusion  12

  Bibliography  14

Outdated education models, technological advances and increasing enrollment of students have led to involve Web-based education in some economics classes of various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.

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.

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

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

(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

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.