# STATISTICAL DATA ANALYSIS COURSE VIA THE MATLAB WEB SERVER

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1 STATISTICAL DATA ANALYSIS COURSE VIA THE MATLAB WEB SERVER Ale š LINKA Dept. of Textile Materials, TU Liberec Hálkova 6, Liberec, Czech Republic Petr VOLF Dept. of Applied Mathematics, TU Liberec Hálkova 6, Liberec, Czech Republic ABSTRACT Internet based courses are at present a quite common tool of learning. While still the most of them consist just of the static texts located on web pages, the objective of many new instruction systems is to make the learning process more dynamic and interactive in comparison with a mere reading the textbook or listening the lessons. Moreover, it is a feature of mathematics that it can hardly be studied by mere memorizing the texts. That is why we searched, when preparing a series of internet courses on mathematical statistics, data analysis and quality control, for an environment enabling such an interaction and supporting the preparation and use of numerical and graphical procedures. Finally we decided to utilise the Matlab Web Server. In this environment, the author can combine the text with Matlab computational algorithms and graphical tools, the user can work with them without having its own Matlab installation. The system thus consists from text files, the Matlab programs and the procedures controlling the interface, input and output connection between the web pages accessed by the user and the Matlab algorithms (prepared by the author or used directly from Matlab toolboxes). In such a way, a student is provided simultaneously with relevant information, the examples, and graphs, he can enter his own data, too, and is offered the tests checking his knowledge. In the present contribution the system will be described and examples of its use presented. Key words : Mathematical statistics, tutoring system, Matlab Web Server.

3 - The tutoring text, including the theory and formulas, and practical recommendations. - Illustrative examples, figures. The numerical examples are generated randomly. The user, in some cases, is challenged to solve the example independently and to check the correctness of his approach afterwards. - The examples, exercises testing the level of knowledge of the user. - Statistical data analysis calculator which can process even the data from the file on user s computer. - Finally, a set of Matlab algorithms, developed by authors (and, naturally, the standard Matlab procedures and tool-boxes which are a part of Matlab installation). At present, the material covers several chapters of basic courses on probability, mathematical statistics and quality control. Namely 1. Distribution of random variables. The most frequent types of distribution (both discrete and continuous) are presented both mathematically and graphically, their typical use is demonstrated on simple examples. 2. Explorative data analysis (EDA) methods. This part deals with basic empirical characteristics of distribution of given data, their computation and graphical presentation with the aid of several types of plots. 3. Statistical tests of hypotheses. Again, the main methods of both parametric and nonparametric tests are recalled, its methodology explained and illustrated on examples. 4. Regression analysis presents the material on linear and nonlinear models, the least squares methods and nonparametric smoothing approaches. 5. Control charts provide the motivation, methodology, and examples of Shewhart charts for the mean value and variance, and also the EWMA smoothing method. 6. Methods of quality control in textile industry The theme follows from the specialisation of the Faculty of Textile Engineering of TU Liberec and provides the basic approaches to textile metrology and quality control. 7. The section provisionally named Matlab-Web contains a selection of examples to all topics. The orientation in the system is provided by the menu of themes and sub-themes. The main page is shown on Figure 1. Thus, the user can either select its own theme (sequence of themes) or he can follow the recommended sequence (which actually corresponds to the order of menu bars) and links to examples in the text of textbook chapters.

4 3. Example control charts Figure 1. The main panel Let us assume that we are interested in a brief tutorial on control charts. First, we can follow the menu bars and select tutoring text under Quality Control / Control Charts. There, a student obtains information (description, definition, purpose, probabilistic background and way of utilisation) of basic charts, among them the Shewhart s control charts for the mean (X-bar), for the standard deviation (S-bar), and also exponentially weighted moving average (EWMA) diagram with onestep delay. Then, the link leads to the computational example. The user is first asked to enter data and he has four possibilities: He can write the data directly to the corresponding line in the input frame on display, he can use Matlab random generator and generate the data through the MWS, further, he can select one of demonstration data files prepared on the server, and he can also enter his own data from his computer. In the last case the user should be aware (and he is informed in tutoring text) that the form of data should correspond to the procedure for instance the control charts work with a matrix (n k, say) of n groups à k observations. Finally, the user is asked to select, in another window, the type of chart (e.g. EWMA together with smoothing parameter). Then the charts are computed and displayed graphically (see Figure 2).

5 Figure 2. An example graphs of control charts 3.1 An example of seminar exercise Let us assume that the theme of the exercise is the polynomial regression, including the selection of optimal model. The teacher provides the instructions, the data are artificial, prepared in advance and stored on the server (for students home work) or they can be generated by students, again, according to an instruction, for example: 1. Generate the data (e.g. a complicated sinusoidal function with Gaussian random noise). The following instructions are: 2. Plot the data, with the aid of polynomial regression procedure. 3. Select the degree of polynomial. 4. Evaluate the regression model, analyse the significance of its parameters. The procedure computes regression parameters, corresponding 95 % confidence intervals, residual variance, and also Schwarz s BIC criterion penalising the models with too high degree. Students should already know the meaning of all these variables and parameters. The next step is: 5. Change the degree of the model and repeat the analysis. Compare the results, with special attention to the values of BIC criterion. etc. Finally, the procedure evaluates the model once more, omitting statistically non-significant parameters (and model components). The student is expected to perform the whole exercise, to write a report, and, eventually, to demonstrate and comment the process and results of solution to

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