1. Fundamentals of Data Analysis Lecture 1 Introduction dr inż. Tomasz W. Wojtatowicz Building B14 room 3.18B e-mail: tomasz.wojtatowicz@p.lodz.pl

2. OUTCOMES After completion of course student should: 1. optimally design and assemble the measuring system 2. properly proceed measurements 3. identify sources of measurement errors 4. interpret the results of statistical tests 5. carry out statistical analysis of measurement results and errors 6. properly collect and present the results of the measurements

3. LECTURE 1. Deduction and induction. Organization of the experimental research. Research planning. 2. Error theory. Kinds of error. Uncertainty class. Applications of the Error theory. 3. Selected topics from the probability and statistics. Statistical distributions applied in physics and data analysis. Test for nonrandomness. 4. Statistical hypotheses. Parameters of the distribution. Parametric estimation - most important estimators. Selected statistical programmes. 5. Statistical hypothesis testing. Parametrical and non- parametrical tests. 6. Managing data sets. Outliers. The rule of the huge error. The Dixon, Grubbs, Youden and Cochran Tests

4. LECTURE 7. Correlation and regression. Two-variable case. Correlation and regression for more than two variables. 8. Methods of the parametrical estimation. The Least Square Method and Maximum Likelihood Method. 9. Improving measurement precision. Application of the Fourier Transform. Smoothing. Calculations. Verification of the algebraic. Extrapolation and interpolation. Commercial mathematical programms. 10. Presenting data. Charts and graphs. Selected graphical and presentation applications. Scientific publication preparing.

5. TUTORIALS 1. Verification of the parametric hypothesis 2. Verification of the non-parametric hypothesis 3. Correlation and regression 4. Least square method 5. Extrapolation and interpolation

6. Books W. Krysicki i in., Rachunek prawdopodobieństwa i statystyka matematyczna w zadaniach, cz. II, Statystyka matematyczna, PWN, Warszawa 1986. G. L. Squires, Praktyczna fizyka, PWN, Warszawa 1992. H. Abramowicz, Jak analizować wyniki pomiarów?, PWN, Warszawa 1992. E. Bright Wilson jr., Wstęp do badań naukowych, PWN, Warszawa, 1968. S. Brandt, Analiza danych, PWN, Warszawa, 1998. L. Gajek, M. Kałuszka, Wnioskowanie statystyczne. Modele i metody. WNT, Warszawa 1994.

7. Topics for discussion n How important are currently the experimental investigations? n Computer in a scientific life. n Significance of the Internet at the work of researcher

8. Measurement n Measurement is a process of assigning numbers to objects or observations; In other words, some form of quantification expressed in numbers n Measurement is the process of comparing objects with standards n Measuring abstract concepts like ‘happiness’ is much more difficult than measuring physical objects, i.e., abstract concepts and non-standardised measurement tools lead to less confidence about accuracy of measurement

9. Research Methodology 1. Selection and formulation of research problem 2. Research design and plan 3. Experimental designs 4. Sampling and sampling strategy or plan 5. Measurement and scaling techniques 6. Data collection methods and techniques 7. Testing of hypotheses 8. Statistical techniques for processing & analysis of data 9. Analysis, interpretation and drawing inferences 10. Report writing

10. Ethic of research n Plagiarism, claiming credit for results of others, misreport sources or invent results, data with questionable accuracy, concealing objections that cannot be rebutted, caricaturing or distorting opposing views, destroy or conceal sources and data important for those who follow

11. Deductive and inductive reasoning n Deduction - the process of reasoning in which a conclusion follows necessarily from the stated premises; inference by reasoning from the general to the specific. n Induction - the process of reasoning, by which a general conclusion is drawn from a set of premises, based mainly on experience or experimental evidence. The conclusion goes beyond the information contained in the premises, and does not follow necessarily from them.

12. Hypotheses in data analysis n The hypothesis is a trial theory of the nature and relationship of individual observations. n The concept of a null hypothesis is used differently in two approaches to statistical inference, though the same term is used, a problem shared with statistical significance.

13. Hypotheses in data analysis n In the significance testing approach of Ronald Fisher, a null hypothesis is potentially rejected or disproved on the basis of data that is significantly under its assumption, but never accepted or proved. n In the hypothesis testing approach of Jerzy Neyman and Egon Pearson, a null hypothesis is contrasted with an alternative hypothesis, and these are decided between on the basis of data, with certain error rates.

14. Steps in Planning a Research Experiment n State the hypothesis to be tested. You will be looking for a hypothesis that can be tested statistically. For instance: “The blood pressure of patients with hypertension will decrease more by Altase than by Brand X” n Formulate a context. For example, if you are to test whether blood pressure correlates with number ofr cigarettes smoked per day, who will the subjects be? Will they be selected from an existing database or will a group of heart patients be selected and tested for blood pressure? Which hospitals will be used? Or, will you randomly select people off the streets, give them a questionnaire and then measure their blood pressure. On which street will you set up your experiment?

15. Steps in Planning a Research Experiment n Formulate a theoretical model. a. This will help you validate the experimental results. b. By looking at the theoretical model, you will know what variables you must keep track of during the experiment. For example, if viscosity shows up explicitly in the model, you know you must measure it. Furthermore, you may need to measure some hidden variables, such as temperature, if some of the variables depend on it.

16. Steps in Planning a Research Experiment n Design the experiment. a. Variables to be measured b. Sketch of Experimental Setup c. Equipment and supplies that will be needed d. Method for data analysis e. Experimental Protocol

17. Steps in Planning a Research Experiment n Construct the experiment n Test the experimental apparatus a. Perform any calibrations that are necessary b. The best way to test the apparatus is to make sure that it provides the results you would expect from some simple experiment. For example, if you are looking at something related to pipe flow, you might look at pressure drops across a venturi, or pressure drop in the straight pipe (Poiseuille flow) and show that they correspond to theory.

18. Steps in Planning a Research Experiment n Perform preliminary experiments a. You should design your experiment to work the first time you try it, but do not be surprised if it does not. You need to try the apparatus out, which means following your experimental protocol from beginning to end. Odds are that you will find one or two flaws in your experiment that may need to be fixed. Also, you will gain experience in this stage that will allow you to run the experiment more quickly and accurately next time. b. You will want to examine your results to make sure that they make sense. Even if it is clear that the results you have obtained are incorrect, run through the calculations needed to reduce the data and test the hypothesis. Create all graphs that are needed. If you do the analysis correctly, you will have set up the equations in Excel so that the next time you run the experiment the data analysis will be much easier.

19. Steps in Planning a Research Experiment n Perform the experiment. a. Make sure you record everything. This may include temperature, barometric pressure, time of day, and other variables that do not seem too important at the time. b. It is a good idea to do some of your data analysis while you are performing the experiment to make sure that the data are in the right ball park. This will help you find errors in the experimental protocol and elsewhere.

20. Steps in Planning a Research Experiment n Clean up the experiment. n Perform the data analysis, including statistical tests. n Write up the experiment and make conclusions.

21. Thank you for attention !