工程应用数学-统计基础与Statistica软件.ppt

1、 统计基础与 STATISTICA软件2IntroductionqIntroduction There are many aspects of science and engineering problems. Understanding and solving such problems often involves certain quantitative aspects, in particular the acquisition and analysis of data. Treating these quantitative problems effectively involves

2、 the use of statistics. Statistics can be viewed as the prescription for making the quantitative learning process effective.3The Learning ProcessqThe Learning Process (认知过程 ) An experiment is like a window through which we view nature. Our view is never perfect. The observations that we make are dis

3、torted. The imperfections that are included in observations are “noise”. A statistically efficient design reveals the magnitude and characteristics of the noise. It increases the size and improves the clarity of the experimental window. Using a poor design is like seeing blurred shadows behind the w

4、indow curtains or, even worse, like looking out the wrong window. 4The Learning ProcessqLearning is an iterative process5The Aim qIntroduction to the general kind of engineering problem and the statistical concepts and methods to be discussed.qCase Study introduces a specific example, including actu

5、al data.qAnalysis shows how the data suggest and influence the method of analysis and gives the solution. Many solutions are stepped in detail, and results shown. The problems were solved using available computer programs (e.g., STATISTICA、 SAS、 SPSS、 S-PLUS、 MINITAB etc.). 6Definitions and Basic Co

6、nceptsq Population(总体 ) and Sample(样本 ) The sample is a group of n observations actually available. A population is a very large set of N observations (or data values) from which the sample of n observations can be imagined to have come.q Random Variable(随机变量 ) “the value of the next observation in

7、an experiment.” “A random variable is the soul of an observation” and the converse, “An observation is the birth of a random variable.”q Experimental Errors(实验误差 ) A guiding principle of statistics is that any quantitative result should be reported with an accompanying estimate of its error. Replica

8、ted observations of some physical, chemical, or biological characteristic that has the true value will not be identical although the analyst has tried to make the experimental conditions as identical as possible. 7Definitions and Basic Conceptsq Experimental Errors(实验误差 ) This relation between the t

9、rue value and the observed (measured) value yi is yi = +ei , where ei is an error or disturbance. Error, experimental error, and noise refer to the fluctuation or discrepancy in replicate observations from one experiment to another. In the statistical context, error does not imply fault, mistake, or

10、 blunder. It refers to variation that is often unavoidable resulting from such factors as measurement fluctuations due to instrument condition, sampling imperfections, variations in ambient conditions, skill of personnel, and many other factors. Such variation always exists and, although in certain

11、cases it may have been minimized, it should not be ignored entirely. 8Exampleq ExampleA laboratorys measurement process was assessed by randomly inserting 27 specimens having a known concentration of =8.0 mg/L into the normal flow of work over a period of 2 weeks.This arrangement means that observed

12、 values are random and independent. The results in order of observation were 6.9, 7.8, 8.9, 5.2, 7.7, 9.6, 8.7, 6.7, 4.8, 8.0, 10.1, 8.5, 6.5, 9.2, 7.4, 6.3, 5.6, 7.3, 8.3, 7.2, 7.5, 6.1, 9.4, 5.4, 7.6, 8.1, and 7.9 mg/L.q The population is all specimens having a known concentration of 8.0 mg/L. q T

13、he sample is the 27 observations (measurements). q The sample size is n=27. q The random variable is the measured concentration in each specimen having a known concentration of 8.0 mg/L.q Experimental error has caused the observed values to vary about the true value of 8.0 mg/L. The errors are 6.9 8

14、.0=1.1, 7.88.0=0.2,+0.9,2.8,0.3,+1.6,+0.7, and so on.9Plotting Dataq The most effective statistical techniques for analyzing data are graphical methods. They are useful in the initial stage for checking the quality of the data, highlighting interesting features of the data, and generally suggesting

15、what statistical analyses should be done. Graphical methods are useful again after intermediate quantitative analyses have been completed. And again in the final stage for providing complete and readily understood summaries of the main findings of investigationsq The first step in data analysis shou

16、ld be to plot the data. Graphing data should be an interactive experimental process. Do not expect your first graph to reveal all interesting aspects of the data. Make a variety of graphs to view the data in different ways.10Plotting DataqPlotting the Data may: 1. reveal the answer so clearly that l

17、ittle more analysis is needed. 2. point out properties of the data that would invalidate a particular statistical analysis. 3. reveal that the sample contains unusual observations 4. save time in subsequent analyses. 5. suggest an answer that you had not expected. 6. keep you from doing something foolish.