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Engineering Statistics Handbook Episode 1 Part 2

Tham khảo tài liệu 'engineering statistics handbook episode 1 part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 1.1.6. An EDA Graphics Example 9.00 8.77 9.00 7.11 8.00 8.84 11.00 9.26 11.00 7.81 8.00 8.47 14.00 8.10 14.00 8.84 8.00 7.04 6.00 6.13 6.00 6.08 8.00 5.25 4.00 3.10 4.00 5.39 19.00 12.50 12.00 9.13 12.00 8.15 8.00 5.56 7.00 7.26 7.00 6.42 8.00 7.91 5.00 4.74 5.00 5.73 8.00 6.89 Quantitative Statistics for Data Set 2 A quantitative analysis on data set 2 yields N 11 Mean of X 9.0 Mean of Y 7.5 Intercept 3 Slope 0.5 Residual standard deviation 1.237 Correlation 0.816 which is identical to the analysis for data set 1. One might naively assume that the two data sets are equivalent since that is what the statistics tell us but what do the statistics not tell us Quantitative Statistics for Data Sets 3 and 4 Remarkably a quantitative analysis on data sets 3 and 4 also yields N 11 Mean of X 9.0 Mean of Y 7.5 Intercept 3 Slope 0.5 Residual standard deviation 1.236 Correlation 0.816 0.817 for data set 4 which implies that in some quantitative sense all four of the data sets are equivalent . In fact the four data sets are far from equivalent and a scatter plot of each data set which would be step 1 of any EDA approach would tell us that immediately. http www.itl.nist.gov div898 handbook eda section1 eda16.htm 3 of 5 5 1 2006 9 56 15 AM 1.1.6. An EDA Graphics Example Scatter Plots Interpretation of Scatter Plots Conclusions from the scatter plots are 1. data set 1 is clearly linear with some scatter. 2. data set 2 is clearly quadratic. 3. data set 3 clearly has an outlier. 4. data set 4 is obviously the victim of a poor experimental design with a single point far removed from the bulk of the data wagging the dog . Importance of Exploratory Analysis These points are exactly the substance that provide and define insight and feel for a data set. They are the goals and the fruits of an open exploratory data analysis EDA approach to the data. Quantitative statistics are not wrong per se but they are incomplete. They are incomplete because they are numeric summaries which in the .