1. ETM 620 - 09U 1 Statistical inference “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.” (H.G. Wells, 1946) “There are three kinds of lies: white lies, which are justifiable; common lies, which have no justification; and statistics.” (Benjamin Disraeli) “Statistics is no substitute for good judgment.” (unknown) ETM 620 - 09U 1

2. 2 Statistical inference Suppose – A mechanical engineer is considering the use of a new composite material in the design of a vehicle suspension system and needs to know how the material will react under a variety of conditions (heat, cold, vibration, etc.) An electrical engineer has designed a radar navigation system to be used in high performance aircraft and needs to be able to validate performance in flight. An industrial engineer needs to validate the effect of a new roofing product on installation speed. A motorist must decide whether to drive through a long stretch of flooded road after being assured that the average depth is only 6 inches. ETM 620 - 09U 2

3. 3 Statistical inference What do all of these situations have in common? How can we address the uncertainty involved in decision making? a priori a posteriori ETM 620 - 09U 3

4. 4 Probability A mathematical means of determining how likely an event is to occur. Classical (a priori): Given N equally likely outcomes, the probability of an event A is given by, _______________ where n is the number of different ways A can occur. Empirical (a posteriori): If an experiment is repeated M times and the event A occurs m A times, then the probability of event A is defined as, ____________________ We’ll talk more about this next time … ETM 620 - 09U 4

5. 5 5 Descriptive statistics Numerical values that help to characterize the nature of data for the experimenter. Example: The absolute error in the readings from a radar navigation system was measured with the following results: 17, 31, 22, 39, 28, 147, and 52 the sample mean, ̅ x = _________________________ the sample median, x = _____________ the sample mode = ________________ ~ ETM 620 - 09U

6. 6 6 Descriptive Statistics Measure of variability Our example: 17, 31, 22, 39, 28, 147, and 52 sample range: sample variance: ETM 620 - 09U

7. 7 7 Variability of the data sample variance, sample standard deviation, ETM 620 - 09U

8. 8 8 Other descriptors Discrete vs Continuous discrete: continuous: Categorical and identifying categorical: unit identifying: Distribution of the data “What does it look like?” ETM 620 - 09U

9. 9 9 Graphical methods Dot diagram and scatter plot useful for understanding relationships between factor settings and output example (pp. 174-175) ETM 620 - 09U

10. 10 Using graphical methods … Which factor(s) (or independent variable(s)) appears to have an effect on the output (or dependent variable), and what does that relationship look like? ETM 620 - 09U 10

11. ETM 620 - 09U 11 Graphical methods (cont.) Stem and leaf plot example (radar data): 17, 31, 22, 39, 28, 147, and 52 ETM 620 - 09U

12. 12 Another example Bottle-bursting strength data (pg. 176) StemLeafFrequency 1761 1872 1973 200586 210459 22013813 2311455519 24223568826 250001344788837 26000012334455555577899(21) 270112444456678842 280000113367 29034689918 30017811 31787 32185 33473 3461

13. ETM 620 - 09U 13 Graphical methods (cont.) Frequency Distribution (histogram) equal-size class intervals – “bins” ‘rules of thumb’ for interval size 7-15 intervals per data set √ n more complicated rules Identify midpoint Determine frequency of occurrence in each bin Calculate relative frequency Plot frequency vs midpoint ETM 620 - 09U

14. 14 Relative frequency histogram Example: stride lengths (in inches) of 25 male students were determined, with the following results: What can we learn about the distribution of stride lengths for this sample? Stride Length 28.6026.5030.0027.1027.80 26.1029.7027.3028.5029.30 28.60 26.8027.0027.30 26.6029.5027.0027.3028.00 29.0027.3025.7028.8031.40 ETM 620 - 09U

15. 15 Constructing a histogram Determining relative frequencies Class IntervalClass Midpt. Frequency, F Relative frequency 25.7 - 26.926.350.2 27.0 - 28.227.690.36 28.3 - 29.528.980.32 29.6 - 30.830.220.08 30.8 - 32.031.410.04 ETM 620 - 09U

16. 16 Relative frequency graph ETM 620 - 09U

17. 17 What can you see? Unimodal, Bimodal, or Multi-modal distribution Recognizable distribution? Skewness ETM 620 - 09U

18. 18 Another example … Bottle-bursting strength data (pg. 176) (from Minitab) (from Excel)

19. ETM 620 - 09U 19 Other useful graphical methods Box plot (aka, box and whisker plot) bottle bursting data and another example (viscosity measurement, pg. 181)

20. ETM 620 - 09U 20 Other useful graphical methods (cont.) Pareto diagram frequency count for categorical data arranged in descending order of frequency of occurrence useful for identifying “high value” targets sources of defects level of effort required in maintenance activities etc. Time plot plot of observed values vs a time scale (hour of day, day, month, etc.) useful for identifying patterns effect of time of day on electricity usage seasonal effects etc.

21. ETM 620 - 09U 21 Your turn ** … Look at problem 8-8 on page 194 do parts a & b draw conclusions ** - time permitting (Note: this also makes a good study problem) ETM 620 - 09U