Data Analysis Techniques

1. Data Analysis Techniques David Butler School of MAE Nanyang Technological University Singapore

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4. Error • Every measurement has a degree of uncertainty associated with the measurement • Error is the difference between the measured value and the true value of the object being measured. • Uncertainty is a quantification of the doubt about the measurement result. 4

5. Type of answers • How many apples are there in this picture? • How many particles are there in this picture? 5

6. Data & Data Analysis Datarefers to the collection of organized information. It can be numbers, words, images of measurements or observations. Data Analysis • The process of looking at and summarising data to extract useful information and develop conclusions. • Exploratory Data Analysis discovering new features in the data • Confirmatory Data analysis- confirming or falsifying existing hypotheses 6

7. Examples of data 7

8. Numerical Data Analysis • There is no general method for treating qualitative data • For quantitative data, there are a number of standard techniques • Not all standard numerical techniques are applicable to all types of research • Be careful when trying to quantify qualitative data 8

9. Accuracy & Precision • Accuracy is the proximity of answer to the true value and the absence of systematic errors • Precision is ability to tell the same story over again The influence of random error can be minimized by averaging a large data set 9

10. Types of error • Systematic errors – typically can be attributed to the measurement instrument used. Two examples are calibration error (failure to calibrate) and zero error • Random errors arise due to accidental errors in measurement such as estimating the reading, random fluctuations, incorrectly copying down the results 10

11. Systematic errors • Can not be estimated by repeating the equipment with the same equipment • Can be minimized • Careful calibration • Best possible techniques 11

12. Random Errors • These can be reliably estimated by repeating measurement • Can typically be quantified using the standard deviation formula • This is the most common error 12

13. How to determine the measurement error numerically Determination of Boiling Point of a liquid You measure 32oC. You then repeat the experiment many times and collect a set of results The best estimate is the average of the 5 measured results 13

14. How to determine the measurement error numerically • Take the difference between the highest measured value and the average will give the maximum deviation 32.2-32.02 = 0.18 • The best estimate is to get the average deviation known as standard deviation. The boiling point of the liquid is 32.0 oC ± 0.2oC 14

15. Histograms • Take a large number of measurements and count the number of occurrence of each value 31.9, 32.1, 31.8, 32.2, 32.1, 31.8, 32.1, 32.4, 32.1, 32.2, 32.3 15

16. Normal Distribution • The uncertainty of an average decreases as more data points are averaged. • The plot will typically follow a normal distribution curve • It is a property of a normal distribution curve that 68% of the measurements lie within one standard deviation on either side of the mean 16

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18. So a typical Singaporean male is taller than an Indonesian Male! 158 170 18

19. So a typical Singaporean male is taller than an Indonesian Male! 158 170 19

20. So a typical Singaporean male is taller than an Indonesian Male! 158 170 20

21. So a typical Singaporean male is taller than an Indonesian Male! Be careful of making statements without a full data analysis!ca 158 170 21

22. Error Propagation • Consider the ideal gas equation. Aim: to determine the number of moles of gas in a sample • We need to measure Pressure, Volume and Temperature to get the value of n. • Each measured quantity has an error value • To determine the error in nwe need to propagate the error in the individual measurement • We want to measure a quantity V • The result is f (V) (V0 – σ) < V0< (V0 + σ) • The desired property f s then within the range : f (V0 – σ) < f (V0)< f (V0 + σ) 22

23. Error Propagation • If a function only contains additions and subtractions the propagated error can be calculated as: • If a function only contains multiplications and division operations the propagated error can be calculated as: 23

24. Example Lets measure the molar heat of solvation in LiCl in water. • Weighing an mount of LiCl • Measuring the volume of water • Measuring the temperature change when the material dissolve The heat of solvation (H) is expressed in terms of the three measurements as: The function H contains multiplication and division operations. 24

25. Example • Step 1: to calculate the uncertainty in m = m1+m2 using the error propagation rule Lets measure the molar heat of solvation of LiCl in water If two separate masses were weighed and added to the solvent, the equation is given as: • Step 2: Then use the total mass and its calculated error and determine H and σH 25

26. Example • Determine the diameter of the bottle using a set of digital calipers 26

27. Possible Error Sources Man Machine Eyesight Varying force Stiffness No calibration resolution alignment Different grips Reading of scale Calculation errors Measurement variation exact reference? Temperature stability calibration Appropriate equipment Lighting Unclear instructions hardness datum Ergonomics Alignment of jaws shape Method Measurand Environment 27

28. Calculated Values This looks impressive • Watch your number of decimal places Realistically this is what you can measure 28

29. Calculated Values mm1 29

30. Summary • Error does not mean a mistake or blunder but refers to imprecision in measurement • Random or indeterminant errors are inherent in all measurements • The source of systematic errors are Instrumental errors, method errors and personal errors • Numerical results without error analysis are as good as useless 30

31. Thank You Acknowledgement to • Dr G. RooshanDeen, NTU http://www.sigmaxi.org/programs/ethics 31

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