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

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3. Hmmmm 3

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

6. Data & Data Analysis
Data refers 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 QUALITATIVE QUANTITATIVE Scores in a test
Measurement of wind speed
Number of mosquitos collected in a trap
The speed of light in a vacuum
A robot
Graph of intensity vs angle
High speed video of a bullet
Videos of interviews 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. Precision is ability to tell the same story over again
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. These can be reliably estimated by repeating measurement
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
Trial Number 1 2 3 4 5
Measured value
31.9
32.1
31.8
32.2
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
= 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 ± 0.2 oC 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. f (V0 – σ) < f (V0)< f (V0 + σ)
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 n we 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)
Type equation here.
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. Lets measure the molar heat of solvation of LiCl in water
Example
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 1: to calculate the uncertainty in m = m1+m2 using the error propagation rule
Step 2: Then use the total mass and its calculated error and determine H and σH 25

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

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

28. Watch your number of decimal places
Calculated Values
This looks impressive
Watch your number of decimal places
Calculated
Average
24.498 mm
Std Dev
Used
24.50
0.64
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. Rooshan Deen, NTU 31

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