Class Photo HW: Summary Due Before class Friday Chapter 2 - - PDF document

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Feb 14, 2023 366 likes •416 views

Today Today: Benfords Law HW: Applications of Benfords Law Benfords Law Wednesday Benfords Law Conclusion Real World Digit Patterns Friday Chapter 2 Discussion (Quiz?), Class Photo HW: Summary Due

SLIDE 1

Maria Hybinette, UGA

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Maria Hybinette, UGA

Benford’s Law Real World “Digit” Patterns

Maria Hybinette, UGA

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Maria Hybinette, UGA

Today

 Today: Benford’s Law

» HW: Applications of Benford’s Law

 Wednesday

» Benford’s Law Conclusion

 Friday

» Chapter 2 Discussion (Quiz?), » Class Photo

 HW: Summary Due Before class Friday

» Chapter 2 » Hardcopy due: Friday before class » Softcopy due midnight before the class Friday.

Maria Hybinette, UGA

3

Maria Hybinette, UGA

Benford’ Law is about Number Distributions

 Specifically about the Distribution of the First

Digit in real world data.

 Before getting into the trenches of Benford’s

Law lets simply talk about (review) different Distributions.

» What do they look like?

 So lets explore:

» What is a numeric Distribution?

Maria Hybinette, UGA

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Maria Hybinette, UGA

Oh No! Coin-toss Again

 Uniform Distribution

» Excel’s Random : 0 to .99

=IF(INT(RAND()+0.5)=1,"H","T") INT: Rounds down to the nearest INT Add .5 so half the numbers rounds down to 1 and half to zero.

50 Number of Heads Number of Tails

Maria Hybinette, UGA

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Maria Hybinette, UGA

1000 Roles of a Single Die

 Uniform Distribution

=IF(INT(RAND()+0.5)=1,"H","T") INT: Rounds down to the nearest INT Add .5 so half the numbers rounds down to 1 and half to zero.

Maria Hybinette, UGA

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Maria Hybinette, UGA

Example: Human Height

 IF we take the population of earth and then

sort them according to height

 Normal Distribution : Gaussian Distribution

SLIDE 2

Maria Hybinette, UGA

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Maria Hybinette, UGA

Bell Curve

 Heights of people  Size of things produced by machines  Blood pressure  Test Grades in a LARGE class.  http://www.mathsisfun.com/data/standard-

normal-distribution.html

Maria Hybinette, UGA

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Maria Hybinette, UGA

What about Benford’s Law? What is its Distribution?

Numeric Data Leading DIgit 235 2 975 9 124 1 536 5 611 6 385 3 196 1 745 7 385 3

Maria Hybinette, UGA

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Maria Hybinette, UGA

Example: Population of all the countries in the world

Maria Hybinette, UGA

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Maria Hybinette, UGA Maria Hybinette, UGA

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Maria Hybinette, UGA Maria Hybinette, UGA

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Maria Hybinette, UGA

The Ideal: Benford’s Law

SLIDE 3

Maria Hybinette, UGA

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Maria Hybinette, UGA

 Benford’s Law works Accurately when:

» Numbers Span several order of magnitudes

 Example: Populations Goes from 10s to

billions!

» Benford’s Law applies YAY!

Maria Hybinette, UGA

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Maria Hybinette, UGA

When does it not work well?

 When number’s are assigned! Or there are

thresholds (max/min).

» Check numbers » Invoice numbers » Number’s with built in max and minimum

Maria Hybinette, UGA

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Maria Hybinette, UGA

Benford’s Law

 Read Resource: Wikipedia!  http://en.wikipedia.org/wiki/Benford's_law

Maria Hybinette, UGA

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Maria Hybinette, UGA

More Examples

http://testingbenfordslaw.com/twitter-users-by-followers-count

Maria Hybinette, UGA

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Maria Hybinette, UGA Maria Hybinette, UGA

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Maria Hybinette, UGA

SLIDE 4

Maria Hybinette, UGA

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Maria Hybinette, UGA

 Heights of buildings  Amount of money in your wallet  Rolling of a die

» 1 Die, value of ‘dots’ have a uniform distribution » 2 Dice: Question: Are Values of the dots:

– Uniform – Non-Uniform – Benfordian

Maria Hybinette, UGA

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Maria Hybinette, UGA

1

Benford’s Law Real World “Digit” Patterns

2

Today

 Today: Benford’s Law

» HW: Applications of Benford’s Law

 Wednesday

» Benford’s Law Conclusion

 Friday

» Chapter 2 Discussion (Quiz?), » Class Photo

 HW: Summary Due Before class Friday

» Chapter 2 » Hardcopy due: Friday before class » Softcopy due midnight before the class Friday.

3

Benford’ Law is about Number Distributions

 Specifically about the Distribution of the First

Digit in real world data.

 Before getting into the trenches of Benford’s

Law lets simply talk about (review) different Distributions.

» What do they look like?

 So lets explore:

» What is a numeric Distribution?

4

Oh No! Coin-toss Again

 Uniform Distribution

» Excel’s Random : 0 to .99

=IF(INT(RAND()+0.5)=1,"H","T") INT: Rounds down to the nearest INT Add .5 so half the numbers rounds down to 1 and half to zero.

5

1000 Roles of a Single Die

 Uniform Distribution

=IF(INT(RAND()+0.5)=1,"H","T") INT: Rounds down to the nearest INT Add .5 so half the numbers rounds down to 1 and half to zero.

6

Example: Human Height

 IF we take the population of earth and then

sort them according to height

 Normal Distribution : Gaussian Distribution

7

Bell Curve

 Heights of people  Size of things produced by machines  Blood pressure  Test Grades in a LARGE class.  http://www.mathsisfun.com/data/standard-

normal-distribution.html

8

What about Benford’s Law? What is its Distribution?

Numeric Data Leading DIgit 235 2 975 9 124 1 536 5 611 6 385 3 196 1 745 7 385 3

9

Example: Population of all the countries in the world

10

11

12

The Ideal: Benford’s Law

13

 Benford’s Law works Accurately when:

» Numbers Span several order of magnitudes

 Example: Populations Goes from 10s to

billions!

» Benford’s Law applies YAY!

14

When does it not work well?

 When number’s are assigned! Or there are

thresholds (max/min).

» Check numbers » Invoice numbers » Number’s with built in max and minimum

15

Benford’s Law

 Read Resource: Wikipedia!  http://en.wikipedia.org/wiki/Benford's_law

16

More Examples

17

18

19

 Heights of buildings  Amount of money in your wallet  Rolling of a die

» 1 Die, value of ‘dots’ have a uniform distribution » 2 Dice: Question: Are Values of the dots:

– Uniform – Non-Uniform – Benfordian

20

More Examples

 http://www.youtube.com/watch?

v=O8N26edbqLM

 10 minute Videos:

» http://www.youtube.com/watch?v=vIsDjbhbADYs » http://www.youtube.com/watch?v=XXjlR2OK1kM

– (country from last video)