Session 3 of data analysis course

1. session#3 Divényi János @divenyi.janos

2. b.socrative.com
Student login
into room BMEADAT

3. QUESTION
DATA
ANALYSIS
PRESENTATION

4. QUESTION
DATA

5. QUESTION
DATA
ANALYSIS

6. How to find answers
to relevant questions
using data

10. http://boredbug.com/wp-content/uploads/2015/08/onesecondbeforedisaster.jpg

11. http://www.webpages.uidaho.edu/ed571/571-Modules/M3/Sampling_Design-Funny.gif

12. QUESTION
DATA
ANALYSIS

13. How does
a new piece of
information
affects
what we know
about the world?
www.bigstockphoto.com

16. P(A|B)
conditional probability
probability that A occurs
given than B has occurred

17. Explained Visually

18. Problem #1
Mr. Jones has two children.
The older child is a boy. What is the
probability that both children are boys?

19. Problem #1
Mr. Jones has two children.
The older child is a boy. What is the
probability that both children are boys?
1/2

20. Problem #2
Mr. Smith has two children.
At least one of them is a boy. What is the
probability that both children are boys?

21. Problem #2
Mr. Smith has two children.
At least one of them is a boy. What is the
probability that both children are boys?
1/3

22. Problem #3
Mr. Gardner has two children. At least one of
them is a boy born on Tuesday. What is the
probability that both children are boys?

23. Problem #3
Mr. Gardner has two children. At least one of
them is a boy born on Tuesday. What is the
probability that both children are boys?
13/27

24. https://xkcd.com/795/

25. How does
a new piece of
information
affects
what we know
about the world?
www.bigstockphoto.com

27. Down syndrome screening

28. Unconditional risk 1:400 = 0.0025
Discovery rate 0.83
False positive rate 0.047

29. Unconditional risk 1:400 = 0.0025
Discovery rate 0.83
False positive rate 0.047
Down if positive?

34. Down if positive?

35. Down if positive?

36. Down if positive?
P(+, Down) / (P(+, Down) + P(+, not Down))

37. Unconditional risk 1:400 = 0.0025
Discovery rate 0.83
False positive rate 0.047
P(+, Down) / (P(+, Down) + P(+, not Down))

38. Unconditional risk 1:400 = 0.0025
Discovery rate 0.83
False positive rate 0.047
P(+, Down) / (P(+, Down) + P(+, not Down))
0.83*0.0025 / (0.83*0.0025 + 0.047*0.9975)

39. Unconditional risk 1:400 = 0.0025
Discovery rate 0.83
False positive rate 0.047
Down if positive 0.0424
P(+, Down) / (P(+, Down) + P(+, not Down))
0.83*0.0025 / (0.83*0.0025 + 0.047*0.9975)

41. Unconditional risk 1:400 = 0.0025
Discovery rate 0.83
False positive rate 0.047
Down if positive 0.0424
P(+, Down) / (P(+, Down) + P(+, not Down))
0.83*0.0025 / (0.83*0.0025 + 0.047*0.9975)

43. Bayes’ Theorem
P(B|A) =
P(A|B) ∙ P(B)
P(A)
P(B|A) =
P(A|B) ∙ P(B)
P(A|B) ∙ P(B) + P(A|not B) ∙ P(not B)

44. 1% prevalence
99% accurate test
positive result means risk of
Simplistic example

45. 1% prevalence
99% accurate test
positive result means risk of
50%
Simplistic example

46. In 1999 Sally Clark was accused for murdering her
2 children after she sequentially claimed that
they died in sudden infant death syndrome (SIDS).
The probability of SIDS is 1 in 8500.

47. In 1999 Sally Clark was accused for murdering her
2 children after she sequentially claimed that
they died in sudden infant death syndrome (SIDS).
The probability of SIDS is 1 in 8500.
1. If you were the judge
what other probability
you would want to know?
2. Would you convict her?

48. In 1999 Sally Clark was accused for murdering her
2 children after she sequentially claimed that
they died in sudden infant death syndrome (SIDS).
The probability of SIDS is 1 in 8500.
1. If you were the judge
what other probability
you would want to know?
2. Would you convict her?
3. Do you think she was convicted?