GeorgeMatthews
January 28, 2017
140

# Inductive Reasoning

Eleventh slideshow for a course on science.

January 28, 2017

## Transcript

1. ### Inductive Reasoning thinking about what might, maybe, probably is true

George Matthews CC 2017

4. ### Going Beyond Proof ! Generalization What can we tell reliably

about a large group based on a small sample?
5. ### Going Beyond Proof ! Generalization What can we tell reliably

about a large group based on a small sample? How do we apply generalizations to particular individuals?
6. ### Going Beyond Proof ! Generalization What can we tell reliably

about a large group based on a small sample? How do we apply generalizations to particular individuals? ! Reasoning by analogy
7. ### Going Beyond Proof ! Generalization What can we tell reliably

about a large group based on a small sample? How do we apply generalizations to particular individuals? ! Reasoning by analogy When do analogies work and when do they break down?
8. ### Going Beyond Proof ! Generalization What can we tell reliably

about a large group based on a small sample? How do we apply generalizations to particular individuals? ! Reasoning by analogy When do analogies work and when do they break down? ! Causal reasoning
9. ### Going Beyond Proof ! Generalization What can we tell reliably

about a large group based on a small sample? How do we apply generalizations to particular individuals? ! Reasoning by analogy When do analogies work and when do they break down? ! Causal reasoning How can we tell what caused what?

12. ### Generalizations ! Eggs break when you drop them. ! Shakespeare’s

plays are written in blank verse.
13. ### Generalizations ! Eggs break when you drop them. ! Shakespeare’s

plays are written in blank verse. ! Water ﬂows downhill.
14. ### Generalizations ! Eggs break when you drop them. ! Shakespeare’s

plays are written in blank verse. ! Water ﬂows downhill. ! Shy people tend to be quiet at parties.
15. ### Generalizations ! Eggs break when you drop them. ! Shakespeare’s

plays are written in blank verse. ! Water ﬂows downhill. ! Shy people tend to be quiet at parties. ! Spider webs are stronger than steel.
16. ### Generalizations ! Eggs break when you drop them. ! Shakespeare’s

plays are written in blank verse. ! Water ﬂows downhill. ! Shy people tend to be quiet at parties. ! Spider webs are stronger than steel. ! Time moves in one direction only.
17. ### Generalizations ! Eggs break when you drop them. ! Shakespeare’s

plays are written in blank verse. ! Water ﬂows downhill. ! Shy people tend to be quiet at parties. ! Spider webs are stronger than steel. ! Time moves in one direction only. ! f = m∗a
18. ### Generalization 95 percent of the shy people I know are

quiet at parties. Thus all shy people are quiet at parties.
19. ### Generalization 95 percent of the shy people I know are

quiet at parties. Thus all shy people are quiet at parties. ! Inductive arguments appeal to experience to justify generalizations.
20. ### Generalization 95 percent of the shy people I know are

quiet at parties. Thus all shy people are quiet at parties. ! Inductive arguments appeal to experience to justify generalizations. ! How can we sure that our generalizations are accurate?
21. ### Generalization 95 percent of the shy people I know are

quiet at parties. Thus all shy people are quiet at parties. ! Inductive arguments appeal to experience to justify generalizations. ! How can we sure that our generalizations are accurate? ! How do we know that the future will be like the past?

know.
24. ### How Not to Take a Sample ! Ask people you

know. ! Look at a few famous or clear cases and go from there.
25. ### How Not to Take a Sample ! Ask people you

know. ! Look at a few famous or clear cases and go from there. ! Send out a survey and see who responds or put a survey on your website.
26. ### How Not to Take a Sample ! Ask people you

know. ! Look at a few famous or clear cases and go from there. ! Send out a survey and see who responds or put a survey on your website. ! Ask leading or unclear questions.
27. ### How Not to Take a Sample ! Ask people you

know. ! Look at a few famous or clear cases and go from there. ! Send out a survey and see who responds or put a survey on your website. ! Ask leading or unclear questions. ! Ask for personal or demographic information ﬁrst.

29. ### Sampling Basics population sample size conﬁdence level margin of error

1000 100 90% ±8
30. ### Sampling Basics population sample size conﬁdence level margin of error

1000 100 90% ±8 1000 100 95% ±10
31. ### Sampling Basics population sample size conﬁdence level margin of error

1000 100 90% ±8 1000 100 95% ±10 1000 500 95% ±4
32. ### Sampling Basics population sample size conﬁdence level margin of error

1000 100 90% ±8 1000 100 95% ±10 1000 500 95% ±4 300M 500 95% ±5
33. ### Sampling Basics population sample size conﬁdence level margin of error

1000 100 90% ±8 1000 100 95% ±10 1000 500 95% ±4 300M 500 95% ±5 4000 100 95% ±10
34. ### Sampling Basics population sample size conﬁdence level margin of error

1000 100 90% ±8 1000 100 95% ±10 1000 500 95% ±4 300M 500 95% ±5 4000 100 95% ±10 4000 100 80% ±7

36. ### Strong or Weak? I asked 100 of my closest friends,

all of whom go to PSU, whether they believe that aliens are living among us, 45% said yes, 40% said no, 15% were not sure. Therefore we can be very conﬁdent that more PSU students believe that aliens are living among us than do not believe this.
37. ### A study of the rates of a certain form of

rare cancer has found that:
38. ### A study of the rates of a certain form of

rare cancer has found that: A. Some rural counties have lower than average rates of this cancer among their residents.
39. ### A study of the rates of a certain form of

rare cancer has found that: A. Some rural counties have lower than average rates of this cancer among their residents. B. Some rural counties have higher than average rates of this cancer among their residents.
40. ### A study of the rates of a certain form of

rare cancer has found that: A. Some rural counties have lower than average rates of this cancer among their residents. B. Some rural counties have higher than average rates of this cancer among their residents. How can we explain this?
41. ### Insensitivity to Sample Size A study of the rates of

a certain form of rare cancer has found that: A. Some rural counties have lower than average rates of this cancer among their residents. B. Some rural counties have higher than average rates of this cancer among their residents. How can we explain this?
42. ### 10110101 00111011 11011101 11101001 11011111 11010111 00110111 11010010 00011001 01101101

10100110 00110110 01110110 01000100 11111011 11011010 11010000 01001111 10011001 00010010 11001111 10100110 01011100 11101111 00100111 11001010 11110100 11011111 00111010 01101010 01000100 10111101 00101011 01011100 01000001 00000111 11001001 01110101 01110001 11010100 11011110 10100011 11101110 10101000 01100010 10010001 01011100 11000111 01100000 11100001 00011000 10001100 01110110 00100101 11100111 10110101 10010001 11011000 11010001 11111100 10110011 00010001 11001101 01011000 10001100 10001100 01010000 10110101 01101110 00101001 00010110 00010001 01011001 11101100 01101011 11011011 11110001 01101011 11000001 00001111 11101000 10000011 01011001 01111101 01011000 11111111 11110110 01111110 01101110 11101100 10100101 10111101 01101001 00010000 01011011 01000010 01010010 11011101 11111100 11000001 01001100 00101111 11101111 01011011 10110101 00011011 00011111 10011000 01111011 11110010 10101001 00011000 10000000 01011110 11110101 11010111 10101001 10010110 00001100 00010010 11101100 10011100 10110111 11000011 00100101 11011001 01110011 11011000 10010111 11001100 00010111 00000110 11000111 10110010 00100011 01100011 00111110 00001111 11101101 10011110 10000011 10000111 01011110 00110010 01010001 01100010 01011001 01000110 01000101 10001011 11000011 10111010 10010001 11101000 11101111 10110010 11111110 00001001 01000100 01011101 10001001 01010001 11101101 10010001 01111100 00011110 11011100 00111001 11101111 10101101 10010000 10011000 00110000 00001101 10001000 00111000
43. ### The Hot Hand A basketball player scores on an average

50% of her shots. Sometimes she shoots better than average, sometimes she shoots worse. Is she more likely to score after she has scored on six shots in a row?
44. ### Which would you pay more for: insurance against death by

terrorist attack, or death by any cause?
45. ### Dramatic Instances Eﬀect Which would you pay more for: insurance

against death by terrorist attack, or death by any cause?

47. ### Argument by Analogy Rats get cancer when they smoke cigarettes.

Rat bodies are analogous with human bodies. Thus cigarettes cause cancer in humans.

49. ### Strong and Weak Analogies Galileo was ridiculed at ﬁrst, but

then his ideas prevailed. The same is true of my theory of free energy, you may ridicule it now but it too will prevail.
50. ### Strong and Weak Analogies Newton showed how the movement of

the moon around the earth is analogous with the movement of cannon balls on earth – both result from the combined eﬀects of inertial motion and gravitational acceleration.
51. ### Strong and Weak Analogies Darwinian evolution operates by means of

“natural selection” which is just like selective breeding of domestic animals and plants except that there is no breeder.
52. ### Strong and Weak Analogies Just like historically important events have

wide-reaching consequences, so their causes must be equally signiﬁcant. Hence JFK could not possibly have been shot by “one lone nut” but there must have a been a massive conspiracy to assassinate him and a cover-up afterwards.
53. ### Mary was a ﬁnance major who was an outspoken advocate

for women’s rights in college. Which is more likely to be true about her?
54. ### Mary was a ﬁnance major who was an outspoken advocate

for women’s rights in college. Which is more likely to be true about her? A. She works at a bank.
55. ### Mary was a ﬁnance major who was an outspoken advocate

for women’s rights in college. Which is more likely to be true about her? A. She works at a bank. B. She is a feminist who works at a bank.
56. ### Conjunction Fallacy Mary was a ﬁnance major who was an

outspoken advocate for women’s rights in college. Which is more likely to be true about her? A. She works at a bank. B. She is a feminist who works at a bank.
57. ### Suppose I ﬂip a fair coin and get 5 heads

in a row. Which is more likely on the next ﬂip, heads or tails?
58. ### Gambler’s Fallacy Suppose I ﬂip a fair coin and get

5 heads in a row. Which is more likely on the next ﬂip, heads or tails?
59. ### Whenever I have a bad cold I drink a bottle

of whiskey and then in a day or two I feel better. Thus whiskey cures colds.
60. ### False Cause Fallacy Whenever I have a bad cold I

drink a bottle of whiskey and then in a day or two I feel better. Thus whiskey cures colds.
61. ### When the players on the team do really well and

I praise them for their eﬀorts, they do less well afterward. But when they do poorly and I yell at them, their playing soon improves.
62. ### When the players on the team do really well and

I praise them for their eﬀorts, they do less well afterward. But when they do poorly and I yell at them, their playing soon improves. What does this show about positive and negative reinforcement?
63. ### Base Rate Fallacy When the players on the team do

really well and I praise them for their eﬀorts, they do less well afterward. But when they do poorly and I yell at them, their playing soon improves. What does this show about positive and negative reinforcement?

65. ### Illusory Correlation Subjects were given sentences to read about the

behavior of two groups, identiﬁed only as group A and group B.
66. ### Illusory Correlation Subjects were given sentences to read about the

behavior of two groups, identiﬁed only as group A and group B. behaviors group A group B total desirable 18 (69%) 9 (69%) 27 undesirable 8 (30%) 4 (30%) 12 total 26 13 39 Hamilton, D; Giﬀord, R (1976).
67. ### Illusory Correlation Subjects were given sentences to read about the

behavior of two groups, identiﬁed only as group A and group B. behaviors group A group B total desirable 18 (69%) 9 (69%) 27 undesirable 8 (30%) 4 (30%) 12 total 26 13 39 Test subjects asked about these groups associated group B more strongly with undesirable behaviors. Why? Hamilton, D; Giﬀord, R (1976).

69. ### Monty Hall Problem Suppose you’re on a game show, and

you’re given the choice of three doors:
70. ### Monty Hall Problem Suppose you’re on a game show, and

you’re given the choice of three doors: ! Behind one door is a car; behind the others, goats.
71. ### Monty Hall Problem Suppose you’re on a game show, and

you’re given the choice of three doors: ! Behind one door is a car; behind the others, goats. ! You pick door 1.
72. ### Monty Hall Problem Suppose you’re on a game show, and

you’re given the choice of three doors: ! Behind one door is a car; behind the others, goats. ! You pick door 1. ! The host, who knows what’s behind the doors, opens door 3, revealing a goat.
73. ### Monty Hall Problem Suppose you’re on a game show, and

you’re given the choice of three doors: ! Behind one door is a car; behind the others, goats. ! You pick door 1. ! The host, who knows what’s behind the doors, opens door 3, revealing a goat. Should you switch to door 2?