Induction Reasoning

Question 1

Properties of inductive arguments

Answer 1

• Strong or weak
• Conclusion of a strong inductive argument is likely true
• If argument is strong and its premises are true (or probably) the argument is cogent

Question 2

What is an inductive argument?

Answer 2

Is an argument intended to supply only PROBABLE support for its conclusion

Question 3

Types of inductive reasoning

Answer 3

1. Enumerative induction
2. Statistical syllogisms
3. Analogical induction
4. Casual arguments
5. Mixed arguments

Question 4

Enumerative Induction

Answer 4

• Reasons from characteristics of a group to those of a member of that group
• Use sample and target groups, relevant property

Question 5

Sample

Answer 5

the members of the target group that were actually observed

Question 6

Target group/population

Answer 6

Class of individuals or objects we wish to draw a conclusion on

Question 7

Relevant property

Answer 7

Property or characteristic in which we are interested

Question 8

Example of Enumerative Inductions

Answer 8

“40% of people in our survey said they support Party A. So, we expect the As to get 40% of votes in this election.”

Target group: Canadian voters
Sample: people surveyed
Property: voting/supporting Party A.

Question 9

Example of weak induction

Answer 9

“All the corporate executives Jacques has worked for have been crooks. Therefore, all corporate executives are probably crooks.”

• Probably the sample size is too small.

Question 10

Two important factors in enumerative induction

Answer 10

Can fail to strong in 2 conditions:

1. Sample size is too small
2. Sample size is not representative

Question 11

Homogeneity and Sample Size

Answer 11

The more homogenous the target group, the smaller the sample can be. (and visa versa)

Question 12

Sample Must be Representative and not biased

Answer 12

Ex. Worst case: “We examined 1,000 horses. From this we conclude that no cows have mad cow disease.” - doesn’t represent cows!

Question 13

How to choose an unbiased sample

Answer 13

1. Should have all relevant characteristics
2. It should have those characteristics in the same proportion that the target group does (ex. : If you think gender matters to the property in question, your sample should be about 50% women)

Question 14

Issues with Opinion Polls

Answer 14

1. Sample size must be large enough to represent target population in all relevant aspects
2. Data must be accurately reflect what they purport to be about

Question 15

Random Selection

Answer 15

A sample of 1,000 out of a population of 25 million can give representative results if the sample is selected randomly.

Question 16

Margin of error

Answer 16

Used in opinion polls

Example: “Party A will receive 38% of the vote, +/- 3%.”

Question 17

Confidence level

Answer 17

probability that the sample represents the target group to within the margin of error.

Question 18

Statistical Trade-offs

Answer 18

The larger the sample, the smaller the margin of error, because larger samples are likely to be more representative.

If you’re willing to have less confidence in your results, a smaller sample size will do.

The larger the margin of error, the higher the confidence level can be.

Question 19

Mean

Answer 19

The arithmetic average of a distribution of values

Question 20

Median

Answer 20

Middle point of a series of values

Question 21

Mode

Answer 21

The most common value