Properties of inductive arguments
- 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
What is an inductive argument?
Is an argument intended to supply only PROBABLE support for its conclusion
Types of inductive reasoning
- Enumerative induction
- Statistical syllogisms
- Analogical induction
- Casual arguments
- Mixed arguments
Enumerative Induction
- Reasons from characteristics of a group to those of a member of that group
- Use sample and target groups, relevant property
Sample
the members of the target group that were actually observed
Target group/population
Class of individuals or objects we wish to draw a conclusion on
Relevant property
Property or characteristic in which we are interested
Example of Enumerative Inductions
“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.
Example of weak induction
“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.
Two important factors in enumerative induction
Can fail to strong in 2 conditions:
- Sample size is too small
- Sample size is not representative
Homogeneity and Sample Size
The more homogenous the target group, the smaller the sample can be. (and visa versa)
Sample Must be Representative and not biased
Ex. Worst case: “We examined 1,000 horses. From this we conclude that no cows have mad cow disease.” - doesn’t represent cows!
How to choose an unbiased sample
- Should have all relevant characteristics
- 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)
Issues with Opinion Polls
- Sample size must be large enough to represent target population in all relevant aspects
- Data must be accurately reflect what they purport to be about
Random Selection
A sample of 1,000 out of a population of 25 million can give representative results if the sample is selected randomly.
Margin of error
Used in opinion polls
Example: “Party A will receive 38% of the vote, +/- 3%.”
Confidence level
probability that the sample represents the target group to within the margin of error.
Statistical Trade-offs
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.
Mean
The arithmetic average of a distribution of values
Median
Middle point of a series of values
Mode
The most common value
