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1. Presentation: “Induction – Generalizations" Bring textbook to every class!

2. Homework • Introductory Logic • pp. 49 – 63 • Analysis and Critique • Identify the 3 parts of an inductive generalization • Explain what are the basic evaluative criteria by which to judge the strength of the generalization • Ex. 8.2A & B (as assigned in recitation) • Follow directions from 8.2B • pp. 63 – 79 • Next class: Causal Arguments

3. Inductive Reasoning Non-formal logic

4. Non-formal Logic • Subject Matter • Inductive Reasoning • Informal Fallacies • “Final” exam • 20% of total grade • Date / Time: see Presentations schedule Exam is not cumulative

5. 2 Kinds of Logic • Formal Deductive Reasoning • If conclusion follows with certainty, the argument is deductively valid • Non-Formal Inductive Reasoning • To what degree of probability does the conclusion follow? • Strong(>50%) – high degree • Weak(<50%) – low degree Truths follow from truths. A question of likelihood. Probability can be assessed mathematically

6. Inferential Connection Either you pass or you fail this class. You earned 85% on your first exam and 70% on the second exam. Your quiz grades are very high. Plus, you haven’t missed a single lecture or recitation, which adds 5% to your total score. Clearly you won’t fail. Therefore you will pass. The only question is what grade do you need to get an A or a B. I've noticed a correlation over the years between success on the final and success on the first two exams. Though the tests are all different, students who've done well on the first two exams tend to do well on the final. I expect that this will hold true again this semester. Notice the valid form (vE) Conclusion follows with some degree of probability from the given premises

7. Inductive Reasoning I. inductive Generalizations

8. Generalizations • Conclusion asserts something about a class or a group of things • Premises detail observations about members of this group

9. Generalizations • Conclusion asserts something about a class or a group of things • Conclusion concerns a certain population • Premises detail observations about members of this group • Premises articulate the sample

10. Generalizations • Conclusion asserts something about a class or a group of things • Conclusion concerns a certainpopulation • Premises detail observations about members of this group • Premises articulate the sample • Target Characteristic • observed in sample • inferred of population

11. What are Generalizations? • Generalizing Inference I • Premises about particular members • Conclusion about general group • Generalizing Inference II • Premises express what is observed to be the case • What is known empirically • Conclusion asserts a likely observable truth • What is unknown but likely true

12. What are Generalizations? Example from Lexington Herald-Leader, 11/6/07 Kentucky Secretary of State Trey Grayson predicted about 42 percent of the voters in Kentucky will cast ballots. Kentucky has 2.8 million registered voters, including about 1.6 million Democrats, about 1 million Republicans and 186,451 people registered as "other." Grayson, Kentucky's top election official, said the projection was based in part on an increase in absentee ballots cast in the days before Tuesday's election. The number was up by about 20 percent from the 2003 election. What is the conclusion?

13. What are Generalizations? Example from Lexington Herald-Leader, 11/6/07 Kentucky Secretary of State Trey Grayson predicted about 42 percent of the voters in Kentucky will cast ballots. Kentucky has 2.8 million registered voters, including about 1.6 million Democrats, about 1 million Republicans and 186,451 people registered as "other." Grayson, Kentucky's top election official, said the projection was based in part on an increase in absentee ballots cast in the days before Tuesday's election. The number was up by about 20 percent from the 2003 election. Trey Grayson predicted a 20% increase in the number of voters, about 1.17 million or 42% of all registered voters, will cast ballots in the 2007 gubernatorial election What is the conclusion?

14. What are Generalizations? Example from Lexington Herald-Leader, 11/6/07 Kentucky Secretary of State Trey Grayson predicted about 42 percent of the voters in Kentucky will cast ballots. Kentucky has 2.8 million registered voters, including about 1.6 million Democrats, about 1 million Republicans and 186,451 people registered as "other." Grayson, Kentucky's top election official, said the projection was based in part on an increase in absentee ballots cast in the days before Tuesday's election. The number was up by about 20 percent from the 2003 election. What are the premises?

15. What are Generalizations? Example from Lexington Herald-Leader, 11/6/07 Kentucky Secretary of State Trey Grayson predicted about 42 percent of the voters in Kentucky will cast ballots. Kentucky has 2.8 million registered voters, including about 1.6 million Democrats, about 1 million Republicans and 186,451 people registered as "other." Grayson, Kentucky's top election official, said the projection was based in part on an increase in absentee ballots cast in the days before Tuesday's election. The number was up by about 20 percent from the 2003 election. • Projection based on: • Count of absentee ballots in 2007 • Other factors – not articulated • Record of count from 2003 (“historical trends”) What are the premises?

16. Inductive Generalizations Identifiable Elements

17. Elements of a Generalization Always identify these 3 elements! • Population • 2.8 million registered KY voters • Sample • Absentee ballots cast in 2007 Kentucky election (“in part”) • Target Characteristic • Voting, specifically proportion of population

18. Refining a Generalization • Statistical analysis • What percentage of Republicans cast absentee ballots? • an increase or a decrease • What percentage Democrats? • What percentage “Libertarian”? • What percentage “other”?

19. Inductive Generalizations Critique

20. Critique • Representativeness (p. 54ff) • The more representative a sample, the stronger the generalization • A sample is representative of a population to the degree that the target characteristic found in the sample occur (i) with the same frequency or (ii) in the same proportion as they occur in the population

21. Critique • Representativeness (p. 54ff) • The more representative a sample, the stronger the generalization • A sample is representative of a population to the degree that the target characteristic found in the sample occur (i) with the same frequency or (ii) in the same proportion as they occur in the population

22. Critique • Representativeness • Implies a current knowledge of the population • Character of population • Relevant differences within population Randomness Each member of the population has an equal chance of occurring in the sample, i.e., the sample is randomly selected

23. Critique Randomness mathematically defined • Every member of the population has an equal chance of being selected as a member of the sample • Sampling Methodologies • Simple Random • Stratified Random

24. Critique Randomness mathematically defined • Every member of the population has an equal chance of being selected as a member of the sample • Sampling Methodologies • Simple Random • Stratified Random

25. Sample Selection and Construction • Simple Random Sampling Methodologies • Target characteristic presumed to be evenly distributed throughout the population • Population is fairly homogenous See exercise 8.2A: 1 (p. 59)

27. Sample Selection and Construction • Stratified Random Sampling Methodologies • Target characteristic not evenly distributed throughout the population • The population: heterogeneous groupings • These groupings are strata • Sample to be constructed to reflect statistical proportion of strata within total population See exercise 8.2B, #9 (p. 62)

29. Critique Two Issues Affecting Strength • Representativeness of Sample (biased sample) • Sample too small • Size is a function of representativeness • Sample fails to reflect the diversity (heterogeneity) of population • Not proportionately composed • Interviewer Bias • Target characteristic not clearly defined • Survey method skews results in a particular direction Randomness Each member of the population has an equal chance of occurring in the sample, i.e., the sample is randomly selected

30. Critique Strong or Weak? Example from Lexington Herald-Leader, 11/6/07 Kentucky Secretary of State Trey Grayson predicted about 42 percent of the voters in Kentucky will cast ballots. Kentucky has 2.8 million registered voters, including about 1.6 million Democrats, about 1 million Republicans and 186,451 people registered as "other." Grayson, Kentucky's top election official, said the projection was based in part on an increase in absentee ballots cast in the days before Tuesday's election. The number was up by about 20 percent from the 2003 election. Sample size? Statistical representation of different strata? What other “partial” factors were considered?

31. Generalizations • What are these? • Arguments that move from particulars to generalities • What are their elements? • Population • Sample • Target Characteristic • How to critique • Representativeness • Same Size • Methodology • Interviewer bias

32. Homework • Introductory Logic • pp. 49 – 63 • Analysis and Critique • Identify the 3 parts of an inductive generalization • Explain what are the basic evaluative criteria by which to judge the strength of the generalization • Ex. 8.2A & B (as assigned in recitation) • Follow directions from 8.2B • pp. 63 – 79 • Next class: Causal Arguments