POSC 202A: Lecture 2

1. POSC 202A: Lecture 2 Today: Introduction to R Today: Research Designs, Mean, Variance

2. Research Design Research Design- A strategy for evaluating the truth of a proposition

3. Research Design Two related issues: • Finding evidence that one thing causes another. We observe a relationship. • Finding evidence that alternative explanations do not cause the observed relationship.

4. Research Design How do we find evidence that alternative explanations do not cause the observed relationship? We try to compare cases in which the relationship occurs (and does not) occur to varying degrees.

5. Research Design So comparison is done through case selection. 9 factors characterize “goodness” in case selection. By maximizing particular characteristics in the cases we select we gain confidence about our inference.

6. Research Design: 9 Criteria • Plenitude • Boundedness • Comparability • Independence • Representativeness 6. Variation 7. Replicability 8. Mechanism 9. Causal comparison Research design is governed by tradeoffs among these different criteria rather than by fixed rules

7. Research Design: 9 Criteria Plenitude- The accumulation of comparative reference points constitutes evidence. The more cases, the more evidence.

8. Research Design: 9 Criteria Boundedness- A proposition should cover cases that are fundamentally similar, comparable or relevant. Sometimes increasing the N might require inclusion of inappropriate cases.

9. Research Design: 9 Criteria Comparability-

10. Research Design: 9 Criteria Comparability- Cases must be similar to one another in some important respect(s). Refers to the internal properties of the sample. -Data driven processes need to be similar

11. Research Design: 9 Criteria Independence-

12. Research Design: 9 Criteria Independence- The selection of a case for examination should not be related to, or affect the likelihood of selecting another case that is being examined. -This is often violated

13. Research Design: 9 Criteria Independence- Examples: • Selection of a card from a deck changes the likelihood of the next card being selected. • But if we put the card back in the deck, shuffle them, and select again, the draws are independent.

14. Research Design: 9 Criteria Representativeness-

15. Research Design: 9 Criteria Representativeness- The degree to which the sample is an accurate description of the characteristics of the population. -Think about generalizability – not all designs are interested in this.

16. Research Design: 9 Criteria Representativeness- Example: Experiments of the effect of drug use on rats may not be generalizable to humans because rats are different in some important ways. But note that the rats themselves are comparable with one another (i.e. they are similar).

17. Research Design: 9 Criteria Variation- The range of values registered for a given explanatory (x) or outcome (y) variable. Important because causation occurs when two things vary together. -This is critical to thinking about your data when evaluating relationships

18. Research Design: 9 Criteria Replicability- A good research design produces reliable results that do not vary across iteration. The results are repeatable. -Run same models/statistics on different survey datasets

19. Research Design: 9 Criteria Mechanism- Explains the link between cause and effect. We remain skeptical of a causal relationship until two factors can be linked. Example: Time of Day is negatively associated with light (as it gets later it gets darker) but lacks a mechanism for causing it.

20. Research Design: 9 Criteria Causal Comparison- We must evaluate rival explanations to provide evidence for a particular cause. An argument is verified when evidence indicates that one causal story is superior to others that explain the same event.

21. Review: Research Design By maximizing particular characteristics in the cases we select, we gain confidence about our inferences.

22. Research Design: Methods 3 general types of methods: • Case Study (N=1) • Small or Medium “N” • Large “N” Exhibit the 9 criteria to varying degrees

23. Research Design: Methods Case Study- The study of a single unit.

24. Research Design: Methods Case Study The study of a single unit. It allows us to understand the mechanisms that connect a particular X with a particular y.

25. Research Design: Methods Case Study Types: Extreme Case Crucial-Case Typical-Case

26. Research Design: Methods Extreme Case- Selection of a case that exhibits a high (extreme) level of the thing we wish to study. Example: A campaign that is highly competitive. This allows us to examine what factors are associated with competition.

27. Research Design: Methods Typical Case- Selection of a case that is most representative or typical of the thing we want to study. Example: A campaign that is not very competitive(!).

28. Research Design: Methods Crucial Case- A case in which alternative explanations for the same phenomena predict different outcomes. These are often hard to find But you want to find examples that fit all case-types, and the poles

29. Research Design: Methods Case Study It allows us to understand the mechanisms that connect a particular X with a particular y. BUT It lacks plenitude (i.e., case size is small) so it may be hard to tell whether the mechanism is systematic across cases or unique to the case being examined.

30. Research Design: Methods Small or Medium “N” Studies Analyses that employ small or medium sized samples and generally focus on variation across the primary unit of analysis.

31. Research Design: Methods Small or Medium “N” Study Types • Most Similar • Most Different

32. Research Design: Methods Most Similar- Looks for a few cases that are as similar as possible in all respects except for the outcome of interest which is expected to vary.

33. Research Design: Methods Most Similar-

34. Research Design: Methods Most Different- Look for a few cases that are as different as possible in all respects except for the outcome of interest which is expected to be the same.

35. Research Design: Methods Most Different- BUT these are more useful for eliminating possible causes than providing proof for a cause.

36. Research Design: Methods Large “N” Methods that draw on large numbers of cases or examples.

37. Research Design: Methods Large “N” • Experimental • Statistical

38. Research Design: Methods Large N studies maximize the largest number of the criteria for research design

39. Research Design: Methods

40. Describing Data Variable- A thing or quantity that varies across individuals, or objects (which are usually referred to as observations)

41. Describing Data Distributions: Tell us what value a variable takes and how frequently they take them.

42. Describing Data The most famous is the Normal distribution. What is it?

43. Describing Data Measures of central tendency mean, median, mode Measures of dispersion (spread) IQR, standard deviation, variance

44. 80 20 Describing Data Nth Percentile The percentage of observations in a distribution that fall to the left of point n. 20th percentile

45. Describing Data Quartile A range containing 25% of the observations in a distribution.

46. Describing Data 5 number summary: Minimum, 1st quartile, median, 3rd quartile and maximum

47. Describing Data 5 number summary: Minimum, 1st quartile, median, 3rd quartile and maximum 1st Quartile 3rd Quartile Median

48. Describing Data Inter-quartile range: The distance between the first and third quartiles. 1st Quartile 3rd Quartile

49. Describing Data Variance: A number that summarizes how far all of the observations are from the average of the distribution.

50. Describing Data Variance: