Units of Analysis

1. Units of Analysis The Basics Chuck Humphrey Atlantic DLI Training March 14, 2002

2. Outline • An illustration • Definitions • Elements of the unit of analysis • Complexity • Data structure

3. An Illustration A group of students in an econometrics class were sent to the Data Library to find some data for an assignment.

4. An Illustration A typical request was like this one. “I want to look at crime rates and a person’s level of education.”

5. An Illustration This request raises problems. • crime rates are usually associated with spatial units or a time series • a person’s education is an attribute of individuals

6. An Illustration What are we looking for? • does the student want crime rates and the percentage of the population with certain education levels for specific cities? This would be data aggregated over geography.

7. An Illustration What are we looking for? • does the student want the crime rate for one city over time, such as the number of homicides in Edmonton over the past 40 years. This would be data aggregated over time.

8. An Illustration What are we looking for? • does the student want the education level of criminals? This would be a special subpopulation of individuals convicted of crimes and consist of a microdata file of criminals.

9. An Illustration What are we looking for? • does the student want the education level of victims of crimes? This would be a special subpopulation of individuals who were victimized and consist of a microdata file of victims.

10. An Illustration Looking at crime rates and level of education can differ depending upon the unit of analysis. • individuals • geographic areas • changes over time

11. An Illustration After walking the student through these steps, he chose to build a model predicting income on the basis of highest educational attainment and a few other variables from the Census individual-level public use microdata file. He completely abandoned his interest in crime!

12. An Illustration Unfortunately, the student’s initial request not only failed to specify a clear unit of analysis, it included a mix of different units, which suggests that the concept was not understood.

13. The Point of the Illustration The unit of analysis is fundamental to the data and statistical reference interview. Early identification of the unit of analysis will help focus a search on (a) statistics, (b) aggregate data, or (c) microdata.

14. The Point of the Illustration Furthermore, the unit of analysis is fundamental to secondary data analysis. It may be that knowledge of the unit of analysis is even more crucial in secondary analysis than in primary analysis, where the unit is implicit in the sample design, if not otherwise explicit.

15. The Point of the Illustration Finally, the unit of analysis is a fundamental characteristic of statistical data structures, which are the formal ways in which data are organized for processing.

16. Where We’re Headed Let’s look closer at the concepts behind the unit of analysis and then we’ll look at how these concepts end up being converted into data structures.

17. Definitions The unit of analysis is the basic entity or object • about which generalizations are to be made based on an analysis, and • for which data have been collected

18. Definitions How does the unit of analysis relate to the unit of observation? The unit of observation is the entity in primary research that is observed and about which information is systematically collected.

19. Definitions The unit of observation and the unit of analysis are the same when the generalizations being made from a statistical analysis are attributed to the unit of observation.

20. Definitions • Unit of Observation • in original data collections, the unit of observation is determined by the method by which observations are selected • Unit of Analysis • in secondary analysis, the unit of analysis is determined by an interest in exploring or explaining a specific phenomenon

21. Identifying a Unit of Analysis As hinted in the earlier illustration, the unit of analysis is shaped by three attributes: • social entities • time • space

22. Research Outputs Let’s begin by looking at a finished product to examine these attributes more closely. We’ll use a table from the Health Indicators Database about suicide.

23. Geography and Time held constant Social Characteristics Emphasized

24. Geography and Age held constant Ordered by Time

25. Time and Age held constant Geography Emphasized

26. Social Entities • observations of a single social entity, such as a person or an institution • observations of multiple entities with a defined relationship, such as family, employer-employee

27. Social Phenomena • transactional observations that are the result of actions among entities, such as labour strikes or international conflicts, including wars

28. Time • observations made at one point in time; commonly referred to as a cross-sectional study

29. Time • observations made at multiple points in time • the data may be organized by time; commonly referred to as a time series • time may structure some form of repeated measures of content or subjects

30. Space • observations made within a specific spatial area • observations made within a hierarchy of spatial areas

31. Substituting Units There may be requests for which data for a desired unit of analysis can’t be delivered but for which data are available summarized over one of the other attributes of the unit of analysis.

32. Substituting Units Example: • Request for firm-level data for NAICS 312 Beverage and Tobacco Product Manufacturing • Ideal source: microdata on companies from the Canadian Census of Manufacturers • No access to enterprise microdata

33. Substituting Units Example: NAICS 312 • Alternatives: are there aggregate data summarizing the firms within NAICS 312? • Possibilities: summaries over time (time series) or geography (small-area business statistics)

34. Complexity Complexity occurs when multiple entities are introduced within the same study. Examples parent  child  teacher person  activities  time person  cars  trips

35. Complexity Complexity can arise within one of the attributes just discussed. • a study of parents, children, and teachers, which are all social units or between attributes • a study of people, their daily activities, and the length of time of each activity

36. Complexity Complexity is often represented in an hierarchy when the units can be grouped or nested within one another. For example, children may be grouped with their parents.

37. Parent 1 Parent 2 Child 1 Child 2 Child 3 Complexity Children grouped (nested) with Parents.

38. Household 1 Household 2 Family A Family A Person i Person i Person ii Person ii Complexity Parents and their children may be grouped into families and families grouped into households.

39. Complexity Complexity may also be represented by combinations of entities among units. Those entities that are associated with one another are combined and those that aren’t associated, aren’t combined.

40. Complexity These combinations are often described as having been crossed. For example, activities may be crossed with people.

41. Activity 1 Activity 2 Person A Activity 4 Activity 3 X Person B Activity 5 Activity 6 = Person A Activity 3 Activity 6 Person B Activity 1 Activity 5 Complexity Activities crossed with people.

42. Complexity Up to this point, complexity has been described conceptually. We’ve mentioned how complexity can be created through multiple units of analysis and the ways in which these units are related.

43. Complexity Complexity also manifests itself structurally through the ways in which data are organized to represent the nesting or crossing of multiple units of analysis.

44. Thinking about Units of Analysis • Conceptually • What is the content? This is what we’ve been reviewing up to this point. • Structurally • How is this complexity organized? This takes us to a discussion about data structure.

45. Statistical Data Structure Let’s review basic data structure. The unit of analysis defines the underlying structure of a data file.

46. Statistical Data Structure This structure consists of a series of rows with each row containing the data of one member of the unit of the unit of analysis. This simple structure is known as the flat, rectangular data matrix.

47. Case 1 Case 2 Case 3 * * * Case n Statistical Data Structure Case n-1

48. Statistical Data Structure All of the information collected for each member of the unit of analysis is organized in a fixed location in the file called fields or variables.

49. Field k-1 Field 3 Field k Field2 Field 1 * * Case 1 Case 2 Case 3 * * * Case n Statistical Data Structure Case n-1

50. Field k-1 Field 3 Field k Field2 Field 1 * * Case 1 Case 2 Case 3 * * * Case n-1 Case n Statistical Data Structure