1. Units of Analysis
The Basics

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 reference interview. Early identification of the unit of analysis will help focus a search on statistics, aggregate data, or 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. 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

17. 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.

18. 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.

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

20. Identifying a Unit of Analysis
As hinted in the earlier illustration, the unit of analysis is shaped by three attributes:
Social Phenomena
Time
Space

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

22. Social Characteristics
Geography and Time held constant

23. Geography and Age held constant
Ordered by Time

24. Time and Age held constant
Geography Emphasized

25. Social Phenomena
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

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

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

28. 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

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

30. Complexity
Complexity occurs when multiple types of entities are introduced within the same study.
Examples
parent  child  teacher
person  activity  time
person  car  trips

31. Complexity
This 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

32. 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.

33. Complexity Children grouped (nested) with Parents. Parent 1 Parent 2

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

35. 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.

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

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

38. Complexity
Up to this point, complexity has been described conceptually. We’ve mentioned how multiple units of analysis and the ways in which they are related can create complexity.

39. 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.

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

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

42. 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.

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

44. 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.

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

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

47. Statistical Data Structure
This structure looks like the grid of a spreadsheet. However, there is one very important difference between a statistical data structure and a spreadsheet.

48. Statistical Data Structure
The spread sheet is organized around individual cells, while the statistical data structure is organized around the rows.

49. Statistical Data Structure
Spreadsheet

50. Statistical Data Structure
Spreadsheet
Cell B2
Cell C5
Cell E3
Cell F7

51. Statistical Data Structure
Row 1
Row 3
Row k-1

52. Statistical Data Structure
The next slide presents the way that this simple statistical data structure appears in SPSS.

54. Row 1

55. Row 1
Row 8

56. Row 1
Row 8
Row 15

57. Field 8
Row 1
Row 8
Row 15

58. Person: GSS 10 Main

59. WGHTFNL
DVAGECAP
DVSEX
RECID
PROV

60. Adding Complexity to Data
Structurally
hierarchical : order & different record layouts for different units of analysis
relational : 1 to n relations
compound records : combination of units represented on each record

61. Complex Data Structure
Hierarchical Data Structure
Household 1
Person 1
Person 2
Household 2
Household 3
Person 3

62. Geography: 1991 Census
N9101 Population 15 years and over by age groups (17) and marital status (6a), showing labour force activity (8) and sex (3) RM RM RM T T T RM RM

63. CSD Type
CCS
CMA/CA
PROV
FED EA CD
CSD RM RM RM T T T RM RM

64. CSD Type
CCS
CMA/CA
PROV
FED EA CD
CSD RM RM RM T T T RM RM

65. Complex Data Structure
Relational Data Structure
R1 C1
R1 C2 R1 R2 R3 R4 R5
R1 C3
R1 C4
R3 C1
R3 C2
R4 C1
R5 C1
One to Many
R5 C2

66. Person: GSS 10 Union

67. UNIONTYP
UNIONRNK
RECID

68. GSS 10 Main
GSS 10 Union

69. GSS 10 Main
GSS 10 Union

70. Complex Data Structure
Compound Data Structure
R1 x T1 x A1
R1 x T2 x A4
R1 x T3 x A7
R1 x T4 x A3
R1 x T4 x A1
R2 x T1 x A2
R2 x T2 x A9

71. GSS 2 Episode

72. NO_EPISO
ACT_CODE
SEQNUM
DDAY

73. NO_EPISO
ACT_CODE
SEQNUM
DDAY