1. Aggregate Data and Statistics
Wendy Watkins Carleton University
Chuck Humphrey University of Alberta
Title page
Greetings: Good morning everyone, glad to be with you for this workshop.
If you have questions through out our presentation please just ask and we can elaborate more on these questions you have.
Statistics Canada Data Liberation Initiative
CAPDU/DLI Training May 29th, 2002

2. Outline What are aggregate data? Why aggregate? How to aggregate?
Computing exercise

3. What are aggregate data?
Let’s start with the relationship between statistics and data.

4. Statistics and Data Data Statistics numeric facts/figures
numeric files created and organized for analysis
requires processing
not ready for display
Statistics
numeric facts/figures
created from data, i.e, already processed
presentation-ready

5. Statistics and Data

7. Statistics and Data

8. Statistics and Data
In short, statistics are created from data and represent summaries of the detail observed in the data.

9. What is aggregation?
Building on this previous example, let’s explore aggregation.
We see a table with the number of smokers summarized over categories for age, education, sex, geography, and different time points.

10. Categories of Periods
A Statistic
Categories of Sex
Categories of Region

11. What is aggregation?
Aggregation involves tabulating a summary statistic across all of the categories or levels of a set of variables.

12. The summary statistic
The summary statistic in this example is the total number of smokers.

13. Variables and categories
The variables and their categories are:
Region (11): Canada and the ten provinces
Age (5) : Total, 15-19, 20-44, 45-64, 65+
Sex (3) : Total, Female, Male
Education (4) : Total, Some secondary or less, Secondary graduate or more, Not stated
Periods (5) : 1985, 1989, 1991, ,

14. Variables and categories
The tabulation consists of determining the combinations of all categories across variables and then counting the number of smokers within each of these combinations.
11 x 5 x 3 x 4 x 5 = 3300 category
combinations

15. Tabulating or aggregating
One might be wondering if there is a difference between tabulating and aggregating?
Usually, they are the same thing.

16. Tabulating = aggregating
In creating tables from data, the variables are arranged in various combinations along the columns and the rows.

17. Tabulating = aggregating
Placing multiple variables along the columns or rows is called nesting.
Tables may have variables nested on both the columns and rows.

18. Categories of Sex nested within Periods

19. Categories of Education nested within Sex
Categories of Sex nested within Region

20. A quick summary Up to this point, we have noted that
statistics are created from data
aggregations consist of tabulating statistics within the categories of select variables
variables may be nested within columns and rows to display these tabulations

21. What are aggregate data?
What is the difference between a tabulation or aggregation and aggregate data?
The display of the aggregation, that is, the structure of the tabulated output.

22. What are aggregate data?
A statistical data structure is a fixed, two-dimensional matrix with the variables in the columns and cases in the rows. V1 V2 V3 V4 V5 V6 V7
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
Case 7

23. What are aggregate data?
Aggregate data require the same type of statistical data structure.
Consequently, aggregate data are a special type of tabulation where variables are nested along the rows but not along the columns.

24. (11)
(5)
(3)
(4)

25. Aggregate Data Structure
To create an aggregate data structure for the example tabulation, the combination of categories representing geography (region), three social variables (age, sex, and education), and time (period) must all be nested along the rows, as shown in the previous slide.

26. Another example
This time the table consists of the average length of stay in hospital by sex, age, diagnostic chapter, region, and time period.

28. Variables and categories
diagnostic chapter : 19 levels
sex : 3 levels
age : 6 levels
region : 13 levels
period : 28 levels

29. Aggregate data structure
The number of category combinations is equal to:
13 x 28 x 3 x 6 x 19 = 124,488 category
combinations

31. Aggregate average length of hospital stays in days
The aggregate structure is represented by the 124,488 cells created by the combination of all categories from these five variables.
The statistic is the average length of stay in the hospital in days.

32. What are aggregate data?
Definition: Statistical summaries over categorical variables representing social phenomena, geography, and time that are organized in a specific data structure.

33. Time series aggregate data
When the data structure of the summaries is organized around time, these aggregate statistics are called a time series.

34. Time Series aggregate data structure

35. Annual Time Series

36. Geo-spatial aggregate data
When the data structure of the summaries is organized around geography, we recognize these aggregations as geo-spatial or geo-referenced statistics.

37. Geo-spatial aggregate data structure

38. Province
Census Divisions
Census Sub-divisions

39. Why aggregate?
Statistics Canada creates aggregate statistics from its major surveys, including the Census, as a way of publishing selected findings.
The release of aggregate statistics is a partial safeguard against the possible disclosure of respondents.

40. Why aggregate?
Furthermore, the geographic distribution of statistics in Canada is important. As a result, aggregate statistics are released by Statistics Canada for different levels of geography – from the nation to small areas.

41. Why aggregate?
Statistics organized into time series is another way in which Statistics Canada publishes a large amount of statistical information. These time series reflect summaries of data that are repeatedly collected over time and permit studies about trends and change.

42. Why aggregate? To publish findings To safeguard against disclosure
To provide geographic distributions of statistics
To present statistics over time

43. Why aggregate? Other reasons to aggregate
To modify geo-referenced statistics for GIS applications
for example, finding postal codes within their corresponding EA and then aggregating data from the postal code level up to the EA level

44. Why aggregate? Other reasons to aggregate
To change the unit of analysis
for the purposes of a specific research question
to create a common, higher-level unit of analysis that can be used in merging files

45. How does one aggregate?
Identify the grouping structure that represents all of the variables and their categories over which the aggregation is to be conducted.
This group structure defines a new unit of analysis.

46. How does one aggregate?
Establish the sort order for the grouping variables, i.e., decide which variable increments the fastest, the next fastest, until you reach the variable that changes the slowest.
Select the summary statistics, such as sums, averages, minimums, maximums, etc.

47. How does one aggregate?
The actual aggregation is performed using statistical software such as SAS or SPSS.
SAS offers a couple of different procedures and the Data step that can be used to aggregate data, including Proc Summary, Proc Tabulate, and Proc Means.

49. How does one aggregate?
SPSS has the Aggregate command.

50. Aggregation Only nesting of the row variables
Multiple levels of geography and time
Aggregation

51. Tabulating = aggregating
Furthermore, geography and time may not play a prominent role in the data and consequently, tables from these data will not include variables for geography and time.

52. Tabulating Aggregating Geography and time are each a single category
Sex and age nested in the column variables
Tabulating
Aggregating