Carl James Schwarz
Simon Fraser University
Journal of Statistics Education v.5, n.2 (1997)
Copyright (c) 1997 by Carl James Schwarz, all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the author and advance notification of the editor.
Key Words: Design of sample surveys; Instructional computing; Statistics education; Teaching statistics; World Wide Web material.
StatVillage is a hypothetical city based on real data that is suitable as a teaching aid for an introductory class in survey sampling. It uses a World Wide Web-based interface to allow the students to actively select sampling units; it then returns the corresponding data for further analysis. The underlying data are actual census records extracted from public use microdata files.
1 For many students, their first course in survey sampling is the quintessential cookbook course -- formulae for estimators and their theoretical and estimated standard errors are presented in rapid succession with little time spent on actually doing data collection or survey design. There have been a number of compilations of data collection exercises (e.g., Scheaffer, Gnanadesikan, Watkins, and Witmer 1996), but these have been mostly for simple surveys (e.g., simple random samples). However, it is difficult to design and have students collect data under more complex sampling schemes. It is even more difficult to repeat the data collection on the same real population using different sampling schemes so that students can compare the designs in practice.
2 Consequently, computer simulations seem to offer a solution whereby students can design and execute different surveys of hypothetical populations. For example, Chang, Lohr, and McLaren (1992) presented a FORTRAN computer program that allows students to select households from the hypothetical Lockhart City to study questions related to the provision of cable television. The "data" are generated using pseudo-random numbers with a pre-specified correlation structure. Students obtain data in a two-stage process. First the student uses a computer program to generate an address file containing the units to be surveyed. Then this address file is passed to another program that generates the datafile for subsequent analysis.
3 Stat City (Gitlow 1982) is another hypothetical population that can be used in a similar fashion. Stat City contains a map of the city showing the location of every dwelling. After students select dwellings to be surveyed, the information is extracted from a file containing computer-generated data. No software was provided to facilitate the extraction of the data.
4 Both of these examples used hypothetical data. While this allows the instructor to generate data quickly, it lacks realism. It is very difficult for an instructor to capture the true dynamics of relationships among variables from a simple correlation matrix. Indeed, it may be difficult to even specify realistic correlations among many variables.
5 The use of specialized computer programs also presents difficulties in this age of distributed computing. Separate versions must be prepared for each of the different platforms in use. Maintenance and enforcing consistency on different platforms is time consuming.
6 Consequently, StatVillage was "created" to extend these previous examples in two important ways. First, it uses the standard World Wide Web (WWW) HyperText Markup Language (HTML) to present students with a clickable map showing the locations of every dwelling unit in the village. After students select the dwelling units to be surveyed, they send a request using the browser to the WWW server, which returns the data. Second, these data are actual census observations extracted from the 1991 Census Public Use Microdata File on Households and Housing (Statistics Canada 1994).
7 StatVillage may be accessed by pointing a WWW browser to
8 The following script is very similar to an exercise used for a course that used StatVillage. It demonstrates how StatVillage can be used in a course in survey sampling.
9 A very pressing need in StatVillage is day care for pre-school children. A day care provider wishes to estimate the size of the market for this service. The provider approaches the Statistical Consulting Service of the StatVillage First University for assistance.
10 The consultant explains that one of the first things that needs to be done is to carefully define the target population and obtain a frame of units within the population. Fortunately, StatVillage is fairly small, and the households within StatVillage are arranged in a regular array of 128 blocks with each block consisting of 8 dwelling units arranged around a central core, for a total of 1024 dwellings. (A map is shown in Figure 1.) The day care provider indicates that all of the households within StatVillage are potential clients.
Figure 1. The StatVillage Clickable Map.
11 Because the provider will visit each of the households in person, a cluster sample was designed. The Statistical Consulting Service helped the provider select a random sample of blocks; the provider will interview all households in the selected blocks. The selected units are indicated by x's in Figure 1.
12 The provider does the survey and returns with the data in a file as shown in Figure 2. (This is obtained by pressing the submit button at the bottom of the village map on the WWW screen.) A portion of the codebook for the fields on the file is shown in Figure 3.
Figure 2. Sample Display of Results Returned to Students.
Figure 3 (14.4K gif)
Figure 3. Portion of the Codebook Available Online.
13 The provider can analyze the data using any preferred software. The file can be easily loaded into a spreadsheet program or can be read using a statistical package such as SAS.
14 There are three configurations for StatVillage. Figure 1 shows the maximal configuration consisting of a regular array of 128 blocks with each block consisting of 8 dwelling units arranged around a central core, for a total of 1024 dwellings. This version of StatVillage uses a simple rather than a complicated layout because students in a first course in survey sampling should concentrate on comparing survey designs in simple populations before progressing to more complex populations. Nevertheless, this layout allows students to select units using simple random, systematic, cluster, two-stage, and two-phase sampling plans. The introductory screen to StatVillage (not shown in this paper) also hints at an income stratification. Two additional configurations are also available -- a mini-version consisting of 60 blocks and a micro-version consisting of 36 blocks. These smaller versions may be useful in situations where hardware or software problems make the larger map infeasible (see Section 3.2 below) or as demonstration versions in a computer lab.
15 The map for StatVillage was built using standard HTML forms to create a grid of check boxes. These are arranged into a series of nested tables with the borders selectively displayed to show the block and town boundaries. The actual HTML commands may be seen by downloading the source code for the page using the WWW browser. The HTML code for the three versions was generated using a SAS program that is available from the Journal of Statistics Education; it can easily be modified to generate other configurations.
16 Students will typically print a blank copy of the layout using the browser. They will select dwelling units according to some survey protocol and will then return to the WWW page to select their units. Extensive labeling of the units was deliberately omitted so that students would face problems of establishing listings and ensuring that the proper households are actually surveyed.
17 Forcing the students to physically click and select the survey units has a beneficial side effect of reinforcing the idea that travel costs are an important aspect of the design. For example, it is much more time consuming to click on 80 randomly selected dwellings than to find 10 randomly selected blocks and select all the units within those blocks.
18 After selecting the survey units, students submit the page to the WWW server where a perl script extracts the data from a file and returns it to the student (Figure 2). The student can then save this extracted information to a file and process it with appropriate software. (The current version of StatVillage includes a link to a sample SAS DATA step that can be used to read and process the data. Similar aids can be easily written for other statistical packages such as Minitab.)
19 The data for StatVillage were randomly selected (about a 1/12 sample) from the records for households living in single family dwellings or in single story apartment dwellings in Vancouver, BC, Canada, from the 1991 Census Public Use Microdata File on Households and Housing (Statistics Canada 1994).
20 The microdata file contains samples of anonymous responses to the 1991 Census long questionnaire. A subset of 34 data fields in the following categories were selected from those on the microdata files.
21 Each field is documented in the on-line codebook (see Figure 3) extracted from the actual code book for this survey (Statistics Canada 1994). The data were sorted by total income plus noise before being assigned to the dwelling units in StatVillage. This corresponds to the income stratification observed in most cities.
22 All platforms (UNIX, Macintosh, and non-Macintosh) will require Netscape or an equivalent. Most of the software testing has been done on a Macintosh machine with only occasional testing on non-Macintosh machines. We have tested StatVillage with both Netscape 2.02 and Netscape 3.0. Some users have reported problems in loading the entire village (see below). Two smaller villages are also available that seem to solve this problem.
23 Because of widely differing hardware and operating system options found on UNIX workstations, we are unable to outline any hardware requirements with any degree of certainty. However, most workstations usually have large amounts of RAM so we do not expect a problem in running the WWW browser.
24 Our student computer lab is equipped with Macintosh PowerPCs running System 7.5 with 16 Mb RAM. We have had no reports of problems from students in loading the entire village on these machines. The authors have also tested the village on a Macintosh 040 machine with 16 Mb RAM and also found no problems.
25 Some students have smaller Macintosh machines at home, and they have experienced problems when they only have 8 Mb RAM. The system software left insufficient memory to also run Netscape, and these students received a message indicating that there was insufficient memory to load the browser. A memory upgrade or the use of a program such as RamDoubler solved these problem.
26 We have had only limited experience with non-Macintosh hardware. The most common problem reported is that 8 Mb RAM is insufficient to run Windows and Netscape and still have enough memory to load the entire village. The following symptoms of the problem have been observed:
27 We have had some success with the smaller versions of the village, but recommend that the memory be expanded or that a program such as RamDoubler be used.
28 StatVillage has been used in two types of courses: a one-term course on survey sampling for students majoring in statistics (about 15-20 students per class) and a one-term general introductory course for students majoring in other disciplines (200+ students per class).
29 For students in the first group, StatVillage was used extensively in the assignments to illustrate sampling using a variety of methods. Students were responsible for selecting units and computing the estimates and the estimated standard errors based on the returned data. For students in the second group, usage was limited to selecting samples of various sizes (typically 10, 20, and 30 units) using a simple random sample (SRS) and computing the estimates by hand.
30 Students in both groups sent the instructor e-mail messages containing their final estimates so that the instructor could make a summary plot of the results from the entire class.
31 Fortunately, both sets of students had been exposed to using the WWW. The major students regularly use computer packages, and many of the instructors in our group regularly use the WWW to distribute handouts and assignments. The non-majors were enrolled in a special section that was experimenting with a WWW-based delivery of course material and had received a general introduction to the WWW earlier in the term. Consequently, only a few problems were encountered in having students locate and use the material on the WWW or in using e-mail to send estimates back to the instructor. When using StatVillage with a less computer-literate class, some instruction in using the WWW will be required.
32 Four minor problems were encountered with using the computer:
33 There are few computer packages that can be easily used to analyze survey data. With small datasets, students can do the computations by hand, but this becomes infeasible with larger sample sizes. (Most assignments for the major class had sample sizes of around 100.) Students who used SAS or S-PLUS to analyze the data required a fair amount of assistance in using the package, even for the simplest non-SRS design (e.g., a stratified sample). Sample programs showing how to use the package will be helpful for students. Students who used a spreadsheet (e.g., EXCEL) required much less assistance.
34 Novices often tend to view things differently from experts. I was surprised at some of the conceptual problems that were exposed through reading the assignments and marking the exams.
35 To an instructor in statistics, the rationale for sampling seems obvious -- it gives information about the population that is either unattainable or only attainable at a great cost from the population. Yet a sizable minority of students (even among the major students) were unclear about why sampling needs to be done. I tried to motivate the use of StatVillage with a real-world problem, e.g., how to estimate the number of pre-school children in a district to plan for day care spaces. Yet students would often suggest that a census be undertaken and that all households of StatVillage be surveyed. From our in-class discussions, it appeared that this notion arose from an incorrect view of exactly what information is available. For example, students would respond with "ask the government," or "check with the school board" to obtain the exact count. They seemed to be unaware that much information is not routinely available. In addition, the small size of the village may have contributed to this conceptual problem -- with only 1024 dwellings, it is certainly conceivable to the students that a complete census could be done. To avoid this problem, the instructor must be very careful to elicit from the class the assumptions that they are making about what data might be available in real world examples, as well as the actual size of the population that is being sampled.
36 Some students failed to make the connection between the design used to sample the households and the method used to compute estimates. For example, they would use the formulae from a simple random sample when analyzing the results from a more complex design. Apparently they erroneously assume that because the final data structures are similar -- i.e., all case by variable structures -- that the analyses would be the same. I have found a similar problem in teaching classes in experimental design where students tend to analyze all data using a single-factor fixed-effects analysis of variance model, regardless of whether subjects (or seedlings or albino rats) were assigned to experimental conditions using a completely randomized design, a randomized block design, or a Latin Square design. In future years, I intend to emphasize that the meta-data (the information on how the survey was collected) is very important and must also be considered in any analysis.
37 Possibly the most complex concept for students to master is that of a sampling distribution. The most evident success in using StatVillage was that students actually saw point estimates that varied from student to student! Pairs of students (particularly in the non-major class) would come to my office wanting to know which answer was "correct" because they had obtained quite different values. After an assignment was complete, students were shown a dot-plot or histogram of the estimates from the class, and some students commented to me that they were shocked at how variable the estimates were around the true population value.
38 An even more gratifying response came from questions about the confidence intervals that each had computed -- particularly from students whose interval failed to cover the true population value. For some of the students, it was quite evident that this was unexpected, even though they could all recite from memory the definition of a confidence interval!
39 The ability to select units from the same population using different survey designs also gave students majoring in statistics a better appreciation of the differences among the designs. This was reinforced by having the students print out a copy of their clickable map after having selected units, but before pressing the submit button. The differences among a simple random sample, a systematic sample, a single-stage cluster sample, and a two-stage cluster sample were clear when these maps were placed side-by-side. It was less helpful for seeing the differences between a stratified design and a non-stratified design. However, as noted earlier, some students failed to appreciate the differences when confronted with just the raw data. Perhaps it would have been helpful for them to plot the sampled units on a map prior to analysis.
40 Finally, because the data were obtained from actual census data, students majoring in statistics had a better appreciation of the many peculiarities that can arise when dealing with real data. For example, when analyzing employment income, students were perplexed by negative values that can arise from self-employment. This led to a very interesting in-class discussion of why statistics agencies have very detailed criteria for deciding how to code variables such as employment status.
41 StatVillage provides the following benefits for teaching an introductory course in survey sampling:
42 StatVillage may be accessed directly from the Journal of Statistics Education. Alternatively, all files required to install StatVillage at a new site may be obtained from the journal in a zip file. Installation is explained in a README file contained in the zip file.
Chang, T. C., Lohr, S. L., and McLaren, C. G. (1992), "Teaching Survey Sampling Using Simulation," The American Statistician, 46, 232-237.
Gitlow, H. S. (1982), Stat City: Understanding Statistics Through Realistic Applications, Homewood, IL: Irwin.
Scheaffer, R. L., Gnanadesikan, M., Watkins, A., and Witmer, J. A. (1996), Activity-Based Statistics: Instructor Resources, New York: Springer.
Statistics Canada (1994), User Documentation for Public Use Microdata File on Households and Housing, Ottawa, Ontario: Statistics Canada.
Carl James Schwarz
Department of Mathematics and Statistics
Simon Fraser University
Burnaby, BC, Canada V9A 1S6
Download zip file containing all files required to install StatVillage locally, including this paper and Figures 1, 2, and 3, to a local file