CENTRAL PLACE FUNCTIONS IN BUTTE COUNTY

(Exercise modified from one originally designed by Dr. E. Rovai)

The purpose of this exercise is to examine the economic functions of and relationships among central places (or settlements). This kind of exercise works best in a more rural environment, which includes the very smallest types of central place. At this level, collecting data on numbers of businesses and of business types becomes a manageable task.

So, I've picked Butte County, a mostly rural county in the North State (about an hour or so north of Sacramento). The county includes three larger towns: Chico (a college town), Oroville (the county seat and a poverty-stricken old mining town, which was hard-hit by the end of construction on the Oroville Dam in the late 1960s), and Paradise (an amenity town favored by LA and Bay Area retirees and a bedroom community for Chico and Oroville: "West Covina in the Pines"). There are 32 other central places, some of them with well under 100 residents. So, this county gives us representatives of the very bottom of the "urban" hierarchy.

SUPPLIES NEEDED

Butte County Yellow Pages (one copy to share)

Paper (ideally, large sheets)

Pencil, ruler, and (no doubt) eraser

Calculator (not necessary if you use a spreadsheet)

Spreadsheet computer program (recommended but not necessary)

COLLECTING THE DATA

Setting up the Data Collection Form:

On the first page of the Yellow Pages in your telephone directory, you will find a list of communities covered by the Yellow Pages. The name of each community is given, together with the abbreviations used by the telephone company.

Turn a sheet of paper on its side, so that it is oriented horizontally. Ideally, use a large sheet, such as 11" x 17" or 8.5" x 14." Make one thin column (about .5") down the leftmost side of the sheet. Divide the rest of the paper into columns about 1"-1.5" wide. Across the top, draw a horizontal line and, above that line, write one community abbreviation at the top of each column. Guess what. You'll need more than one sheet of paper.

Draw a second horizontal line about .25" below the first one. For each community, put in its population as of the 1990 Census (see Table 1).

Developing a Random Sample of Yellow Pages:

Now, select 30 pages from the Yellow Pages. Your selection needs to be a representative sample of the "population" of Yellow Pages. If your sample is drawn in a statistically random manner, it is logically sound for you to generalize results from your sample to the entire population of Yellow Pages (for reasons made clear in GEOG 200, "Research Methods"). You can guarantee representativeness by consulting a random number table at the back of any statistics book. What? You don't just happen to have one off hand?! You mean you actually SOLD your GEOG 200 book? Tsk. Okay, I built one for you from a random number generator, and you may consult it in Table 2.

To use this table, first get the total number of Yellow Pages in your directory (okay, it's 552). This is a three digit number. I'm not going to be as picky about how you get into the table: Just point anywhere on the table and pick a direction to move in (up, down, right, left, it doesn't matter). Pick a group of three numbers. If the resulting 3-digit number is from 001-552 (inclusive), write it down in pencil (because you may have to delete them later, as described below). If it's 000 or more than 552, toss it out. Get the next number and keep going until you have thirty numbers. Throw out any duplicates (sampling without replacement). When you have thirty non-duplicate numbers, all ranging from 001 through 552, enter them in that blank column on the leftmost end of your sheet, under "Yellow Pages p. #." Mark where you left off in the random number table (in case you need new numbers, as described below). You now have thirty rows in which to enter data.

Data Entry:

Now, go to the first page listed. If there's only one big ad on it and no listings, toss that number out and get another one from the random number table (now you know why I said to mark your random numbers in pencil). Ignoring ads, count how many business types there are on that page (the black bars). This is the maximum number of central place functions found on that page. Go back through that page and, for each community, find out how many of those black bars (business types) contain at least one listing for that community. Note that number in the left column under that community's name.

That done, go back and, ignoring the black bars, count all the separate businesses in each community with at least one listing anywhere on that page. Enter that number in the right column under the community's name.

Repeat this process of counting a central place's FUNCTIONS and its NUMBER of establishments for every Yellow Page you included in your sample. You now have a random sample of the business structure of Butte County.

Let's use this sample to estimate the total number of central place functions and total number of establishments for each community. Add up each column, putting the sum in the 31st row. You now have two sums for each community.

Since this is a statistically random sample of functions and establishments, we can infer how many functions and establishments each community is likely to have in total. Simply multiply each of the sums by the total number of Yellow Pages in your directory (552) and then divide that answer by 30 (for the pages in your sample). Put that quotient in the 32nd row. Row 32, then, provides your estimates of the number of central place functions and the number of business establishments each community contains.

PLOTTING THE RESULTS

You can now make four "X-Y" graphs of your results on separate sheets of paper for further analysis. Make sure to read through this whole section of the lab before starting on your graphs, so you don't waste your efforts on unworkable graphs.

The first graph, ideally a scattergram, will plot the estimated number of establishments on the X or horizontal axis against the number of central place functions on the Y or vertical axis:

With the fourth graph, the X axis might best be scaled on a geometric, not arithmetic, scale (i.e., 0-99.9, 100-999.9, 1000-9999.9, ...). Construct bars going up from the X axis to the appropriate height from the Y axis. Since the underlying distribution of population is effectively continuous (instead of categorical, e.g., County A, County B, and County C or male and female), indicate that by having the bars touch one another. This kind of bar chart for effectively continuous data is called a "histogram."

Then, go on ahead and draw your axes, label them, label their scales, and plot the values. It is very important to label your graphs AND their axes AND the values on the axes.

WRITING UP YOUR RESULTS

In class, we'll study your four graphs and the patterns you find. Before the class discussion, make sure to read about Christaller's central place hierarchies in the Lloyd and Dicken reserve reading. In which ways do your results seem to conform with the expectations of central place theory (see Table 3 at the end of this exercise)? In which ways do they deviate? If there are anomalies, identify them and speculate on why you think they exist. Hint: the change in predominant transportation technology from the time of Christaller's case study in Southern Germany back in the 1930s to the time of your case study in the North State of the 1990s plays a rôle; see if you can figure out its relevance. After class discussion, I'd like each of you to write up a brief lab report (about 1 page), summarizing the applicability of central place theory to the central places of Butte County and explaining any disparities between the theory's expectations and the actual central place hierarchy.