GEOG 101: Global Economic Geography

Dr. Rodrigue

Lab 3: Central Place Functions in Butte County

==========

Student name: _____________________________________

==========


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 the central places (or settlements) of Butte County.


==========

SUPPLIES NEEDED

Butte County Yellow Pages
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 phone 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 last Census (see Table 1).

Now, divide each community column into two subcolumns (under the second horizontal line). Draw a third horizontal line about .25" below the second one. For each community, label the left column "Typ" for number of TYPES of business (or central place functions). Label the right column "Est" for the number of establishments or individual businesses.

You should now have something that looks rather like this:


     Yellow | Bngr    | Bery Crk | Bgs      |
     -------|---------|----------|----------|-------------------------------
     Pages  |   150   |    185   |  1,480   |
     -------|---------|----------|----------|-------------------------------
     p. #   | typ| est|  typ| est| typ| est |
     _______|____|____|_____|____|____|_____|_______________________________
            |    |    |     |    |    |     |
            |    |    |     |    |    |     | 

==========

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 215, "Quantitative 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?! 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 in mine). This is a three digit number. Going to your 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. 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. 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:


    # cpf |                   This shows the relationship between num-
          |                   ber of establishments (# est) and diver-
          |                   sity  of  businesses  or  central  place
          |_______  # est     functions (#cpf).                       

The second graph, also best shown as a scattergram, will show the estimated number of establishments on the Y axis as a function of population on the X axis:

    # est |                   This  shows  the  relationship   between  
          |                   market  size (population, or # pop)  and  
          |                   number of businesses (# est) it can sup-  
          |_______  # pop     port                                      

The third graph, again a scattergram, will plot the population of each community on the X axis against the number of estimated number of central place functions on the Y axis:




    # cpf |                   This  shows  the  relationship   between
          |                   market  size (population, or # pop)  and
          |                   diversity of business types (# cpf)     
          |_______  # pop     


The fourth graph, ideally a histogram (or bar chart, with the columns shown touching one another) will plot population size on the X axis against the number of central places of a given size on the Y axis

    # cp  |                   This shows the relationship between  the
          |                   size  of  a community (#  pop)  and  the
          |                   number of communities (central places,or
          |_______  # pop     # cp) at that size.                     


Before you construct these graphs, you need to scale their variables so the graphs will fit properly on your paper. Determine the range of values (i.e., the highest and lowest values) for each variable (i.e., population, number of central places, number of central place functions, and number of establishments). Then, with an idea of the range, create equal intervals, grouping the values so that they will fit neatly on a graph of reasonable size. To make a scattergram, look up each X value on the X axis and then place a dot directly above it at the corresponding height for that community's value on the Y 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

Study your four graphs and state the patterns you see. 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.

Please do your write-up on the back of this lab. This economizes on dead tree products.




======================================================================

Table 1

----------------------------------------------------------------------
POPULATIONS
                                                               
  Bangor                150             Lovelock             35
  Berry Creek           185             Magalia             400
  Biggs               1,480             Nelson               75
  Butte Meadows         415             Nimshew             ~60
  Cana                  ~15             Nord                140
  Challenge             550             Oregon City          20
  Cherokee              125             Oroville         10,350
  Chico Urban Area  ~80,000             Palermo           4,260
  Cohasset              445             Paradise         25,408
  Dayton                105             Pentz                80
  De Sabla              110             Pulga                60
  Durham              4,784             Rackerby            200
  Feather River         350             Richvale            300
  Forest Ranch          340             Stirling City       415
  Gridley             4,270             Thermalito        5,946
  Hamilton City       1,337             Wyandotte           140
  Lake Madrone          ~80             Yankee Hill         135
  Lake Wildwood      ~6,000                                    
----------------------------------------------------------------------
Sources:  U.S. Census.  1990.  Summary Tape File 3A.
          Dr. William Collins. 1993. Personal communication.
----------------------------------------------------------------------




======================================================================

Table 2

----------------------------------------------------------------------
RANDOM NUMBER TABLE

 333 628 346     297 341 838     392 254 402     022 888 882     186 101 871     025 513 474
 494 735 557     009 399 701     541 734 062     566 637 165     678 304 392     752 433 851



 339 426 862     470 015 564     978 392 895     090 121 158     208 258 309     686 056 093
 879 512 925     445 448 164     395 397 809     095 034 639     213 965 270     784 142 582
 362 407 300     021 027 253     392 956 328     188 085 574     453 444 014     111 270 486

 127 201 147     530 411 695     235 389 264     313 821 833     384 716 330     298 745 689
 123 477 889     330 637 532     020 569 475     934 934 538     187 780 389     625 507 370
 969 267 861     079 134 495     770 836 512     692 342 906     414 105 655     470 564 898
 308 450 575     668 874 172     603 015 229     517 654 958     204 718 162     802 606 281
 020 081 179     477 919 858     363 841 670     715 445 418     425 611 133     180 150 761

 120 792 261     942 808 313     372 386 853     626 117 740     313 852 351     112 033 448
 341 807 306     222 937 712     395 275 735     516 129 032     050 813 318     767 326 884
 919 461 653     070 406 201     752 159 185     440 717 795     425 031 281     816 400 647
 534 470 656     852 961 821     772 972 808     564 012 574     378 887 295     700 369 274
 936 277 352     301 400 800     874 141 667     671 498 764     523 728 141     097 231 971

 618 671 224     346 903 897     186 864 834     108 554 338     488 662 374     889 706 107
 522 782 067     420 789 209     277 291 177     303 628 651     374 309 519     675 801 874
 612 292 856     248 542 741     749 076 815     766 808 069     604 693 747     822 626 423
 470 839 564     669 392 987     894 192 328     522 598 956     605 029 450     313 272 500
 415 631 581     512 253 182     036 591 693     271 462 142     509 231 849     219 183 935

 814 386 425     429 761 650     868 221 076     061 494 797     928 128 910     238 013 855
 035 523 545     059 968 871     297 067 171     188 818 018     354 960 784     132 389 294
 269 966 735     141 453 291     202 063 051     745 719 779     876 094 852     155 308 695
 923 184 912     840 723 899     638 019 959     193 609 424     208 227 790     102 389 599
 243 018 891     022 797 327     259 407 331     851 466 414     673 207 801     887 112 033

 897 732 475     395 977 660     111 209 449     543 992 431     686 452 834     594 775 231
 233 069 857     561 876 278     657 918 027     716 971 343     837 305 826     688 222 907
 402 447 584     194 769 127     724 967 193     876 735 740     930 997 650     616 870 632
 646 748 253     274 575 030     938 230 537     859 004 486     958 922 086     326 181 829
 320 078 127     938 413 648     319 742 424     493 240 150     636 555 071     423 108 615

 590 746 788     697 286 905     841 151 158     222 846 156     447 920 164     943 388 165
 555 803 095     004 119 999     827 051 607     866 451 003     419 080 172     574 999 237
 554 338 206     132 175 665     757 011 628     256 172 369     316 110 721     836 695 456
 443 006 684     452 131 718     512 070 070     263 283 181     419 263 283     797 235 023
 619 251 076     275 307 474     753 471 480     428 205 206     858 088 931     185 949 278

 429 944 761     237 952 818     398 022 401     499 069 185     540 360 729     359 721 671
 785 271 767     452 558 977     336 741 234     406 414 991     587 176 122     471 205 786
 384 044 923     681 173 132     238 746 300     513 229 774     413 617 359     332 743 309
 456 495 865     813 196 203     431 897 946     483 077 486     806 634 724     735 984 375
 430 768 761     422 498 245     110 446 486     714 407 788     330 362 865     209 295 938

 878 933 073     089 968 566     734 031 190     228 400 525     235 694 449     358 287 301
 814 294 870     214 178 900     163 396 100     468 672 750     072 054 201     832 422 864
 038 239 692     007 873 775     223 303 934     461 622 974     824 976 348     533 524 583
 721 366 008     318 948 943     594 927 824     475 081 637     174 901 578     450 758 385
 669 972 839     094 973 601     413 006 989     826 136 052     760 490 738     049 165 319

 724 875 637     902 462 844     670 033 876     189 153 722     208 594 012     982 360 302
 544 480 728     190 588 092     519 333 476     586 291 086     801 538 133     231 330 302
 554 429 762     763 878 292     353 068 636     305 978 576     613 879 818     439 558 092
 343 913 083     443 556 017     438 062 685     149 876 400     314 249 092     410 718 101
 290 963 469     184 789 575     684 652 242     223 029 267     890 377 514     074 404 126
----------------------------------------------------------------------



Source:  Random number generator in Statistica®
----------------------------------------------------------------------




======================================================================

Table 3

----------------------------------------------------------------------
A CENTRAL PLACE SYSTEM ORGANIZED ACCORDING TO CHRISTALLER'S K-3 MARKETING PRINCIPLE

                          NUMBER OF CENTRAL           NUMBER OF MARKET
LEVEL OF                  PLACES AT A GIVEN           AREAS AT A GIVEN
HIERARCHY                       LEVEL                            LEVEL

----------------------------------------------------------------------
1.  Metropolis                    1                                  1

2.  Cities                        2                                  3

3.  Towns                         6                                  9

4.  Villages                     18                                 27

5.  Hamlets                      54                                 81
----------------------------------------------------------------------
Source:  de Souza, A. and Foust, J.B. 1979. The World Space-Economy.
----------------------------------------------------------------------

==========
© Dr. Christine M. Rodrigue and Dr. Eugenie Rovai
Last revised: 02/19/99
==========