GEOG 101: Global Economic Geography
Dr. Rodrigue
Lab 3: Central Place Functions in Butte County
Student name: _____________________________________
Student name: _____________________________________
(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.
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.
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.
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.
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Table 1
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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
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Sources: U.S. Census. 1990. Summary Tape File 3A.
Dr. William Collins. 1993. Personal communication.
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Table 2
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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
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Source: Random number generator in Statistica®
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Table 3
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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
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1. Metropolis 1 1
2. Cities 2 3
3. Towns 6 9
4. Villages 18 27
5. Hamlets 54 81
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Source: de Souza, A. and Foust, J.B. 1979. The World Space-Economy.
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