ESE 502 Tony E. Smith ASSIGNMENT 2 As stressed in Assignment 1, your approach to this assignment should be to write a short report on your findings for each of these three “studies”. Since this is your first analytical assignment, it should also be stressed that each study should be a pedagogical study (as in the Example Assignment) that illustrates the application of the relevant analytical method(s). So for example, when applying the Clark-Evans Test below, it is not enough to simply display the output from various software programs. You should give a short development of what this method tests, and exactly how it does so. What assumptions are involved? What test statistics are used? What are the advantages and possible limitations of this procedure? What information does it convey about the data set being studied? (1) In this study you will focus on the type of point pattern analysis done in class for the “Redwood Seedling” data. Here you will use the “Iowa County Seat” data which is displayed in the ARCMAP file, T:\ese502\arcview\projects\Iowa\Iowa_county_seats.mxd.1 Observe first that, unlike the Redwood Seedlings, this point pattern appears to be dispersed in a regular pattern (much like the “Cell Center” data discussed in class). If you open the ‘Iowa counties’ layer, you will see the actual county boundaries. In fact the regularity of this grid-like pattern of county boundaries strongly contributes to the spatial regularity of county seats. But there is more to the story. Notice that especially for interior counties (away from the Missouri and Mississippi Rivers), each seat is near the center of its county. There are several references here that you should look at when interpreting this pattern. These references offer alternative explanations for landscapes like Iowa: - The first is the classic discussion of “Central Place Theory” in the Economics of Location reference by August Lösch. Using the beer-producing area of Southern Germany as his key example, Lösch describes an idealized agricultural economy in which a hierarchy of towns, or “places”, is regularly spaced on a hexagonal grid of small farms. [Pay particular attention to the highlighted sections]. This is actually quite similar to the case of Iowa, especially during the 1800s. (You can view Iowa as a “Löschian landscape” by closing the ‘Iowa counties’ layer, and opening the ‘Voronoi_cells’ layer above it.) A more general discussion of human settlement patterns is given in the Locational Analysis reference by Peter Haggett. - The second pair of references are by Michael Dacey (Dacey_1 and Dacey_2). Here Dacey offers an alternative probabilistic model of “place” patterns that are more regular than Poisson randomness. This is applied directly to county seats in Iowa (in both references). [Be sure to look my notes, DACEY_model.pdf (added to the back of Dacey_1) and also pay particular attention to the highlighted summary sections, Pattern Summaries, p.564 in Dacey_1, and Evaluation and Interpretation of Results, p.540 in Dacey_2.] 1 This data is taken from the National Association of Counties website, http://www.naco.org.2With this background, we turn now to a point-pattern analysis of Iowa: (a) First you will construct nearest-neighbors to each point using MATLAB: 1. Load the workspace Iowa.mat into MATLAB, and observe that the matrix, L, contains the locations of the 99 county seats (with coordinates in State Plane miles). 2. Construct the vector, nn_dist, of (first) nearest-neighbor distances in a manner similar to Problem 1(b) of Assignment 1. Use the commands: » OUT = neighbors(L,1); » nn_dist = OUT(:,4); » nn_dist(1:2,:) The last command is a check, and should yield the values 20.98 and 20.448. (For example the nearest neighbor of county seat 1 is about 21 miles away.) 3. Now save this result to your own directory (say S:\home) by the command » save ‘S:\home\nn_dist.txt’ nn_dist –ascii (b) Next, you will import this data to JMP and examine its properties. 1. Start by opening JMP: [JMP 7] Use the option “Text Import Preview” to import the file, nn_dist.txt, as in Problem 1(b).2 of Assignment 1. [JMP 8] Reset preferences as in Problem 1(b).2 of Assignment 1 and import the file, nn_dist.txt, as a Text file. (Eliminate the empty “Column 1” if necessary. ) Relabel the data column as “nn_dist”. (Check to be sure the first two values are as above.) You will now use this to construct a file which is parallel to Redwoods_data.jmp, used for the analysis of the Redwood Seedlings in class. 2. First add a second column, “rand_relabel”, and use the formula: Random  Col Shuffle. After clicking Apply and OK, you should see a random relabeling of the 99 row numbers in this column. 3. Next, add a new column labeled “Sample”, and as in Problem 1(b).3 of Assignment 1, construct the subscripted variable: __rand relabelnn dist3This yields a random shuffling of the nearest-neighbor-distance values. The first 30 elements of this column then constitute the desired subsample of the nearest-neighbor-distance values to be tested. 4. Next, open the JMP file, CE_Tests.jmp, and copy-and-paste the first 30 values from “Sample” into the “nn_dist” column of this file. 5. To determine the appropriate area, open the ARCMAP file, Iowa.mxd, and observe from the attribute table of the layer, “Iowa_Boundary” that the last field contains the area of Iowa in square miles (56269 sq.ml.). This is the value to be used here. To enter this value into CE_Tests.jmp, right click on the “area” column, select Column Info  New Property  Formula, and in the “Formula” box to the right, click Edit Formula. Now the Calculator window will open, and you can type in the area value. 6. Next, set the “n” value equal to 99 using the same procedure. (Remember that the full sample size is used to estimate point density.) The spreadsheet should now fill in the rest of the values. 7. Observe that the value “mu” gives the theoretical mean nearest-neighbor distance predicted by the CSR theory. Compare this value with the sample mean calculated in the column “s_mean”. What can you conclude from this comparison? (c) Finally, to carry out the Clark-Evans test, you can simply use the P-value columns of the table. 1. For a one-tailed test of “dispersion” versus the null hypothesis of CSR, the