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This worksheet contains the EXAMPLE data set that appears on your lab handout. Follow along step by st Click on the cells to view formulas, but do not WRITE or CHANGE anything on this sheet. It is your exampl 1. Table 1 contains the field collected data or raw data. Use this data to generate the maps of the study plot. 2. Figures 1-3 show an x-y scatter plot and a bubble chart generated using the data. 3. Using the scatter plot, major gridlines were added to the x- and y-axes at 2m. intervals. Then, the number of tr 4. Table 2 contains the number of individuals found in each subplot. This table is used to generate: the total numb mean number of trees per subplot, variance in tree numbers among subplots, and a frequency distribution of tree 5. Table 3 contains the information cacluated using the data in Table 2. 6. Table 4 contains the sorted data from Table 2. From this sorted list you can count the number of individuals in e 7. Table 5 contains the frequency distribution data of observed and expected values, the poisson probability and t 8. Figure 4 is a plot of the frequency distribution for observed and expected values. 9. Using the observed values given by your data and the expected values given by the Poisson probability series, a Using the descriptive statistics given in Table 3, a Variance/Mean Ratio was calculated. Value given in Table 6. Step 2 Step 1 Generate an x-y scatterplot and a bubble chart of your data. The RAW DATA collected from a previous lab assesing information on the relative size of the trees (dbh). What do you t dispersion of Juniperus asheii in a 20x20m plot. is? Clumped, Uniform or Random? Table 1. Tree position and dbh data from 20x20m study plot at BFL. Species X Coordinate Y-Coordinate DBH (in.) Dispersion of Trees along the Q Juniper 1.6 8.1 3.7 20 Juniper 1.6 10.72 5.9 Juniper 15.8 12 13.7 18 Juniper 12.6 2.12 3.6 16 Juniper 13 3.6 5.1 Juniper 18.77 2 2.8 14 Juniper 12.8 4.51 10 12 NW-SE Juniper 13.6 5.92 8.2 Juniper 13.75 5.56 7.2 10 Juniper 13.85 1.7 5.6 8 Juniper 17.3 5.56 9.3 Juniper 10.42 1.65 7.3 6 Juniper 3.78 6.8 4.4 4 Juniper 7.7 7.15 4.7 Juniper 3.1 0.5 9.2 2 Juniper 3.67 15.6 9.9 0 Juniper 4.15 17.9 15.3 0 2 4 6 Juniper 5.9 18.4 2.8 Juniper 8.21 17.95 8.2 Juniper 8.11 16.3 7.4 Juniper 11.25 19.5 6.7 Figure 1. Map of Juniperus asheii in a 20mx20m plot along the Q Juniper 7.7 15.5 6.1 Field Lab. See Figure 3 for an example of a properly formatted f Juniper 5.3 12.9 3.9 Juniper 9.94 15.2 2.8 Juniper 9.9 15.2 8.2 Dispersion of Trees along the Qu Juniper 9.2 16.2 1.7 Juniper 14.4 18.05 24.1 20 Juniper 18 14.6 18.5 18 Juniper 7.65 11.9 6.5 Juniper 12.02 4.55 9.4 16 Juniper 18.2 0.7 6 14 Juniper 17.07 0.06 15.1 12 SE 10 12 NW-SE Juniper 15.28 3.75 13.6 10 Juniper 5.2 0.8 5.2 Juniper 6.62 0.05 6 8 Juniper 7.2 1.48 10.3 6 Juniper 2.67 0.9 2.9 4 Juniper 1.5 9.4 2.5 Juniper 1.8 10.3 3.1 2 Juniper 2 11.5 9.7 0 Juniper 1.85 12.2 2.5 0 2 4 6 8 Juniper 2 12.75 3.9 Juniper 11.15 13.5 2.6 Juniper 1.87 14.4 3.6 Juniper 3.17 14.3 3.2 Juniper 3.5 16.85 4.2 Figure 2. Map of Juniperus asheii , position and relative size (db Juniper 3.65 19.5 7.9 20mx20m plot along the Quarry Trail at Brackenridge Field Lab. Juniper 6.37 13.5 9 of a properly formatted figure. Juniper 5.07 10.2 22.4 Juniper 9.92 16.6 3.6 Juniper 18.65 18.65 23.7 Juniper 14.4 18.8 2.6 Juniper 13.5 18.1 2.8 20 Juniper 12.2 16.2 3.8 18 Juniper 8.7 15.3 2.9 16 Juniper 11.1 16.5 3.5 14 Juniper 10 15.7 1.7 12 NW-SE Juniper 11.8 15.3 3.5 Juniper 10.7 11.7 4.1 10 Juniper 9.6 13.3 5.4 8 Juniper 8.8 13.4 3.2 6 Juniper 8.2 12 3.7 4 Juniper 13.9 17 4.7 2 Juniper 15.5 14.9 6.6 Juniper 19.2 14.5 4 0 Juniper 15.9 11.9 3.8 0 2 4 6 8 10 12 Juniper 11.91 11.52 2.3 NE-SW Juniper 11.75 9.69 3 Juniper 6.45 10.99 4.2 Figure 3. This is what your figure should look like before you imp Juniper 9.2 11.96 3.6 your word document. Juniper 12.65 11.98 4.4 Juniper 18.96 1.1 1.5 Juniper 16.32 1.82 2.3 Juniper 16.61 4.9 3 Juniper 15.19 7.2 4.9 Juniper 10.51 2.5 2.6 Juniper 4.38 5.65 2.2 Juniper 5.76 6.17 3.9 Juniper 4.47 8.88 1.7 Juniper 5.35 8.98 5.1 Juniper 6.17 7.24 4 Juniper 6.6 9.27 3 Juniper 7.81 6.88 2.1 Juniper 8.34 9.41 1.9 Juniper 8.36 7.15 2.8 Juniper 8.45 8.39 5.5 Juniper 9.24 7.13 3.5 Juniper 9.9 8.39 3.7 Juniper 9.2 7.45 2 Juniper 9.74 10.54 2.6 Juniper 10.26 10.93 3.4 Juniper 10.84 11.5 10.8 ut. Follow along step by step. is sheet. It is your example. Do your work on other worksheets. maps of the study plot. als. Then, the number of trees in each subplot was tallied. d to generate: the total number of trees in the plot, equency distribution of tree numbers per subplot he number of individuals in each size class. he poisson probability and the difference between observed and expected values. Poisson probability series, a Chi-Sqare test was conducted. Table 6 contains the p-value. . Value given in Table 6. Step 3 Count the number of trees per subplot. Begin with the top left subplot, cou moving left to right and row by row. Use the following rule, if a tree falls on d a bubble chart of your data. The bubble chart includes subplot, then count the tree as "in" only if it falls on the upper or left bounda of the trees (dbh). What do you think the pattern of dispersion the right boundary, count it for the next subplot; if it falls on the bottom bou om? with the subplot below. Table 2. Number of individuals in each 2m x 2m subplot. Subplot # # Individuals ersion of Trees along the Quarry Trail at BFL 1 0 2 1 3 1 4 0 5 0 6 1 7 1 8 2 9 0 10 1 11 0 12 1 13 1 14 0 15 4 16 1 17 2 18 0 8 10 12 14 16 18 20 19 0 NE-SW 20 0 21 1 heii in a 20mx20m plot along the Quarry Trail at Brackenridge 22 2 example of a properly formatted figure. 23 0 24 1 25 2 ion of Trees along the Quarry Trail at BFL 26 2 27 0 28 1 29 0 30 2 31 2 32 0 33 1 34 1 35 2 36 1 37 0 38 0 39 0 40 0 41 3 8 10 12 14 16 18 20 42 0 43 1 NE-SW 44 2 45 3 46 4 heii , position and relative size (dbh measured in inches), in a 47 1 y Trail at Brackenridge Field Lab. See Figure 3 for an example 48 2 49 0 50 0 51 2 52 0 53 2 54 1 55 3 56 1 57 0 58 0 59 0 60 0 61 0 62 1 63 1 64 3 65 3 66 0 12 14 16 18 20 67 0 SW 68 1 69 0 ure should look like before you import it into 70 0 71 0 72 0 73 1 74 0 75 0 76 0 77 4 78 0 79 2 80 0 81 0 82 0 83 0 84 0 85 0 86 1 87 2 88 1 89 0 90 0 91 0 92 2 93 1 94 2 95 0 96 1 97 1 98 0 99 2 100 3 Step 5 Copy the list of individuals per subplot and paste in a new column. Then, sort the list using the sort function. You can now count up the number of cells with zero individuals, 1 individual, 2 individuals, etc. Type this information into Table 5. Table 4. Sorted list of values from Table 2 0 with the top left subplot, count each subplot 0 ollowing rule, if a tree falls on the boundary of a 0 s on the upper or left boundary. If it falls on 0 t; if it falls on the bottom boundary, count it 0 0 in each 2m x 2m subplot. 0 0 0 Step 4 0 Using Table 2, calculate the sum total of 0 individuals on the plot and the mean number 0 of individuals per subplot. Then, calculate the 0 variance. Use Excel's statistical functions to 0 get these values. 0 0 Table 3. Descriptive statistics for the data in Table 2. 0 Total # Individs. 91 0 Mean # Individs. 0.91 0 Variance 1.153 0 50 0 0 45 0 40 0 35 0 0 30 Frequency 0 25 0 20 0 0 15 0 10 0 0 5 0 0 0 0 1 0 Number of Individ 0 0 0 Figure 4. Frequency distribution of observed and 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 Step 6 The number of individuals column is determined by the maximum number of individuals found in you subplots. In our example, no subplot had more than 4 individuals. (1) Enter the frequency values you determined for each of these size classes under the Obs. Freq. column. The sum should total the number of subplots. (2) Calcualate the Poisson Distribution for the 2m2 subplot and determine the expected number of quadrats for each size class. Using the Poisson function, you will calculate P(x) for each size class. The function will ask for "x" which is the size class (found under the Number of Individs. column, then it will ask for the Mean, which was calculated and entered into Table 3 (M=0.91), then it asks whether you want to calculate the cummulative probability...You do NOT..so type the work "false" into this cell. Do this for each size class. The P(x) column should sum to 1.0. (3) Multiply the Poisson probability by the number of subplots (in our example this is 100). (4) Take the absolute value of the difference between your observed and expected values. Table 5. Frequency distribution of Observed and Expected frequencies along with the Poisson probability and the difference between Observed and Expected values. # of Individ Obs. Freq. P(x) Exp. Freq. (Obs. - Exp.) 0 47 0.403 40.25 6.75 1 27 0.366 36.63 9.63 2 17 0.167 16.67 0.33 3 6 0.051 5.06 0.94 4 3 0.012 1.15 1.85 Sum 100 0.998 99.754 Step 7 Calculate the Chi-square value using the Excel function to determ Observed distributed randomly. If p<0.05 then the data is NOT random. If p Expected random. If the data is significant (therefore non-random), then yo Variance/Mean ratio to determine if the data is uniform or clumped data is RANDOM, but we calculated the V/M ratio anyway to show REMEMBER: if V/M=1.0, individuals are randomly dispersed. If V/ dispersion and if V/M<1.0 uniform dispersion. Table 6. P-value for the Chi-square test and the Variance/Mean R Chi-Square p-value 0.146 V/M ratio 1.268 Data is RANDOM. Even though V/M >1.0, we canNOT say the da 2 3 4 Number of Individuals per Subplot distribution of observed and expected values for the number of individuals per subplot. ng the Excel function to determine if the data is n the data is NOT random. If p>0.05 then the data is herefore non-random), then you can calculate the f the data is uniform or clumped. In this example the d the V/M ratio anyway to show you how it is done. s are randomly dispersed. If V/M>1.0, clumped dispersion. e test and the Variance/Mean Ratio. M >1.0, we canNOT say the data is clumped. REMEMBER that V/M is only an estimate. This worksheet will help you to set up your data and will Step 1 prepare you to conduct the analysis RAW DATA for plants growing in a 20m x 20m plot. of dispersion. Tree position and dbh data from 20m x 20m study plot at BFL. Species X Coordinate Y-Coordinate DBH (in.) Holly? 7.0 8.0 3.3 Water Elm 5.0 12.0 2.0 Water Elm 4.8 12.0 1.6 Water Elm 4.7 12.0 2.8 Water Elm 4.6 12.0 3.2 Water Elm 6.0 8.3 3.2 Oak 4.3 7.1 9.2 Holly? 3.7 5.3 1.8 Holly? 2.6 0.1 1.3 American Holly 2.2 11.0 1.1 Holly? 5.2 15.0 2.7 Holly? 6.2 16.0 1.9 Holly? 6.8 16.6 1.8 Holly? 5.4 16.9 4.4 Holly? 5.3 16.8 2.6 Holly? 5.0 17.2 2.3 Holly? 4.0 15.8 2.4 Holly? 4.8 18.8 2.0 Holly? 8.8 13.1 1.6 Water Elm 5.0 16.2 5.3 Water Elm 6.0 16.0 3.5 Water Elm 6.8 16.0 5.6 Water Elm 6.0 17.3 12.1 Water Elm 13.0 16.0 5.8 Water Elm 8.9 15.3 6.2 Water Elm 13.2 16.1 1.8 Water Elm 16.1 17.9 1.1 Magnolia 17.7 17.9 1.8 Black Jack Oak? 19.1 19.4 2.3 Black Jack Oak? 19.3 16.3 6.6 Holly? 10.0 18.4 1.3 Round Leaf? 11.0 17.7 1.5 Round Leaf? 13.2 12.3 2.8 Round Leaf? 13.4 12.4 2.4 TT? 15.3 19.0 5.6 Water Elm 7.1 0.3 4.3 Water Elm 8.5 0.9 4.8 Water Elm 8.4 2.9 5.5 Water Elm 9.5 0.6 6.8 Oak #1 (no leaf) 10.8 1.5 12.7 Water Elm 12.9 3.0 5.7 Roundleaf 10.0 0.6 1.5 Water Elm 13.5 8.4 1.5 Oak #1 13.2 10.8 7.4 Water Elm 8.9 10.2 4.5 Water Elm 7.5 8.8 2.3 Roundleaf 10.5 16.3 2.4 Oak #1 11.0 16.3 3.3 Oak #3 9.6 19.0 4.0 Oak #1 11.4 17.4 4.7 Oak #1 11.5 18.6 1.8 Durand Oak #2 12.5 18.3 3.3 Roundleaf 12.2 17.3 1.2 Roundleaf 12.8 16.3 1.8 Oak #3 13.3 16.8 2.7 Step 2 Generate an x-y scatterplot and a bubble chart of your data. Enter each species as its own series so that you can distinguish species by color. The bubble chart includes information on the relative size of the trees (dbh). What do you think the pattern of dispersion is? Clumped, Uniform or Random? Step 2b Copy and paste several copies of your x-y scatter plot. Make one plot with major gridlines at 5m, another with 2.5m, and a third with 1m gridlines. **You will only use the 5m gridline map of the x-y and bubble plots in your lab report. Step 3 Step 4 Count the number of trees per subplot. Begin with the top left See the worksheet "Spatial" subplot, count each subplot moving left to right and row by row. Use the following rule, if a tree falls on the boundary of a subplot, then count the tree as "in" only if it falls on the upper or left boundary. If it falls on the right boundary, count it for the next subplot; if it falls on the bottom boundary, count it with the *HINT: Print off your maps so you can cross-out the plots you have counted. Number of individuals in each 5m x 5m subplot. Number of individuals in each 1m x 1m su Number of individuals in each 2.5m x 2.5m subplot. Subplot # # Individuals Sorted Data Subplot # # Individuals Sorted Data Subplot # 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 12 12 12 13 13 13 14 14 14 15 15 15 16 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 36 36 37 37 38 38 39 39 40 40 41 41 42 42 43 43 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 See the worksheet "Spatial" Number of individuals in each 1m x 1m subplot. # Individuals Sorted Data The steps on this page will allow you to complete your analysis of how tree dispersion changes with SPATIAL SCALE in a 20 mx20 m plot. Step 4 Use the tables created in step 2 to calculate the sum total of individuals on the plot and the mean number of individuals per subplot. Then, calculate the variance. Use Excel's statistical functions to get these values. Descriptive statistics for the data. 5m 2.5 m 1m Mean Number of Individuals Variance Maximum Number of Individuals Total Number of Individuals Step 5 We combined steps 3 and 5 on the x-y worksheet. Step 6 The "Number of Individuals" column is determined by the maximum number of individuals found in you subplots. In our example, no subplot had more than 4 individuals. (1) Enter the frequency values you determined for each of these size classes under the Obs. Freq. column. The sum should total the number of subplots. (2) Calcualate the Poisson Distribution for the 2m 2 subplot and determine the expected number of quadrats for each size class. Do this for each size class. The P(x) column should sum to 1.0. (3) Multiply the Poisson probability by the number of subplots (in our example this is 100). (4) Take the absolute value of the difference between your observed and expected values. NOTE: Using the "Poisson" function under "Statistical Functions", you will calculate P(x) for each size class. The function will ask for "x" which is the size class (found under the "Number of Individuals" column); then it will ask for the Mean, which was calculated in Step 4; then it asks whether you want to calculate the cummulative probability...You do NOT want to obtain the cummulative probabilty, you want the probabilty of EACH class..so type the work "False" into this cell. Frequency distribution of observed and expected frequencies along with the Poisson probability and the difference between Observed and Expected values for the 5m x 5m subplots # of Individ Obs. Freq. P(x) Exp. Freq. (Obs. - Exp.) Sum Frequency distribution of observed and expected frequencies along with the Poisson probability and the difference between Observed and Expected values for the 2.5 m x 2.5 m subplots Frequency distribution of observed and expected frequencies along with the Poisson probability and the difference between Observed and Expected values for the 2.5 m x 2.5 m subplots # of Individ Obs. Freq. P(x) Exp. Freq. (Obs. - Exp.) Sum Frequency distribution of observed and expected frequencies along with the Poisson probability and the difference between Observed and Expected values for the 1x1 subplots # of Individ Obs. Freq. P(x) Exp. Freq. (Obs. - Exp.) Sum Step 7 Calculate the Chi-square value using the Excel function to determine if the data is distributed randomly. If p<0.05 then the data is NOT random. If p>0.05 then the data is random. If the data is significant (therefore non-random), then you can calculate the Variance/Mean ratio to determine if the data is uniform or clumped. In this example the data is RANDOM, but we calculated the V/M ratio anyway to show you how it is done. P-value for the Chi-square test and the Variance/Mean Ratio for the 5m x5m subplots Chi-Square p-value V/M ratio Data is/is NOT SIGNIFICANT? Data is RANDOM, CLUMPED OR UNIFORM? P-value for the Chi-square test and the Variance/Mean Ratio for the 2.5m x 2.5m subplots Chi-Square p-value V/M ratio Data is/is NOT SIGNIFICANT? Data is RANDOM, CLUMPED OR UNIFORM? P-value for the Chi-square test and the Variance/Mean Ratio for the 1x1 subplots Chi-Square p-value V/M ratio Data is/is NOT SIGNIFICANT? Data is RANDOM, CLUMPED OR UNIFORM? The steps on this page will allow you to complete your analysis of how dispersion changes with tree size in a 20mx20m plot at BFL. Step 1 Step 2 Copy and paste your RAW DATA collected from a 16x16m plot. Highlight all Generate an x-y scatterplot of your data with data and then using the Sort function, sort the data by DBH. Next, calculate two series on this plot; those less than aver the average DBH of all trees in the plot. Divide your data into 2 groups: Those Do you think the pattern of dispersion varies trees with DBH less than average and those with DBH greater than average. larger size class will show the same pattern For any trees that have a DBH equal to the average, place them in the "greater trees? or will the pattern be different for the s than" group. NOTE: You can plot both series on one map Tree position and dbh data from 16mx16m study plot at BFL. REMEMBER that each series (<DBH and >D Species X Coordinate Y-Coordinate DBH (in.) nerate an x-y scatterplot of your data with major gridlines set at 5m intervals. You will have o series on this plot; those less than average DBH and those greater than average DBH. you think the pattern of dispersion varies with tree size? Do you think the smaller and ger size class will show the same pattern of dispersion as previously determined for all es? or will the pattern be different for the smaller and larger size class? TE: You can plot both series on one map or plot each series on its own map, but MEMBER that each series (<DBH and >DBH) will be analyzed as a separate data set!!! Step 3 Count the number of trees per subplot. Begin with the top left subplot, count each subplot moving left to right and row by row. Use the following rule, if a tree falls on the boundary of a subplot, then count the tree as "in" only if it falls on the upper or left boundary. If it falls on the right boundary, count it for the next subplot; if it falls on the bottom boundary, count it with the subplot below. *HINT: Print off your map so you can cross-out the plots you have counted. LESS THAN AVERAGE DBH Number of individuals in each 5 m x 5m subplot. Subplot # # Individuals Sorted Data 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Step 4 Use the tables created in step 2 to calculate the sum total of individuals (in each category) on the plot and the mean number of individuals per subplot. Then, calculate the variance. Use Excel's statistical functions to get these values. Descriptive statistics for the data at 5m intervals <Average DBH >Average DBH Mean Number of Individuals Variance Maximum Number of Individuals Total Number of Individuals Step 5 We combined steps 3 and 5 above. Step 6 The "Number of Individuals" column is determined by the maximum number of individuals found in you subplots. In our example, no subplot had more than 4 individuals. (1) Enter the frequency values you determined for each of these size classes under the Obs. Freq. column. The sum should total the number of subplots. (2) Calcualate the Poisson Distribution for the 2m 2 subplot and determine the expected number of quadrats for each size class. Do this for each size class. The P(x) column should sum to 1.0. (3) Multiply the Poisson probability by the number of subplots (in our example this is 100). (4) Take the absolute value of the difference between your observed and expected values. NOTE: Using the "Poisson" function under "Statistical Functions", you will calculate P(x) for each size class. The function will ask for "x" which is the size class (found under the "Number of Individuals" column); then it will ask for the Mean, which was calculated in Step 4; then it asks whether you want to calculate the cummulative probability...You do NOT want to obtain the cummulative probabilty, you want the probabilty of EACH class..so type the work "False" into this cell. LESS THAN AVERAGE DBH Frequency distribution of observed and expected frequencies along with the Poisson probability and the difference between Observed and Expected values for the 5mx5m subplots # of Individ Obs. Freq. P(x) Exp. Freq. (Obs. - Exp.) Sum GREATER THAN AVERAGE DBH Frequency distribution of observed and expected frequencies along with the Poisson probability and the difference between Observed and Expected values for the 5mx5m subplots # of Individ Obs. Freq. P(x) Exp. Freq. (Obs. - Exp.) Sum bplot, count each subplot e falls on the boundary of a eft boundary. If it falls on ttom boundary, count it with GREATER THAN AVERAGE DBH Number of individuals in each 5m x 5m subplot. Subplot # # Individuals Sorted Data 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Step 7 Calculate the Chi-square value using the Excel function to determine if the data is distributed randomly. If p<0.05 then the data is NOT random. If p>0.05 then the data is random. If the data is significant (therefore non-random), then you can calculate the Variance/Mean ratio to determine if the data is uniform or clumped. In this example the data is RANDOM, but we calculated the V/M ratio anyway to show you how it is done. NOTE: To complete the Chi Square test use the "CHITEST" function under "Statistical functions". Enter the observed data, then the expected data. P-value for the Chi-square test and the Variance/Mean Ratio for the 5x5 subplots Chi-Square p-value V/M ratio Data is/is NOT SIGNIFICANT? Data is RANDOM, CLUMPED OR UNIFORM? P-value for the Chi-square test and the Variance/Mean Ratio for the 5x5 subplots Chi-Square p-value V/M ratio Data is/is NOT SIGNIFICANT? Data is RANDOM, CLUMPED OR UNIFORM?