# Example by hedongchenchen

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• pg 1
```									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
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20
0
0                             15
0                             10
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0                              5
0                              0
0                                       0               1
0                                                         Number of Individ
0
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0                       Figure 4. Frequency distribution of observed and
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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
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
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See the worksheet "Spatial"

Number of individuals in each 1m x 1m subplot.
# Individuals Sorted Data
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?
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

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?

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