Dot Maps of Three Datasets
Cell
Pine
RedwoodFigure 1. Dot plot representations of the normalized datasets. Leftmost of the screen shows the sample sizes of the biological cell, pine tree and redwood seedling. The mean center was computed for each dataset (see the red dots). The figure on the lower right side is a comparative representation of three datasets along with respective mean centers (se the scatter dots in the respective colors)
The visual representation of three data sets provides information about the distributions. First of all, the average intensity of cell data is very homogenous whereas redwood and pine datasets are distributed inhomogeneous. Accordingly, figure 1 provides information about the stochastic dependence between the data points in a unit area. The neighboring data points of redwood dataset are clustered. Therefore, the data points constructing the same pattern interact with each other. On the other hand, the distribution of pine dataset is random; therefore, the visual representation suggests that the data points are independent. In the case of cell dataset, the distribution of data points is regular. In other words, number of data points in a unit area is approximately equal.
2. Quadrat Counts and Histogram
Three data sets (biological cells, redwood seedlings, and pine trees) are divided into rectangular grids of size 2x2 and 4x4. Figure 2 and 3 show the numbering and location of the quadrats. Tables 1 and 2 represents the data point counts in each quatrad, 2x2 grids and 4x4 grids, respectively. Subsequently, figures 4, and 5 show the histograms of frequency distributions of the quadrat counts for respective grids.
Figure 2. 2x2 grid. Each rectangular unit represents a quadrat. The quadrats were divided into equal sizes.
Figure 3. 4x4 grid. Each rectangular unit represents a quadrat. The quadrats were divided into equal sizes.
Table 1. Number of data points in 2x2 grids.
Quadrat
Cell
Redwood
Pine
1
11
9
13
2
10
18
Histogram of the frequency distribution of the quadrat counts of 2x2 grids.
Table 2. Number of data points in 4x4 grids.
Quadrat
Cell
Redwood
Pine
1
2
0
2
2
2
5
4
3
2
8
5
4
3
2
4
5
3
4
6
6
4
0
1
7
1
2
5
8
4
9
8
9
3
2
6
10
2
7
2
11
4
5
5
12
2
2
4
13
2
9
5
14
3
0
0
15
3
2
4
16
2
5
4
Figure 5. Histogram of the frequency distribution of the quadrat counts of 4x4 grids.
The overall histogram analysis shows the distribution of the data points. The cell data points in figure 4 almost uniformly distributed in 2x2 grids whereas Gaussian distribution function would fit for redwood data (maximum number of data points are in the third quadrat). In the same figure, pine tree data points are randomly distributed in grids. The distribution density changes by changing the size of quadrat area (see Figure 5). For example, 8th and 13th quadrats of redwood data exhibit the highest density of data points whereas 1st, 6th and 14th quadrats do not contain any data point.
In order to test the CRS hypothesis, the appropriate quadrat counts were visually investigated (see Figure 2, 3, and 6. Eventually, the grid size is chosen as…
