Determining optimal plot size based on relative cost of sampling and relative variance of plot counts
 Details
 Written by Omkar
This method uses the product of the relative cost of sampling and the relative variance of plot counts to estimate the optimum size of the plot. Thus the method is not only statistically efficient it also saves time and money in the long run. This method is called Wiegert's Method after it's inventor, R.G Wiegert.
Methodology 

A set of plot sizes is chosen from smallest to largest. Each plot size is used to lay a standard number of plots (multiple plots have to be laid for each plot size so as to properly calculate average time required to sample those plots and the standard deviation of the plot counts.)

A data sheet is made with the following fields, for collecting data for carrying out this method.
Serial Number 
Plot Size in m² 
Plot Count (example  individuals in the plot) 
Time taken to complete the count 
3. In the next step a new table is used, with data derived from the previous table. A hypothetical table has been prepared for this purpose to serve as an example. This table gives an account of the total number of plots taken for each plot size, the average count for that plot size, the standard deviation (which is a measure of variability from plot to plot) and the average time required to complete each plot count.
Plot size in m² 
Number of plots (sample size) 
Average Count of the plots 
Standard Deviation of the Plot Count 
Average time in mins required for one plot. 
1 
5 
26 
17 
5 
1.5 
5 
39 
13 
7 
2 
5 
50 
12 
10 
2.5 
5 
65 
14 
12 
4. From this data the relative cost and relative variance are derived.
Relative cost for a particular plot size =
Average time required to count individuals in the plot of that size
The lowest average time required from all the plot sizes (in this example it is 5)
Relative Variance for a particular plot size =
(Standard Deviation for that plot size) ²
(Minimum SD from all the plot sizes) ²
5. Thus two more columns are obtained, one for the relative cost and one for the relative variance.
Plot Size in m² 
Relative Variance 
Relative Cost 
Product of Relative cost and variance 
1 
1.41 
1 
1.41 
1.5 
1.08 
1.4 
1.51 
2 
1 
2 
2 
2.5 
1.16 
2.4 
2.78 
6. The plot size with the lowest cost and variance product is selected to be the most optimal plot size. In the case of this hypothetical example it is a plot size of 1m² because of the lowest value of the product of relative cost and variance (1.41).
About the Author of this Article
References 
Wiegert, R.G. 1962. The selection of an optimum quadrat size for sampling the standing crop of grasses and forbs. Ecology 43:125129.
Determining Optimum Quadrat Size and Shape, an Introduction