Sampling plan using grade of infestation to estimate population density

Abstract

By a grading method, we classify the infestation level into grades depending on the number of individuals and record the grade of infestation without recording the number of individuals. However, the resultant grade has no clear meaning and hence it currently has only limited use. There are two questions that should be solved to construct a grading method that yields a meaningful grade. (1) Which scale should we use to determine the boundary of grades? For example, is a logarithmic scale such as that divided at x=1, 10, 100, 1000 preferable to an arithmetic scale such as that divided at x=50, 100, 150, 200? (2) Which grade width should we use? When we use a logarithmic scale, for example, is a 5-times width such as that divided at x=1, 5, 25, 125 preferable to a 10-times width such as that divided at x=1, 10, 100, 1000? For the first question, we suggest that we should utilize the scale that improves homoscedasticity to perform ANOVA. For the second question, we provide a procedure to determine the optimal grade width.