High School

We appreciate your visit to Bart and Earnst 2002 describe the use of two phase sampling with ratio estimation to estimate the density of nesting birds The phase I sample. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Bart and Earnst (2002) describe the use of two-phase sampling with ratio estimation to estimate the density of nesting birds. The phase I sample, selected from the 2130 plots in the region of interest, is conducted using a rapid search method involving bird sightings to obtain an approximate count of birds in each phase I plot. Then, a subsample of 12 of the phase I sample plots are surveyed using an intensive method to obtain a more accurate count of the number of nests in each plot.

In the intensive method, a surveyor visits a plot for several hours over a period of days and searches for nests and other indications of territorial males in the plot. In this setting, [tex] x_i [/tex] represents the number of nests counted in plot [tex] i [/tex] using the rapid method, and [tex] y_i [/tex] represents the number of nests counted in plot [tex] i [/tex] using the intensive method.

Using the data in file shorebirds.dat, which were generated using summary statistics from Bart and Earnst (2002), estimate the total number of nests using the two-phase ratio estimator. Give the standard error of your estimate.

Answer :

Using the data in file shorebirds.dat, and applying the two-phase ratio estimator, the estimated total number of nests can be calculated. The standard error of this estimate can also be determined.

The two-phase sampling with ratio estimation method combines information from both the rapid search method and the intensive method to estimate the total number of nests.

In the second phase, a subsample of the phase I sample plots is selected for a more intensive survey. The intensive method involves visiting each selected plot for several hours over a period of days and thoroughly searching for nests and other indications of territorial males. The number of nests counted in each plot using the intensive method is denoted by yi.

To estimate the total number of nests, we use the two-phase ratio estimator. The ratio estimator assumes that the ratio of the number of nests counted using the intensive method to the number of nests counted using the rapid method is approximately constant across all plots. This ratio is denoted by R, which can be estimated as the average ratio of yi to xi for the subsample of plots in the second phase.

Once we have estimated the ratio R, we can use it to estimate the total number of nests. Let N be the total number of plots in the region of interest, and let M be the number of plots in the subsample for the second phase. The estimated total number of nests, denoted by Ŝ, is given by:

Ŝ = (N/M) * ∑(xi * R)

To calculate the standard error of the estimate, we need to consider the variability in the estimates. The standard error can be calculated using the following formula:

SE(Ŝ) = √[(N² / (M² * (M - 1))) * (∑((xi - yi * R) / (M * xi))²)]

To know more about two-phase ratio here

https://brainly.com/question/32998879

#SPJ4

Thanks for taking the time to read Bart and Earnst 2002 describe the use of two phase sampling with ratio estimation to estimate the density of nesting birds The phase I sample. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada