Stat 549 Applied Sampling - Overview
The intent of this handout is to provide a brief overview to some of the topics in applied
sampling which will be covered this semester.
What is sampling?
The purpose of sampling is to estimate some unknown population
Stat 549, Applied Sampling Fall 2010 Mathematical notation: Subscripts: y1 , y2 , . . . , yn
Prerequisite knowledge
Summation notation: evaluate the following when n = 4, y1 = 2, y2 = 4, y3 = 1, y4 = 6, and c = 4:
n n
yi ,
i=1
(yj - c)2 ,
3
n
(3yk + 4),
Methods of Estimating the Detectability Function 1. Parametric Methods: The term "parametric" here simply means we are assuming that the detectability can be expressed as a function of the distance depending on one or more parameters. In the context of de
Distance Sampling (Chapter 17)
Consider sampling with transects to estimate abundance or density of some kind of object (an animal or a plant, for example) in the region. In moving along a transect (whether on the ground or aerially), the observer sees ob
Detectability and Sampling (Chapter 16)
To this point, all sampling methods considered have assumed that the variable is interest is
measured without error and that the only source of variation is natural variation between
the observed sampling units. Par
Line-Intercept Sampling (Chapter 19)
Most of the sampling methods discussed thus far have consisted of choosing a sample from a well-defined population according to some probabilistic mechanism. Consider now taking a sample in some area where there are st
Cluster Sampling & Systematic Sampling (Chap. 12)
Recall that cluster sampling is where we first divide the population into "clusters," then select a simple random sample (SRS) of these clusters, and sample every unit within the selected clusters. This is
Stratified Random Sampling (Chapter 11)
This handout introduces the basic ideas and theory behind stratified random sampling estimators, the stratification principle, allocation in stratified random sampling, a number of examples illustrating the method,
Regression Estimation
Recall that the method of ratio estimation is appropriate when the response variable y is linearly related to some auxiliary variable x, and the value of y = 0 when x = 0. Sometimes, there is a linear relationship between the respons
Ratio Estimation (Chapter 7)
This handout covers the basic idea behind ratio estimation, gives the forms and properties
of the relevant estimators, compares ratio estimation to other estimation methods studied,
and provides some examples which use ratio e
Unequal Probability Sampling (Chapter 6)
Unequal probability sampling is when some units in the population have probabilities of
being selected from others. This handout introduces the Hansen-Hurwitz (H-H) estimator
and Horvitz-Thompson (H-T) estimator, e
Sample Size Considerations (Chapters 4-5)
Up to now, we have assumed that the sample size n was known, and have studied properties
of various resulting estimators of the population mean or total. Taking a step back, we now
consider the more realistic ques
Simple Random Sampling (Chapter 2)
Simple random sampling (SRS) is a sampling design where n units are selected (without
replacement) from a population of N units, such that all samples of size n are equally likely
to be selected. First, though, we introd
Examples of Sampling Problems
For the following situations, identify the population, the sampling units, and the sampling
plan. If it is a multistage sampling plan, identify the population, sampling unit, and sampling
plan at each stage.
1. A researcher h
Stat 549
Fall 2010
Properties of Expectation and Variance
Denition of expected value for a discrete random variable:
= E(X ) =
xP(X = x)
xI
Properties of expected value:
1. Substitution rule:
E[g (X )] =
g (x)P(X = x)
xI
Note: in general, it is not true