Elements of Sampling

1
Elements of Sampling

• How can you tell the what millions of people
  think when you only ask a few hundred?
• References Julio Rivera

2
What is a Sample

• Definition A subset of the population
• It consists of the individuals, objects or
  measurements selected by the sample collector
  from the population

3
Before Getting a Sample

• What are you doing?
• What do you want to know?
• How are you going to know it?
• Planning is key

4
Step 1 Conceptually Define What to Study

• define target population who or what are you
  going to study?
• define target area where are you going to study
  them
• all samples have both a target population and
  target area

5
Step 2 Define the Sample Population and the
Sampling Frame

• sampled population who or what are you actually
  going to collect data from
• sampled area what areas are you actually going
  to take data from
• You sample from a sampling frame
• list of people or things to sample
• in Geography sometimes from a grid coordinate
  system

6
Step 3 Choose Sampling Design

• probability sampling preferred over
  non-probability sampling
• important types of probability samples include
• random, systematic, stratified, cluster, and
  hybrid designs
• there are spatial and nonspatial variations in
  sampling design

7
Step 4 Develop Research Plan

• methods of data collection include direct
  observation, field measurement, mail
  questionnaire, personal interview, and telephone
  interview
• establish protocols for handling all problems or
  situations in the sampling procedure which can he
  anticipated
• complete miscellaneous logistic and procedural
  tasks in the preparation of sample taking

8
Step 4 Develop Research Plan

• Determining the appropriate descriptive and
  inferential data analysis techniques to use

9
Step 5 Conduct Pilots

• Often overlooked--but very important
• trial run or pilot survey of sample data
  collection method
• correct all discovered problems which could lead
  to sampling error
• pretest results may be effectively used to
  determine sample size

10
Step 6 Collect Sample Data

• consistency in collection methods and procedures
  is essential
• assure overall high level of quality control

11
Why do we sample?

• It is often not possible to assess each element
  in most study populations
• Sampling reduces cost and time
• Certain types of sampling can be quite detailed
• Sampling allows replicability and a collection
  over time
• Despite public perceptions, sampling can be
  highly accurate

12
Types of Samples

• How are you going to collect the data
• The methods differ based on your purpose
• Each has its place in statistics

13
Census

• You go out and collect data from every element in
  the population
• If I wanted to know the average age of students
  at UWM, and used a census method, I would have
  the reported age for each student in my sample.
• This is often impractical unless the data is
  already done for you

14
Sampling

• You want to construct a sample which is
  representative of the population
• You want to create a good Sample Design
• Judgment Samples (non-probability)
• Probability Samples

15
Judgment Sample

• Samples are selected on the basis of being
  typical
• The person selecting the sample chooses items
  that s/he thinks are representative of the
  population
• Validity rests on the judgment of the sample
  designer.
• Not generally recommended

16
Probability Samples

• Samples in which the elements to be selected are
  drawn on the basis of probability. Each element
  of the population has a certain probability of
  being selected as part of the sample
• IMPORTANT Statistical inference requires that
  the sample design be a probability sample
• Lets look at some probability samples

17
Simple Random Sample

• One of the most familiar and common types
• A random sample selected in such a way the every
  element in the population has an equal
  probability of being chosen
• effort must be made to ensure that each element
  has an equal probability of being selected.

18

• Mistakes are frequently made because the term
  random (equal chance) is confused with haphazard
  (without pattern).
• The proper procedure for selecting a simple
  random sample is to use a random number generator
  or a table of random numbers.

19
Example

• Assume you want to survey a population of
  students at a small college.
• There are 4265 students.
• Assign each student a number consecutively (0001,
  0002, 0003, etc.)
• Using a random number generator or a table of
  random numbers, select the number of students you
  need

20
Systematic Sample

• A sample in which every kth item in the sampling
  frame is selected
• This method of selection uses the random number
  table only once, to find the starting point
  (first data).
• It is not necessary to number the elements in the
  sampling frame or

21
Systematic Sample

• It is not necessary to know the total count of
  items in the sampling frame.
• This is a good procedure for sampling a
  percentage of a large population.
• Dangers in using the systematic sampling
  technique.
• When the population is repetitive or cyclical in
  nature, systematic sampling should not be used.

22
Strata

• When sampling very large populations, sometimes
  it is possible to divide the population in
  subpopulations based on some characteristic
• These subpopulations are called strata

23
Stratified Sample

• A sample obtained by stratifying the sampling
  frame and then selecitng a fixed number of items
  from each strata
• The population is divided into various strata
• A subset is drawn from each strata
• Randomly, systematically or other methods
• Subsamples are combined into one sample of data
  for further use

24
Quota or Proportional Sample

• A slight modification to the stratified method
  results in a quota or a proportional sample.
• A sample obtained by stratifying the sampling
  frame and
• Then selecting a number of items from each
  stratum according to a quota or in proportion to
  the size of the stratum.

25
Cluster Sample

• A sample obtained by stratifying the sampling
  frame and then selecting sample items from some,
  but not all, of the strata.
• The cluster sample is obtained by using either
  random numbers or a systematic method to first
  identify the strata (clusters) to be sampled
• Then to select the items from within these
  strata.
• Then the subsamples are combined to form the
  sample.

26
Spatial Sampling

• What we have talked about up to this point has
  been largely non-spatial
• Geographers deal with data in space
• Soil type and quality
• Water issues
• Medical Geography
• The list goes on.

27
How are you going to sample spatially

• Point samples
• Line Samples
• Area Samples

28
Simple Random Sample

• Define Study Area
• Use a random number table or generator
• Generate random xs matched with random ys

29
Systematic Point Sample

• Define Study Area
• Randomly select a starting point and a distance
  interval between samples
• Representative method
• Widely used method

30
Stratified Point Sampling

• Define Study Area
• Proportional Sample
• Study Area is 60 non-wetland 40 wetland.
• If you have 50 sample points--20 wet--30 non-wet

31
Stratified Point Sampling

• Define Study Area
• Disproportional sample
• Study Area is 60 non-wetland 40 wetland.
• What if you have to monitor one of these areas
  more closely?
• Sample more points in the area

32
Cluster Analysis

• Define Study Area
• Used to lower cost and overcome logistical
  problems
• Good for very large coverage areas
• Problems can occur when the phenomenon varies
  widely in study area

33
Stratified Systematic--Unaligned

• Define Study Area
• Create grid--randomly number axies
• Select a point in each grid square
• Good choice for a number of designs

34
Hybrid Samples

• You can continually alter these
• Be sure your design meets your needs and
  represents your data

35
Notes on Sampling

• The sampling plan used in a particular situation
  depends on several factors
• (1) the nature of the population and the variable
• (2) the ease (or difficulty) of sampling
• (3) the cost of sampling.
• These and other factors must be weighed, with
  tradeoffs usually occurring, before the exact
  sampling technique is determined.