Advantage of sampling

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Advantage of sampling

• Reduced cost
• Faster
• Greater scope
• Greater accuracy

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• Target population
• Sample frame
• Inferential population

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Principal steps in sampling

• Purpose of investigation
• Define the population from which the samples will
  be drawntarget population
• Decide which data should be sampled
• Determine degree of desired precision
• Method of measurement
• Describe sampling procedure (including
  organization of field work and so on)
• Sampling (may be preceded by a pretest)
• Data processing
• Summary and analysis of the data

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Why is it important to identify the most
appropriate sampling method?

• To get the a good estimate of the
• parameter(s) of interest.
• Goodunbiased, small variance and cost
• effective

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Common sampling methods

• Simple Random
• Stratified Random
• Systematic
• Multistage
• Multiphase
• Cluster
• Sequential
• Adaptive

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SIMPLE RANDOM SAMPLE (SRS)

• Random selection of n units out of population
• with N such that every set of n samples has
• the same probability of being drawn.
• In practice a simple random sample is drawn
• unit by unit, and each unit in the population
• has the same chance being included in the sample.

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SIMPLE RANDOM SAMPLE (SRS)

• Advantages
• Easy to obtain
• Easy to explain
• Easy to analyze
• Disadvantages
• May not lead to adequate sample sizes to analyze
  subpopulations
• May not be impossible to do
• May for a given cost not lead to the most
  efficient estimates

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SIMPLE RANDOM SAMPLE (SRS)

• Can be used when
• Sample frame lists all possible sampling units in
  target population
• Sample units are identified by random numbers or
  random location

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SIMPLE RANDOM SAMPLE (SRS)

• Assumptions
• All sample units have the same chance of being
  samples
• Units are selected independent of each other
• Sampling of units is done in one stage

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Stratified sampling

• The population of N individuals is first divided
  into
• subpopulations strata
• These strata are non-overlapping and together
  they
• comprise the whole population
• A sample is then drawn independently from each
• strata

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Stratified random sampling

• A simple random sample is drawn from each
• strata

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When is random stratified sampling most
appropriate?

• For heterogeneous populations which can be
  subdivided into homogeneous strata

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The density of trees varies among different areas
of a natural pine forest
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Advantages of stratified sampling

• 1. Ensures that each strata (subpopulation) is
• well estimated

2. Can result in estimates with smaller standard
errors if sampling is well allocated
3. Different samples can be sampled with
different sampling strategies
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Disadvantages of stratified sampling

• 1. More complicated than SRS

2. Need to identify strata ahead of time. Hence,
more information needed prior to sampling than
than for SRS
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Systematic sampling

• Suppose that the units of the population are
  numbered from 1 to N in some order.
• To select a sample of n units, we take a unit at
• random from the k units and every kth unit
• thereafter.
• For example if k is 15 and if the first unit
  drawn is
• 13 then the subsequent units drawn are 28, 43, 58
• and so on.

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Advantages of systematic sampling

• 1. Very easy to conduct the sampling if the units
  can be numbered

2. If you use area sampling you may construct a
spatial distribution map at the same time
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Disadvantages of systematic sampling

• Can result in biased parameter estimates
• for populations with periodic variation and
• autocorrelation

2. Need to have substantial knowledge of the
population prior to sampling
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When to use systematic sampling
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Stratified systematic sampling

• In sampling an area, the simplest extension of
• the one-dimensional systematic is a square
• grid pattern. A sample is then taken at the
• same position for each grid. A version
• of this is unaligned sampling in the grid
• system.

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Cluster sampling (single stage)

• Assume that the individuals of a population
• naturally occur in clusters. Then randomly
• sample clusters. Each individual of the
• sampled clusters is then assessed or measured.

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Two stage sampling

• Subsampling with units of equal size
• Subsampling with units of unequal size

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Multi-stage sampling

• Cluster sampling subsequent sampling within
• the cluster (for example SRS)

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Complex sampling

• Combines multiple design components
• It may for example combine stratified
• sampling, cluster sampling and unequal
• probability sampling

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Double sampling (two phase sampling)

• Use a more precise (and more costly)method for a
  small sample in the population.
• Use a less precise (and less expensive) method to
  measure a larger (or all) individuals in the
  population.
• Then, the mean of the less precise measurements
  on
• all individuals in the study are adjusted using
  the
• (linear) relationship between the more precise
  and
• less precise measurements taken on the smaller
• sample.

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Double sampling (two phase sampling)

• The effectiveness of double sampling is
• dependent on how strong the correlation is
• between the two measurement methods.
• And also if relationship really is linear

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Adaptive sampling

• Adaptive sampling refers to sampling designs
• in which the procedure for selecting sites or
• units to be included in the sample may depend
• on values of the variables of interest observed
• during the survey

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Sequential sampling

• Sample first a specific number of units from the
• population, determine the mean and variance for
  the
• parameter. If satisfied, stop sampling. If not,
  sample
• another set of units and determine the mean and
• variance for all sampled units. If satisfactory,
  stop
• sampling. If not, repeat procedure until
  satisfactory
• results obtained.

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How large should the sample size be?

• -Depends on the analysis you plan to do
• -The accuracy (the power) you require
• -Your budget
• -Your sampling design

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How large should the sample size be?

• Review relevant articles
• Conduct a small pilot study to get an idea of
• the variability (maybe even the power)
• Interview experienced researcher(s) studying
• similar populations and questions

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Design effectDeff

• DeffVariance of the sampling design in question
  divided by the variance of SRS
• This assumes equal sample sizes and equal costs
  of the two sample designs

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Surveys involving the forms or phone interview

• Ex.
• 200 questionnaires were sent out but only 80
  questionnaires
• returned.
• Of those 60 are A1 individuals while 20 are A2
  individuals
• So 60/8075 of those who answered are A1
  individuals
• How many are A1 individuals in the original
  sample of 200?

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Surveys involving the forms or phone interview

• To be able to put some limits on proportion A
  individuals
• among the original 200 sampled individuals you
  assume
• all the people who did not answer are
  A1-individuals
• none of the people who did not reply are
  A-individuals
• Pupper_limit(60120)/2000.9 or 90
• Plower_limit600/2000.3 or 30
• So the proportion A-individuals in the original
  sample is
• somewhere between 30 and 90.

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Surveys involving the forms or phone interview

• There is no simple method for how to account for
  the
• people who did not answer. The best one can do is
  to
• try to approach the person again sending out the
  same
• form. (CSN and no-job)

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Quadrat sampling

• A quadrat (plot) is a square, rectangle, circle
  or
• other shape area used as a sample unit.
• Items of interest within the quadrat are counted,
• collected, weighed, etc., and recorded for the
  entire
• quadrat.
• In quadrat sampling, one must choose the
• dimensions, shape and number of the quadrats
  prior
• to implementation.

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Quadrats are used to sample

• Vegetation and trees,
• Slow moving animals,
• Animal burrows, nests, hills,
• Benthic fauna,
• Soil, fauna, and other characteristics.
• Aquatic plants, and many more.

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Quadrats are used when

• The individuals of interest are too numerous to
  be considered separately as sample units.
• It is impossible to create a sampling frame of
  individuals prior to unit selection.
• The parameter of interest relates to area
  coverage or density.

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Capture-recapture to estimate animal abundance

• A set of randomly selected (captured) individuals
  are marked then released back into their original
  population (environment).
• These marked individuals are assumed to mix
  freely with unmarked individuals of the
  population
• One or more follow-up samples of randomly chosen
  individuals are selected and examined.
• The ratio of marked to unmarked individuals in
  the sample is used to estimate abundance.

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Assumptions for capture-recapture

• The population under study should be both
  geographically closed and demographically closed.
  
• Each member of the population has the same
  probability of being captured, and this capture
  probability does not change over time.
• The fact that an individual has been captured
  once does not change its probability of being
  captured in future samples.
• Marked and unmarked individuals mix randomly
  between samples.
• Marks are permanent and always recognizable.