Sampling and Sampling Designs

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Population ??
Sample ??
Sampling ??
? s2
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Generalization ??
Parameter ??
Statistic ???
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Why sample?

• Lower cost
• Greater accuracy of results
• Greater speed of data collection
• Availability of population elements
• Sample vs. Census

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What is a good sample

• Accuracy
• Systematic variance ????
• The variation in measures due to some known or
  unknown influences that cause the scores
  (results) to lean in one direction more than
  another
• Precision
• Sampling error ????
• the degree to which a given sample differs from
  the underlying population
• sampling error tends to be high with small sample
  sizes and will decrease as sample size increases

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??

• Differences between parameters and
  statisticserror
• sampling error ????
• Systematic error ???? (also called measurement
  error)

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Target Population

• group to which you wish to generalize the results
  of the study
• should be defined as specifically as possible

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• Sampling frame ????
• the list of elements from which the sample is
  actually drawn

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Steps in sampling design

• What is the population?
• What are the parameters of interest?
• What is the sampling frame?
• What is the type of sample?
• What size sample is needed?
• How much will it cost?

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What is the population

• Clearly define your population of interest
• Population vs. research subjects

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What are the parameters of Interest?

• Summary of descriptors (mean, variance) of
  variables in the population
• Issue of the scale of measurement

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What is the sampling frame?

• the list of elements from which the sample is
  actually drawn

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What is the type of sample?

• Probability sample vs. nonprobability sample

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What size sample is needed?

• The larger, the better

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Sampling Techniques

• Probability Sampling (random sampling) ????
• Nonprobability Sampling (nonrandom sampling)
  ?????

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Probability Sampling

• sample should represent the population
• using random selection methods
• members of the population have a known and
  non-zero chance of being selected (EPSEM Equal
  Probability of SElection Method)

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Types of Probability Sampling

• Simple random sampling??????
• Systematic sampling?????
• Stratified sampling ??????
• Cluster sampling ????
• Double sampling ????

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Simple Random Sampling

• every unit in the population has an equal and
  known probability of being selected as part of
  the sample (??)

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Random Numbers Table ???

• a table of random digits arranged in rows and
  columns
• after assigning an identification number to each
  member of the population, numbers in the random
  numbers table are used to select those who will
  be in the sample

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???
1 2 3 4 5 6 7 8 9 10
1 49486 93775 88744 80091 92732 38532 41506 54131 44804 43637
2 94860 36746 04571 13150 65383 44616 97170 25057 02212 41930
3 10169 95685 47585 53247 60900 20097 97962 04267 29283 07550
4 12018 45351 15671 23026 55344 54654 73717 97666 00730 89083
5 45611 71585 61487 87434 07498 60596 36255 82880 84381 30433
6 89137 30984 18842 69619 53872 95200 76474 67528 14870 59628
7 94541 12057 30771 19598 96069 10399 50649 41909 09994 75322
8 89920 28843 87599 30181 26839 02162 56676 39342 95045 60146
9 32472 32796 15255 39636 90819 54150 24064 50514 15194 41450
10 63958 47944 82888 66709 66525 67616 75709 56879 29649 07325
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Characteristics of simple random sampling

• Unbiased ???????????????
• Independence ?????????????????????????

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Limitations of simple random samples

• not practical for large populations
• Simple random sampling becomes difficult when we
  dont have a list of the population

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Systematic Sampling?????

• a type of probability sampling in which every kth
  member of the population is selected
• kN/n
• N size of the population
• n sample size

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For example You want to obtain a sample of 100
from a population of 1,000. You would select
every 10th (or kth) person from the list. k
1000/10010
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Advantages/disadvantages of systematic sampling

• Assuming availability of a list of population
  members
• Randomness of the sample depends on randomness of
  the list
• periodicity bias ??????????????????, systematic
  sampling ???????(periodicity bias)

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Stratified Random Sample??????

• Prior to random sampling, the population is
  divided into subgroups, called strata, e.g.,
  gender, ethnic groups, professions,
  etc.??????????(Strata) ????????
• Subjects are then randomly selected from each
  strata????????????(using simple random sampling)

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???
???
. . . . .
?K?
Sample
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• Homogeneity is very high within the strata.
• Heterogeneity is very high between the stratas

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Why use stratified samples?

• permits examination of subgroups by ensuring
  sufficient numbers of subjects within subgroups
  ??????????????????,????????
• generally more convenient than a simple random
  sample

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Potential disadvantages

• Sometimes the exact composition of the population
  is often unknown
• with multiple stratifying variables, sampling
  designs can become quite complex

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Types of Stratified Sampling

• Proportionate Stratified Random Sampling ????????
• Disproportionate Stratified Random
  Sampling?????????

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Proportionate Sampling

• strata sample sizes are proportional to
  population subgroup sizes?????????
• e.g., if a group represents 15 of the
  population, the stratum representing that group
  will comprise 15 of the sample

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Disproportionate Sampling

• strata sample sizes are not proportional to
  population subgroup sizes?????????????????????
• may be used to achieve equal sample sizes across
  strata

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For example Suppose a researcher plans to
conduct a survey regarding various attitudes of
Agricultural College Students at Tunghai U. He
wishes to compare perceptions across 4 major
groups but finds some of the groups are quite
small relative to the overall student population.
As a result, he decides to over-sample minority
students. For example, although Hospitality
students only represent 10 of the Agricultural
student population, he uses a disproportional
stratified sample so that Hospitality students
will comprise 25 of his sample.
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Cluster Sampling????

• used when subjects are randomly sampled from
  within a unit or group (e.g., classroom,
  school, country, etc)
• ????????? (cluster),?????????????????????????????

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k ?
Population
Sample
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Example

• ???????????????
• ??????????????
• ????3??????3????????????
• Compare using cluster sampling technique and
  simple sampling technique

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Why use cluster samples?

• They're easier to obtain than a simple random or
  systematic sample of the same size

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Disadvantages of Cluster Sampling

• Less accurate than other sampling techniques
  (?selection stages, ?accuracy)
• Generally leads to violation of an assumption
  that subjects are independent

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Double sampling ?????

• ???????????????
• Systematic sample cluster/stratified sample

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Nonprobability sampling

• Convenience sampling ?????
• getting people who are most conveniently
  available
• fast low cost
• Purposive sampling ?????
• Judgment sampling
• Quota sampling
• Snowball sampling ??????

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Characteristics of nonprobability samples

• members of the population do not have a known
  chance of being selected
• do not represent any known population
• results cannot be generalized beyond the group
  being tested