Chapter%206%20Introduction%20to%20Inferential%20Statistics%20Sampling%20and%20Sampling%20Designs

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Chapter 6 Introduction to Inferential
StatisticsSampling and Sampling Designs
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What are samples?
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Population ??
Sample ??
Sampling ??
? s2
?2
Generalization ??
Parameter ??
Statistic ???
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??

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

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Sampling error

• the degree to which a given sample differs from
  the population
• sampling error tends to be high with small sample
  sizes and will decrease as sample size increases

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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 Techniques

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

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Nonprobability sampling

• Convenience sampling ????
• getting people who are most conveniently
  available
• fast low cost
• Volunteers ????
• units are self-selected

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Characteristics of nonprobability samples

• members of the population DO NOT have an equal
  chance of being selected
• results cannot be generalized beyond the group
  being tested

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Probability Sampling

• sample should represent the population
• using random selection methods

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Types of Probability Sampling

• Simple random sampling??????
• Systematic sampling?????
• Stratified sampling ??????
• Cluster 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 (??)
• e.g. in obtaining a sample of 10 subjects from a
  population of 1,000 people, everyone in the
  population would have a 1/100 chance of being
  selected (or p of .01)

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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 200
from a population of 10,000. You would select
every 50th (or kth) person from the list. k
10000/20050
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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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• Should select variables that are related to the
  dependent variable
• 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 25 of the
  population, the stratum representing that group
  will comprise 25 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 "cluster" or unit (e.g., classroom,
  school, country, etc)
• ????????? (cluster),?????????????????????????????

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Cluster 1
Cluster 2
Cluster 1
Cluster 4
Cluster 5
Cluster 3
Cluster 3
Cluster 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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Sampling Distribution

• ????

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• For the most part in social science, we want to
  know about the population. In reality, the
  parameters are often unknown.
• The best thing we can do is to guess what our
  population should be like based on the info we
  get from a sample
• results of a samplethe results of a
  population???

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Sampling Distributions????

• The bridge b/w information from the sample to
  the population
• a theoretical, probabilistic distribution of all
  possible samples of a given size,
• ?????????????????,?????????????????????

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The relationship b/w population, sampling
distribution, and sample.
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? 100
etc. for all possible samples of a given N from
the population
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Sampling Distribution ??

• ????normal distribution, ????????????????,
  ??????????normal distribution ???????????

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• ??????????(91, 92, 93, 94,95)???, ???mean ?
  93?????5???(??)?????2???????(n2)?????3???????????
  ?

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When n2
sample Sample mean sample Sample mean
91,92 91.5 92,94 93
91,93 92 92,95 93.5
91,94 92.5 93,94 93.5
91,95 93 93,95 94
92,93 92.5 94,95 94.5
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When n3
sample Sample mean sample Sample mean
91,92,93 92 91,94,95 93.33
91,92,94 92.33 92,93,94 93
91,92,95 92.67 92,93,95 93.33
91,93,94 92.67 92,94,95 93.67
91,93,95 93 93,94,95 94
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• Sampling distribution of sample mean
• Mean of the sampling distribution ?
• St.D. of the sampling distribution (Standard
  Error ) s2/N
• Standard error (?????????)??????????????????????
• ?N, ?Standard Error

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Central Limit Theorem ??????

• ?????????normal distribution, ?????????????????,??
  ???N?? (N?100),???????????normal distribution
• If n is sufficiently large
• X N(?, ?2/n)

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Summary of Sampling Distribution

• ???????????,????????????????
• ??????????,???????????????????????
• ????????????????
• ????????????????

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Exercise

• ??????????????????????,???????10??,????2??????????
  ??????,????16??????????,???16???????????11????????
  

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• Sampling distribution of sample proportion( )
• Mean of the sampling distribution of
• ? P
• Standard error of the sampling distribution of
• ?