Data Collection and Sampling

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Data Collection and Sampling

• Chapter 5

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5.2 Sources of Data

• The reliability and accuracy of the data affect
  the validity of the results of a statistical
  analysis.
• The reliability and accuracy of the data depend
  on the method of collection.
• Three of the most popular sources of statistical
  data are
• Published data
• Observational studies
• Experimental studies

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• Published Data
• This is often a preferred source of data due to
  low cost and convenience.
• Published data is found as printed material,
  tapes, disks, and on the Internet.
• Data published by the organization that has
  collected it is called PRIMARY DATA.

For example Data published by the US Bureau of
Census.

• For example
• The Statistical abstracts of the United States,
• compiles data from primary sources
• Compustat, sells variety of financial data
  tapescompiled from primary sources

• Data published by an organization different than
  the organization that has collected it is called
  SECONDARY DATA.

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• Observational and experimental studies
• When published data are unavailable, one needs to
  conduct a study to generate the data.

• Observational study is one in which measurements
  representing a variable of interest are observed
  and recorded, without controlling any factor that
  might influence their values.
• Experimental study is one in which measurements
  representing a variable of interest are observed
  and recorded, while controlling factors that
  might influence their values.

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• A good questionnaire must be well designed
• Keep the questionnaire as short as possible.
• Ask short,simple, and clearly worded questions.
• Start with demographic questions to help
  respondents get started comfortably.
• Use dichotomous and multiple choice questions.
• Use open-ended questions cautiously.
• Avoid using leading-questions.
• is useful to pretest a questionnaire.
• Think about the way you intend to use the
  collected data when preparing the questionnaire.

• Surveys solicit information from people.
• Surveys can be made by means of
• personal interview
• telephone interview
• self-administered questionnaire

• Surveys

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5.3 Sampling

• Motivation for conducting a sampling procedure
• Costs.
• Population size.
• The possible destructive nature of the sampling
  process.
• The sample population and the target population
  should be similar to one another.

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5.4 Sampling Plans

• Simple random sampling
• In simple random sampling all the samples with
  the same size is equally likely to be chosen.
• To conduct a random sampling
• assign a number to each element of the chosen
  population (or use already given numbers),
• randomly select the sample numbers (members). Use
  a random numbers table, or a software package.

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• Example 5.2
• A government income-tax auditor is responsible
  for 1,000 tax returns.
• The auditor will randomly select 40 returns to
  audit.
• Use Excels random number generator to select
  the returns.
• Solution
• We generate 50 numbers between 1 and 1000 (we
  need only 40 numbers, but the extra might be used
  if duplicate numbers are generated.)

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Round-up
X(100)
383 101 597 900 885 959 15 408 864 139 2
46 . .
50 integral random numbers between 1 and
1000 uniformly distributed
50 Random numbers between 0 and 1000, each has a
probability of 1/1000 to be selected
The auditor should select 40 files numbered 383,
101, ...
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• Stratified Random Sampling
• This sampling procedure separates the population
  into mutually exclusive sets (strata), and then
  draw simple random samples from each stratum.

• With this procedure we can acquire information
  about
• the whole population
• each stratum
• the relationships among starta.

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• There are several ways to build the stratified
  sample. For example, keep the proportion of each
  startum in the population.

A sample of size 1,000 is to be drawn
These are the population proportions of each
income category
Total 1,000
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• Cluster sampling
• Cluster sampling is a simple random sample of
  groups or clusters of elements.
• This procedure is useful when
• it is difficult and costly to develop a complete
  list of the population members
• the population members are widely dispersed
  geographically.
• Cluster sampling increase sampling error, because
  there are probably similarities among cluster
  members.

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5.5 Errors Involved in sampling

• Two major types of errors can rise when a
  sampling procedure is performed.
• Sampling Error
• Sampling error refers to differences between the
  sample and the population, because of the
  specific observations that happen to be selected.
• Sampling error is expected to occur when making a
  statement about the population based on the
  sample taken.

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Population income distribution
m - Income population mean
Sampling error
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• Non-sampling error
• Non-sampling errors occur due to mistakes made
  along the process of data acquisition
• Increasing sample size will not reduce this type
  of errors.
• There are three types of Non-sampling errors
• Errors in data acquisition,
• Non-response errors,
• Selection bias.

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Data Acquisition Error
Population
Sampling error Data acquisition error
If this observation
is wrongly recorded here
Sample
Then the sample mean is affected
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Non-Response Error
Population
No response here...
May lead to biased results here
Sample
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Selection Bias
Population
When parts of the population cannot be selected...
the sample cannot represent the whole population
Sample