Collecting Data Sensibly

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Chapter 2

• Collecting Data Sensibly

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2.1 Statistical Studies Observation and
Experimentation

• Observation Study is a study that an investigator
  observes characteristics of an existing
  population. (We are interested in characteristics
  of a single existing population or in comparing
  two or more populations.)
• What is the average shell thickness of bald eagle
  eggs?
• Experiment is a study that the investigator
  observes how a response variable behaves when the
  researcher manipulates one or more factors. (We
  are interested in the effect of certain
  experimental conditions on a response variable.)
• What would happen to test scores if the chemistry
  lab hours were increased from 3 to 6 hours per
  week?

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2.2 Sampling

• Bias in sampling is the tendency for samples to
  differ from the corresponding population in some
  systemic way.
• Types of Bias in Sampling Tendency for samples
  to differ from the corresponding population
• Selection bias Systematic exclusion of some part
  of the population
• Measurement or response bias The method of
  observation tends to produce values that differ
  from the true value.
• Nonresponse bias Data are not obtained from all
  individuals selected for inclusion in the sample.

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2.2 Sampling A Simple Random Sample

• A simple random sample of size n is a sample that
  is selected from a population in a way that
  ensures that every different possible sample of
  the desired size has the same chance of being
  selected.

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2.2 Sampling

• Commonly used methods of Selecting a Simple
  Random Sample
• Put the name or number of each member of the
  population on a different slip of paper then
  thoroughly mix the slips and select n slips one
  by one
• Create a list (called sampling frame) of the
  members in the population, and each item on the
  list is identified by a number. Then use a random
  number generator (included in most statistics
  software packages ) to produce a sequence of
  random numbers.

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How to Select A Random Sample

• During the previous calendar year, a
  countys small claims court processed 870 cases.
  A legal researcher would like to select a simple
  random sample of 50 cases to obtain information
  regarding the average award in such cases.
  Exercise Describe how a simple random sample of
  size n 50 might be selected from the case files.

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Sample with and without Replacement

• Sample without replacement Once an individual
  from the population is selected for the sample,
  it may not be selected again in the sampling
  process.
• Sampling with replacement (rarely used) After an
  individual from the population is selected for
  the sample and its data are recorded, the
  individual is placed back in the population and
  can be selected again in the sampling process.
• The two methods can be viewed as equivalent if
  the sample size is more than 5 of the population.

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Dotplot of Math SAT Scores for the Entire
Population
The population 5000 Applicants to A State
University
Next slide shows dotplots of the math SAT scores
for five random samples of different size from
the population. Notice that the samples tend to
reflect the distribution of scores in the
population.
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The random selection process allows us to be
confident that the resulting sample adequately
reflects the population, even when the sample
consists of only a small portion of the population
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Other Sampling Methods

• Stratified sampling Divide a population into
  subgroups (strata) and then take a separate
  random sample from each stratum.
• Cluster sampling Divide a population into
  subgroups (clusters) and form a sample by
  randomly selecting clusters and include all
  individuals or objects in the selected cluster in
  the sample.
• 1 in k systematic sample A sample selected from
  an ordered arrangement of a population by
  choosing a starting point at random from the
  first k individuals on the list and then
  selecting every kth individual thereafter.

Dont try these methods Convenience sampling An
easily available of convenient group to form a
sample. Voluntary response sampling Samples
rely entirely on individuals who volunteer to be
a part of the sample.