Observational Studies

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Observational Studies Simple Random
SamplingSection 1.2

• Alan Craig
• 770-274-5242
• acraig_at_gpc.edu

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Objectives 1.2

• Distinguish between an observational study and an
  experiment
• Obtain a simple random sample

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Data Sources
Sources of Data
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Census
Existing Sources
Survey Sampling
Designed Experiments
No attempt to influence the variable of interest
Dont collect data that have already been
collected!
A census is a list of all individuals in a
population with certain characteristics of each
individual
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Definition

• Observational Study
• An observational study measures the
  characteristics of a population by studying
  individuals in a sample, but does not attempt to
  manipulate or influence the variable(s) of
  interest.
• Sometimes called ex post facto (after the fact)
  studies because the value of the variable of
  interest has already been established.

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Definition

• Designed Experiment
• A designed experiment applies a treatment to
  individuals (experimental units) and attempts to
  isolate the effects of the treatment on a
  response variable.

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Example 1
Smoking
Observational Study
Designed Experiment

• Randomly divide into two groups
• One group smokes
• Control groupdoes not smoke
• Treatment smoking
• Response variable rate of cancer

• Interview smokers
• Control groupnon-smokers
• Lurking variables
• Relationship NOT cause

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Observational Study

• Conducted for 2 reasons
• To learn characteristics of a population
• To determine whether an association exists
  between two or more variables where the values of
  the variables have already been determined (ex
  post facto)
• Control of certain variables impossible or
  unethical
• Cannot determine cause and effect

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Designed Experiment

• Conducted when control of one or more variables
  is possible and ethical
• Can take a long time
• Identify cause and effect relationships

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Sampling
Population
Sample
Tradeoff between information and cost
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Four Basic Sampling Techniques

• Simple Random Sampling
• Stratified Sampling
• Systematic Sampling
• Cluster Sampling

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Simple Random Sampling

• Definition
• A sample of size n from a population of size N is
  obtained through simple random sampling if every
  possible sample of size n has an equally likely
  chance of occurring.
• The sample is then called a simple random sample.

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Example

• A study group consists of 5 students Bob,
  Patricia, Mike, Jan, and Maria
• 2 of the students must go to the board to
  demonstrate a homework problem.
• List all possible samples of size n 2 (without
  replacement) from the population of size N 5.
• What is the likelihood of a specific sample being
  selected?

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Simple Random Sampling

• Like drawing names from a hat
• A list of all individuals in the population is
  called a frame.
• To select a random sample, assign each individual
  in the frame a number from 1 to N (population
  size). Then select n (sample size) random
  numbers. The corresponding individuals are the
  random sample.

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Example Obtaining a Simple Random Sample

• There are 30 students in this class.
• How can we obtain a simple random sample of 5
  students to attend a meeting with the Provost?

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Example Obtaining a Simple Random Sample

• Put the students in alphabetical order.
• Number the students from 1 - 30.
• Obtain 5 random numbers between 1 and 30
  (inclusive).
• Select the students whose numbers match the 5
  random numbers.

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Where do we get the random numbers???
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Obtaining Random Numbers

• From a table of random numbers
• 89392 23212 74483 36590
• 61458 17639 96252 95649
• 11452 74197 81962 48433
• From a calculator
• Enter a seed number
• STO-gt
• MATH PRB 1 rand ENTER
• MATH PRB randInt(1,N) where N is population size
• ENTER ENTER ENTER ENTER ENTER

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Questions

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