Chapter 1 Extras

1
Chapter 1 Extras

• More on Simulations and surveys

2
Another Simulation

• What if Wheaties put pictures of athletes on
  trading cards in their cereal boxes. Imagine if
  they put Tiger Woods in 20 of the boxes, Lance
  Armstrong in 30 and Serena Williams in 50 of
  the boxes.
• How could we run a simulation (using cards) to
  predict how many boxes we would likely need to
  buy to end up with the complete set?

3
When doing a simulation

1. Identify the component (the basic event that is
   to be repeated)
2. Identify how you will model the outcomes.
3. Explain how you will simulate the trial.
4. State clearly what the response variable is.
5. Run several trials.
6. Analyze the response variable.
7. State your conclusion in the context of the
   problem.

How many trials??
4
More on Sample Surveys

• Biased Sample over/under emphasizes some
  characteristics of a population.
• Systematic Bias - bias as result of the system
  (i.e. scale that is mis-calibrated)
• Response Bias anything in the way the data was
  collected that influences the response.
• Does anyone know about the Alf Landon vs. FDR and
  the mistake made by the Literary Digest?

Response Bias Wording of a question, order in
which the choices are presented, question
content, question setting, appearance of
questioner
5
More on Sample Surveys

• Parameter a number that represents something
  about a Population (i.e. a Population parameter)
• Parameters are denoted by Greek letters (µ, s)
• Statistic a number that represents something
  about a Sample (i.e. a Sample Statistic)
• Statistics are denoted by Latin letters (x, s)

6
More on Sample Surveys

• Sampling Frame the list of individuals from
  which the sample is drawn
• Samples drawn at random should generally differ
  from one another. This sample to sample
  difference is called sampling variability.
• Multistage sampling sampling schemes that
  combine several methods of sampling

Interesting to note A random sample of 100 can
at times represent a large population rather
well, assuming that 100 is a good representative
sample of the population you are measuring.
7
Experiments and Observational Studies

• A study where data is collected based on the past
  is called a retrospective study.
• Imagine a study which tries to tie music study
  with scholastic performance.
• In an experiment, the assigned treatment can be
  applied in a variety of ways, called levels.
• The treatment is the combination of all levels of
  application.

8
Experiments and Observational Studies

• The four principles of Experimental Design are
• Control (making conditions as similar as
  possible)
• Randomize (so effects of unknown or
  uncontrollable bias are equalized)
• Replicate (an experiment on a single subject is
  not data)
• Block (randomizing to equalize variation across
  all treatment groups) Imagine testing
  fertilizer on plants from two different
  greenhouses By blocking each source of plants
  and applying the treatments in the same way, the
  differences caused by the treatment can be seen
  more easily. Matching subjects

Blocking for Experiments is the same idea as
stratifying for sampling