Title: Chapter 1 Extras
1Chapter 1 Extras
- More on Simulations and surveys
2Another 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?
3When doing a simulation
- Identify the component (the basic event that is
to be repeated) - Identify how you will model the outcomes.
- Explain how you will simulate the trial.
- State clearly what the response variable is.
- Run several trials.
- Analyze the response variable.
- State your conclusion in the context of the
problem.
How many trials??
4More 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
5More 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)
6More 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.
7Experiments 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.
8Experiments 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