February 28, 2000
Notes for February 28, 2000
- Collect Journals. Collect homework
Closure on Rodney King questions:
- Compare question 2 with idea of "unusualness" issue.
The question is to decide between two arguments. The first is that there
was bias in the LAPD's dispatcher's selection of officers regarding
the RK affair, and the evidence offered is that all 15 officers were
white. The second argument is that even if the process was completely
random, then we would expect 11% of all 15-officer dispatches to
be all white 15-officer, assuming that the LAPD's officer corp is 86%
- If we were investigating the case, defending
the case, or prosecuting the case, we could decide to collect
more information on past performance of the LAPD (to get a historical
record of percentages of all-white patrols). But as jurors
you must accept one of the arguments proposed. You may not ask for additional
- As Supreme Court judges, you must decide not on
that case, but on how unusual (relative to what we would expect by chance)
a piece of evidence must be to support a claim that an event happened
not by chance, but by someone introducing a systematic bias.
- Yes, it is easier to reject an argument of bias
than it is to support it.
Run the Sample Space and Long-run Behavior demo:
My intention is that they come to think in this way:
That is, students now tend to think of probability
of events over the long run, but each event has its own "long run." When
they think that way, then they cannot see a link between long-term behavior
and sample space. Rather, they understand the link between long-term behavior
and sample space when they understand that the long-term behavior of a
process in relation to one outcome entails relationships to the other
possible outcomes, too. So, we need to emphasize that we need only
think of one long-run sequence of trials in order to imagine the probability
of any of the processes possible outcomes. When every outcome has
its on long-term repetition of the process, then there is no way to imagine
each in relation to the other. The long-runs are, in a sense, independent
of each other. They need to be imagined in relation to each other, and
imagining them all being contained within a single long run of the process
Review the US Census Bureau table from the point
of view of the previous discussion. "Draw a person at random" you
expect long runs of selections (with replacement) to do what? To reflect
the population composition. So, what percent of the time would you expect
to select a White person? A black person? A black hispanic? Point out
that you can use the population percentages to answer probability questions
because you expect, in the long run, that random selection procedures
will produce long-run results that reflect thepopulation.
Ask, for example, these questions:
- What fraction of the US population is White? Black?
- What fraction of the US population is Hispanic?
Black Hispanic? Native Hispanic?
- What fraction of Native Americans are Hispanic?
What fraction of all Hispanics are white?
- I say, "Pick a US citizen at random. What is the
probability this person is Native American?"
- What does this mean? (When you pick a person
at random many times, what fraction of those times
- Why can we say this? (We expect the composition
of large simple random samples to reflect the population's composition.)
KEY!!!! (Large samples are made by picking individuals one at a time!)
- I say, "Pick a Hispanic person at random. What
is the probability this person is Asian?
- What does this mean? What is your answer?
Show the table also and then the tree diagram as
a shortcut to the table and diagram. But STRESS that the tree diagram
is not a SUBSTITUTE for the others. Rather, it is a way to reason the
same way without having to write so much down.