Week7
Type I and Type II
errors
Statistically speaking, we are generally agnostic to which
is a bigger problem, type I (false positive) errors or type II (false negative)
errors. However, in certain circumstances it may be important to try and put
more emphasis on avoiding one or the other. Can you think of an example of
where you may want to try harder to avoid one type or another? Can you think of
a policy; political, economic, social, or otherwise, that pushes people toward
avoiding one type or another? What are the repercussions of such policies?
Six Sigmas
Many of you will have heard of Six Sigma management. What
you may not realize is that the etymology of the term Six Sigma is rooted in
statistics. As you should have seen by now in your textbook, statisticians use
the Greek letter sigma (?) to denote a standard deviation. So when these Six
Sigma people start talking about “six sigma processes,” what they mean is that
they want to have processes where there are (at least) six standard deviations
between the mean and what would be determined to be a failure. For example, you
may be examining the output of a factory that makes airline grade aluminum. The
average tensile strength of each piece is 65 ksi, and you view a particular
output as a failure if the tensile strength is anything less than 64 ksi. If the
standard deviation is less than .166, then the process is six sigma. The odds
of a failure within a six sigma process are 3.4 in a million, which corresponds
to the 99.9997% confidence level. When we are doing statistics, we usually use
the 95% confidence level, which is roughly 2 sigmas.
In the case of the tensile strength of airline grade
aluminum, 6 sigmas is probably a good level to be at—catastrophic failure on an
airplane could open you up to lawsuits worth billions of dollars. But there are
some other processes that you probably don’t need to be so certain about
getting acceptable products from. Give some examples from your own business
life of random processes that are likely to be normally distributed, and say
how many sigmas you think the process should be at.
Confidence Interval Quiz
As a fun exercise, take the following little quiz. For your
answer to each one, give a 90% confidence level: For example, if the question
were “How many teams are in the NHL,” a student with no idea might
give an answer of 5-40, a student with a good idea might give an answer of
28-32, and so forth. This exercise is intended to get you to think about
confidence intervals and understanding the basic idea of what they are all
about. It also illuminates the duality of confidence intervals–if you are 90%
sure that the correct number is between X and Y, then 90% of all such
confidence levels should contain the true value.
Of course many of these questions can easily be googled, but
try not to do it. The point here is not to learn about MLK or about the moon,
but about confidence intervals.
1. What was Martin Luther King, Jr.’s age at death?
2. What is the length of the Nile River, in miles?
3. How many countries belong to OPEC?
4. How many books are there in the Old Testament?
5. What is the diameter of the moon, in miles?
6. What is the weight of an empty Boeing 747, in pounds?
7. In what year was Mozart born?
8. What is the gestation period of an Asian elephant, in
days?
9. What is the air distance from London to Tokyo, in miles?
10. What is the deepest known point in the ocean, in feet?
