When I ask you to interpret an answer,
usually a value you or someone else computed, then I expect your response
to include:
1. The number itself (make sense of the magnitude for someone who is
not in a statistics class)
2. Units attached to the magnitude
3. Mention the variable itself--involve the situation of the problem
When I ask you to explain an answer, often a choice or determination based on statistical values, then I expect you to provide a logical argument that makes the answer reasonable or understandable. Such an argument will often include interpretations of the values involved. Usually you will expand on the interpretation to involve the problem context and a comparison of values. Sometimes there may not be two values to compare, but you may argue that if some value were larger the decision would be different.
Example:
Problem:
You want to invest a sum of money in one of two stocks, A and B.
The mean annual price change is the same for both stocks, but the standard
deviation of A is larger than the standard deviation of B. If you
are a conservative investor and you want a relatively stable (predictable)
income from your investment, should you invest in A or B? Explain
your answer.
Solution: Notice the interpretation that is part of the explanation.
You should choose stock B. The standard deviation of the annual price changes is smaller for B than for A. A smaller standard deviation means the price changes for B are more similar to their mean from year to year than are the price changes of A. Consequently, there is a greater chance that the price change for B will be about the mean value (more predictable), and there is a greater chance that the price change for B will differ from the mean by a larger amount (less predictable).
Often I provide a template which you must understand well enough to apply to a particular situation.
a. Be sure you
answer the question that is asked and don't stray into irrelevant information
or
redundancy--be
precise and concise.
b. There may
be alternative answers that meet the criteria just mentioned and are reasonable.
Be
careful that
you do not violate or misuse what we've learned in class.
c. You must also
clearly communicate your ideas and information. Make sure that listeners
or readers
can follow your
argument relatively easily and find that it is incomplete.
On tests I expect that I have provided sufficient information for a
direct answer that requires little time if
you are practiced with and informed about the material we have covered.
You can always spend your valuable and limited
time making new assumptions and creating complex answers or a puzzle
that you cannot solve in the allotted time. Save these excursions
for before the tests as you're learning material. Remember you want
to demonstrate that you understand the concepts from class and can apply
them to the information you are given. In any real situation, you must
decide how to allocate time as you balance simplicity and complexity to
accomplish some task.
Sometimes students feel they must memorize what I say. Perhaps there
is some truth here, because I do provide
templates for some interpretations. However, you must be able to insert
variable names, units of measure, and other
aspects of the given situation appropriately. In addition, I typically
ask you to use the interpreted value in a further
task, so if you memorize the template but do not understand the information
content, then your weakness will
appear.
On Your Own:
Suppose the goal of the investor is to make a lot of money and he or
she is willing to risk large losses in the process. Which stock should
he or she choose? Explain.