STAT 401 HW 1 Notes
Geoffrey Thompson
6/01/2013
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General Comments on HW
There were several common mistakes. I will not generally post complete solutions since there are a lot of problems which everybody gets right (good work!),
except for possibly minor arithmetic errors, but I will comment on common or
uncommon mistakes that indicate further clarification is needed.
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2.1
Common Mistakes in HW 1
Problem 8
The question asks about combinations of levels of three different factors. Several
people only varied factors one-at-a-time, and therefore got an answer of 6. I gave
partial credit for this depending on how much work was shown. Note: this is
why it is important to show your work. If you give a wrong answer and no work,
you are not going to have a good time. Some mistakes are more valuable than
others.
The point of a factorial design is that we observe combinations of different
factor levels and therefore can make inferences about the interactions of the
treatment levels.
Here is what is going on: if we were only looking at one factor, there would
be two observations: H and L.
If we add a second factor, again with two levels (H and L), there are now
four observations: HH, HL, LH, and LL. We produce this by taking the planned
observations of the one factor and doing them all for both levels of the new
factor.
If we are looking at a third factor, we take the planned observations of the
second factor and do them all again for all levels of the third factor: HHH, HLH,
LHH, LLH, HHL, HLL, LHL, LLL.
So, the correct answer is 2 · 2 · 2 = 8.
2.2
Problem 38
The problem said to work off of the reported BP values, which are rounded to
the nearest 5. If you worked off of the actual BP values, things will go wrong.
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The median will change from 127.4 to 127.6 instead of 125 to 130 and the later
question about the sensitivity of the median to rounding or grouping of data
will not make much sense.
The idea is that, since the median is one value out of a data set, doing
things that change the individual values might make a big change in the median.
However, the median is robust to outliers.
2.3
Problem 64(b)
The problem said to “carry out such a comparison for the given data”. Several
people neglected this. While the numbers are important, usually we care about
the answer to the question we ask and not necessarily the specific numbers. But
we want the right numbers, too.
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