QSCI 482/Prof. Conquest TAs Kennedy, Malinick, Norman
HW 6 - DUE FRIDAY, NOVEMBER 15, 2002

1. You have been hired as a statistial consultant to the Water Quality
Division of the Municipality of Metropolitan Seattle (METRO). (Even
though you only have one quarter of QSCI 381 and some weeks of QSCI 482,
that puts you way ahead of a lot of other people!) METRO is going to be
comparing two areas (one designated "polluted", one designated a
"reference control site") with respect to a number of measured responses
like dissolved oxygen, turbidity, pH, and a number of toxicants
(polyaromatic hydrocarbons, DDT, polychlorinated biphenyls, heavy metals,
etc.) Since there are so many potential responses to consider, rather than
focus on any one particular response, one way to have a sample size/power
analysis discussion is to do a graph, with "delta/s" on the y-axis and "n
per treatment group (assuming equal n's)" on the x-axis. Because of the
expense involved, the sample sizes per area are going to be rather small,
perhaps as low as 3 samples per area for either sediment samples or water
samples! We're trying to show METRO the what happens statistically in
terms of how the Minimum Detectable Effect changes as the number of
samples per group changes. So, try out the values n = 3, 4, 5, 6, 8, 10,
15, 20 [that's the n *per group*], solve for the quantity "delta/s", and
plot delta/s against n. Use alpha(2) = .10 and power = .90.

After you obtain your graph, what point would you emphasize to the METRO
folks if you were doing a sample-size-power-analysis presentation? (A few
sentences along with your graph. This means that you also have to turn in
your graph.)

2. A soil scientist wants to see if the soil composition (having
something to do with the amount of carbon in the soil--the more carbon
in the soil, the darker the color) is different under two different
Treatments; denoted "T" and "C". Pairs of plots are located throughout a
designated area (see notes p. 11-3 for a diagram). One member of each
pair is randomly assigned the "T" treatment and the other member of the
pair is assigned the "C" treatment. Now, the final measuring instrument
for amount of carbon in the soil is simply a SCORE between 0 and 100,
basedly largely on "carbon color observation" as described above.
Therefore, although a higher score represents "more carbon" than a lower
score, the scientist is not sure that the scores are sufficiently exact
to be treated numerically. Use a *nonparametric* test, then, to test
whether the effects of the two treatments are the same, or whether they
are different. You may use the .10 level of significance. The data are
as follows:
Pair T C

1. 82 63
2. 69 42
3. 73 74
4. 43 37
5. 58 51
6. 56 43
7. 76 80
8. 65 82

What do you conclude?

3. A random sample consisting of 11 automobile drivers was selected to see
if alcohol affected time to complete a specific task. Each person's
response time was measured in a laboratory setting. Under one scenario,
the person would drink a beverage that contained NO alcohol; under another
scenario, the person would drink a beverage WITH alcohol. Treatments were
randomized, and neither the drivers *nor* the people recording the test
results knew which beverage actually contained the alcohol (this is known
as a "double-blind" study). It is expected that the response time will
*lengthen* when alcohol is consumed. The data (response time in seconds)
are as follows:

SUBJECT NO ALCOHOL WITH ALCOHOL
1 7.1 7.4
2 6.3 6.2
3 6.8 6.6
4 8.4 9.3
5 6.9 7.2
6 8.5 8.8
7 7.3 7.6
8 7.7 7.9
9 8.1 8.7
10 7.4 7.9
11 6.6 7.0

At the .10 level of significance, do a *parametric* test to see whether
the consumption of alcohol *increases* reaction time. What do you
conclude?