Statistics 850 yandell
Homework # 2-Due Mon 13 Feb
1. This problem came up in consulting work with a client in horticulture. This person was interested in cloning plants. Basically what she did was place some plant tissue (say a small part of a leaf) in a dish which has a ``food preparation'' on it. The dish is sealed and placed in a controlled chamber with adequate light and proper temperature. The ``food preparation,'' or media, is designed to encourage growth of new plant shoots from the tissue. The response of interest here is the number of ``adventitious shoots'' (advplt), or new plants growing out of the tissue. Basically, the more adventitious shoots one can produce, the better the growing media. The key question is: what is the best growing condition for the shoots?
The researcher wanted to test the effect of two chemicals on clonal growth, BA and TDZ. The original design had 3 levels of BA (0,0.44,4.4) and 4 levels of TDZ (0,0.2,2,20). Further, there is an extra control (trt=20, saline water plus BHTA). The designation of treatment label trt is indicated in the SAS code and in the following table:
TDZ BA 0 0.20 2.0 20 0 0 1 2 3 0.44 4 5 6 7 4.4 8 9 10 --
Unfortunately, tissue did not survive at high levels of both treatments together (presumably they were chemically burned). Thus the two-way part of the treatment structure is unbalanced, with one empty cell. For this problem, consider that there are 12 treatment groups in a one-way layout.
The design structure was a bit complicated. However, for the purpose
of this problem, consider the design to be completely randomized.
An added problem is that advplt is a count, and many values are
zero (0). The suggested transformation to stabilize variance is
square root.
The data can be found in file hwk2.dat (in the usual directory,
st850-1/data), with some SAS suggestions for this problem
in hwk2.sas for your information.
(a) Present one or more key graphs to summarize the data. Comment on
any problems with assumptions.
(b) Find means and standard deviations for each treatment group.
(c) Construct overall test for equal means. If differences are found,
order the means and then perform pairwise t-tests to determine
significant differences.
(d) Repeat (a)-(c) without the zeroes.
(e) Comment on issues of multiple comparison. That is, select two
methods and briefly discuss their merits and short-comings in the
context of this problem.
(f) Comment on the comparison of group means, with and without zeroes,
noting that the trt levels
represent 3 levels of treatment (TDZ=0.2,2,20) plus 2 controls
(TDZ=0 saline water; TDZ=-1 BHTA).