Stat 705 HW 19 Due Monday April 7, 2008.
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Consider the R dataset OrchardSprays which can 
be found in the base R package. 

Use help(OrchardSprays) to get some background on 
what the dataset was measuring. Then do the 
following task in both R (with the lm() function, 
defining factor predictors with defined contrasts 
or with design-matrix columns defined directly) 
and SAS (with either PROC REG, or more simply, with 
PROC GLM  using the CLASS statement to work with
dummy variables without having to code them 
yourself in a DATA step).

PROBLEM: Since the levels A,B,...,G,H correspond to an 
increasing concentration of applied chemical, an 
interesting set of parameters to estimate is the 
difference betweeen the average response with 
treatment B versus treatment A, treatment C versus 
treatment B, D versus C, etc., through G versus F.
Note that the "response" variable "decrease" is a 
measure of the volume of sugared water that the bees 
absorb, so larger values correspond to a less effective 
treatment (because fewer bees have been repelled when 
more sugared water is used up.)

Estimate the parameters mu_B-mu_A, mu_C-mu_B, etc., and 
give the estimated (7x7) variance-covariance matrix 
of your estimates. Use the resulting estimates and 
estimated variances [or the software's reported 
hypothesis tests about contrasts] to perform 7 separate 
hypothesis tests to find whether B is less effective 
than A in honeybee repulsion (i.e., mu_B-mu_A>0), 
whether C is less effective than B, etc., all the way 
through whether H is less effective than G.

NOTE: see the new (as of 4/5/08) handout Contr.txt
under the Handouts portion of the course web-page 
for further elaboration on how to define customized
contrasts.


EXTRA: in either R OR SAS [you need not do this part 
in both packages], fit an augmented model 
incorporating the mean treatment effect parameters 
as above together with the binary parameter: 
I{rowpos > 3). Show that this extra parameter is 
highly significant, and with this parameter in the 
model re-examine which contrasts B vs. A, C vs. B, 
..., H vs. G are [individually] significant.