STA 2004F Homework 3.
1. In the following highly idealized sets of data from two-level experiments, each value
given is the mean of observations for the relevant factor combinations. The means can
be treated as independent, with standard error 1. Without
STA 2004F Final Homework. Please work alone.
Due: Dec 19 at 5 p.m. (or sooner).
Submit all the computer code you used as an appendix, but do not submit raw code as your
solutions to the problems. You may cut and paste the relevant bits, or retype or rewri
Analysis of two factor experiments
Suppose we have two treatment factors, A and B, with a and b levels respectively, and we have r replications of a completely randomized design in these
treatments. The linear model can be written as
Yijk = + i + j + ( )i
STA 2004F Homework 3 Solutions (Sketch).
1. In part (a) the estimated main eects of A and B are 2.6 and 3.5, respectively. These
are signicantly dierent from zero, as the standard error of an eect estimate is
2 2 /2 = 1 and = 1. The estimated AB interacti
STA 2004F Final Homework: Sketch of solutions
1. An experiment was conducted to study the eects of drying time in hours and temperature in degrees Centigrade on the content of undesirable compounds in a resin. The
response is measured in parts per million
STA 2004F Homework 2 Solutions.
1. Two types of extended Latin square designs were given: (a) 3 replicates of a 44 design,
and (b) intermixed 4 4 Latin squares. What types of systematic error are eliminated
using design (a)? What types of systematic error
Technical note on analysis of covariance
This follows, but is slightly simpler than, CR pp. 59,60. Suppose we t
the following model with treatment eects and a single covariate:
yjs = + j + (zjs z. ) +
where j is the treatment eect associated with the j
STA 2004F Eciency of RB design compared to CR design
The eciency of a randomized block design with r blocks and v units per
block is estimated by
SSB + r(v 1)M SE
(rv 1)M SE
where SSB is the sum of squares due to blocks, and M SE is the mean square
STA 2004F: September 12, 2006
An elegant design due to Hotelling
This is taken from Cherno.1 . We have eight objects, whose weights we wish to estimate with
as much precision as possible, using a pan balance, which measures the dierence between
STA 2004F Homework 1.
1. (cf. CR 1.3) Find a news article that reports the results of a medical study, and then
nd the source article on which the news article is based. Describe the type of study,
the experimental (or observational) units, the treatments
List of Errata for DOE book
(Thanks to Radu Craiu, Hyo-Duk Shin, David Oakes, .)
p. 37 Rosenbaum (1999) reference missing
eqn (3.12) and (3.13) remove bars on YTs etc.
p. 55 eqn (3.39) delete leading r, also last term in sum should be SSL(v1) , not S