STAT 516 HW 5 (due Wednesday, April 12)

HAND CALCULATIONS & CONCEPT QUESTIONS:

1.  Table 10.20 on p. 499 gives the results of an experiment on the oxygen consumption 
of oysters under several conditions.  The response values (Y) given in the table are the 
oxygen consumption values for each oyster.  The three treatments considered were the  
environments in which oysters were placed:  Seawater (Control); Treatment Water; and Gas.
The experiment had to be done twice (on two different days), so each day served as 
a separate block.

Do the following by hand, SHOWING WORK. 

(a) What is the value of t (# of treatments)?  What is the value of b (# of blocks)?

(b) Explain why this is an example of what we call a "Randomized Block Design with Sampling".

(c) Note that for this experiment, SS(Trts) = 2.76566; SS(Blocks) = 1.58015; 
SS(Exp. error) = 2.12975; and SS(Samp. error) = 4.87763.  Calculate the correct mean squares 
for each of these sources of variation.

(d) Calculate the correct F-statistic for testing whether environment has a significant 
effect on the mean oxygen consumption.  At the 5% level, is this result significant?

(e) Calculate the correct F-statistic for testing whether there is significant variation 
in oxygen consumption across days.  At the 5% level, is this result significant?

2.  You are asked to design the following experiment.  You want to compare the mean time it 
takes to type mathematical documents across four word processing systems:  LaTeX, MS Word, 
WordPerfect, and EXP.  There are four sample documents, and each of four typists will type 
each document.  You want to control the variation due to typist and the variation due to 
document.  The main response variable is typing speed (words per minute) and the factor of 
interest is the word processing system.  Set up a Latin Square Design for this experiment, 
explaining your notation and the design carefully, so that a non-statistician could carry 
out the experiment according to your instructions.

COMPUTER CALCULATIONS:

3.  Forty architecture students were each asked to judge 5 different building structures.  
The response variable of interest is the judge's overall satisfaction (SAT), where a higher 
score is better.  We wish to compare the mean satisfaction rating across the five buildings,
so the factor of interest is BLDG.  The data are in Table 8.33 of the book on page 414, and 
they are also given as buildingsdata.txt on the course web page.

(a) Why does it make sense to use the judge (denoted SUBJ in the data set) as a blocking 
variable?  Why should we treat this block as a random effect?

(b) Analyze the data as a RBD, where SAT is the response, BLDG is the treatment factor, and 
SUBJ is the block.  Based on the appropriate F-test, is there a significant difference 
in mean satisfaction rating across the five buildings?  NOTE: Use a 10% significance level.

(c) Based on the appropriate F-test, is there significant variation among the judges? NOTE: 
Use a 10% significance level.

(d) Of particular interest to the investigators is whether the mean satisfaction for 
building 1 differs significantly from the mean satisfaction for the other four buildings.  
Use an ESTIMATE statement to test the appropriate contrast here.  NOTE: Use a 10% 
significance level.

4.  Table 10.31 on p. 507 gives the wheat yield for three different varieties of wheat 
(A, B, and C).  The data are also given as wheatdataLS.txt on the course web page. Two 
blocking factors were considered:  the orientation of the plantings and the locations.
A Latin Square Design was used, so we will analyze this experiment as a Latin Square. (Treat 
Location and Orientation as FIXED effects.)

(a) Use the appropriate F-test to test whether there is a significant difference in mean 
yield for the different varieties.  NOTE: Use a 10% significance level.

(b) Use Tukey's procedure to determine which pairs of varieties have significantly 
different mean yields.  NOTE: Use a 10% (experimentwise) significance level.

(c) Based on the SAS output, would it have been reasonable to conduct this experiment as a 
RBD, with only a single blocking factor?  If so, which variable would you use for the 
blocks?