STAT 516 HW 6

Please write your answers neatly and clearly!

You MUST make sure your answers to these questions are
written in the same order as the questions are listed in 
the assignment. 

CONCEPT QUESTIONS:

1.  Look at the data in Table 11.27 on page 627.  These data measure the 
"recognition score" for children exposed to a certain medium.  The two 
factors are Medium Type (levels: TV, Audio Tape, Written Material) and 
Exposure Time (levels: 5, 10, 15, 20 minutes).  The data are given in the 
course web page under "recognitiondata.txt" (for use in SAS). 

(a) Why are these data considered unbalanced?

(b) Which sums of squares are the proper ones to examine here if we wish 
to study the effect of the factors on recognition score?  (Type I SS or 
Type III SS?)

COMPUTER CALCULATIONS:

Write a SAS program to analyze the Table 11.27 data using PROC GLM and 
to answer part (c):

(c) Fit the model with main effects and interaction in PROC GLM.
Verify that (at alpha = .05) there is no significant interaction between 
Medium and Exposure Time (give the P-value of the test for interaction).  
Using the proper type of SS, test whether medium has a 
significant effect on recognition score and test whether exposure time 
has a significant effect on recognition score.  For each test, use 
alpha = .05 and give evidence (such as a P-value) to support your conclusion.

2.  Look at the data in Table 11.23 on page 623.  These data measure the 
circumference of trees in Colorado.  The main factor of interest is the side 
(north or south) of the mountain on which the tree grows.  A covariate which 
may influence the circumference is the number of rings the tree has (i.e., 
its age).  Use SAS to fit an equal-slopes Analysis of Covariance model for 
these data.  The data are given in the course web page under "treedata.txt" 
(for use in SAS).

(a) Based on the overall F-statistic, is the ANCOVA model useful?  Use 
alpha = .05 and give evidence (such as a P-value) to support your conclusion.

(b) Does the covariate "Rings" have a significant effect on tree circumference?  
Use alpha = .05 and give evidence (such as a P-value) to support your conclusion.

(c) Does the factor "Side" have a significant effect on tree circumference?
Use alpha = .05 and give evidence (such as a P-value) to support your conclusion.

(d) For the ANCOVA model for the tree data, carefully interpret the estimated 
slope parameter.

(e) For the ANCOVA model for the tree data, test whether the equal-slopes 
model is sufficient.  Use alpha = .05 and give evidence (such as a P-value) 
to support your conclusion.

3.  Table 13.13 on page 686 lists, for 71 patients, the size of the ventricle 
(a part of the brain), as well as whether brain wave (EEG) readings are 
normal (0) or abnormal (1).The data are given in the course web page under 
"braindata.txt". 

(a) Write the form of the logistic regression model to be used if we want 
to determine whether ventricle size is related to the probability of abnormal 
brain wave behavior.

(b) Use PROC LOGISTIC (with DESCENDING and LACKFIT options) to fit the 
logistic regression model.  Write the estimated logistic regression model.

(c) Based on the Hosmer-Lemeshow test, does the logistic regression model 
seem appropriate?

(d) Test whether ventricle size has a significant effect on the probability 
of abnormal brain wave behavior.

(e) Find and interpret the estimated odds ratio.

(f) Is a person with a smaller venticle size estimated to have a lesser 
or greater probability of abnormal brain wave behavior than a person with 
a larger ventricle size?

(g) Use SAS to plot the estimated regression curve and give the plot.