STAT 516 HW 6 

CONCEPT QUESTIONS:

1.  Look at the data in Table 11.30 on page 554.  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". 

(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 11.30 data using PROC GLM and 
to answer part (c):

(c) Note that (at alpha = .05) there is no significant interaction between 
Medium and Exposure Time (P-value = .0812).  Fit the no-interaction model 
in PROC GLM.  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 11.25 on page 550.  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". 

(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.

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++


PRACTICE PROBLEMS FOR THE FINAL:  Only turn in problems 1 and 2 for homework 6.  
The problems given BELOW can be used as practice problems for the final exam.

PRACTICE PROBLEM 1:  
(a) For the ANCOVA model for the tree data, carefully interpret the estimated 
slope parameter.

(b) For the ANCOVA model for the tree data, find the ADJUSTED sample mean 
circumferences for each value of "Side".

(c) For the ANCOVA model for the tree data, test whether the equal-slopes 
model is sufficient.

PRACTICE PROBLEM 2:

Table 11.26 on page 551 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.

(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.