STAT 516 HW 3 (due date: March 15)


HAND CALCULATIONS:

1.  We will analyze the data in Table 6.28 on pg. 281 of the textbook.  The dependent (Y) 
variable (Y) is the time needed for the mouse to complete the maze and the factor is the 
color of the maze door.  The 3 levels for this factor are red, green, and black.

Do the following by hand, SHOWING WORK.  You may use SAS to check your answers if you want.

(a) Calculate the sums of times for each door (the Y-i-dot values) and the overall sum of 
all the times (the Y-dot-dot value).

(b) Use your answers from part (a) to find the SSB, SSW, and then the MSB and MSW.

(c) Calculate the F ratio and write the complete ANOVA table for this problem.

(d) Perform the ANOVA F-test by comparing the F ratio to the appropriate value from the 
F table (use a significance level of .05).  Among the different door colors, is there a 
significant difference in mean time needed to complete the maze?

(e) Calculate the residual for the first mouse listed for the Red door.

COMPUTER CALCULATIONS:

2.  Look at the data in Table 6.34 on page 283 of the textbook.  These data are also 
given in the SAS code "insectdata.txt" on the course web page.

(a) Use PROC GLM to test whether the mean number of insect deaths differs across insectide 
types.

(b) For the analysis in part (a), use Levene's test (alpha = 0.05) to check the 
equal-variances assumption.  Also, perform a residual plot and a Q-Q plot of the 
residuals to check for violations in the assumptions.  Summarize your findings.

(c) If the residual plot shows any outlier(s), which data value is responsible?

(d) Perform's Tukey's multiple comparison procedure (using alpha = 0.05) and summarize 
which insecticides are significantly different from each other, in terms of mean 
number of deaths.

3.  Look at the data in Table 6.39 on page 285 of the textbook.  These data are also 
given in the SAS code "bankdata.txt" on the course web page.

(a) Use PROC GLM to test whether the mean number of days of sick leave differs across 
bank branches.

(b) In particular, suppose the bank manager suspects the employees at branches 1 and 3 have 
a different mean sick-leave count than those at branch 2.  Using an ESTIMATE statement, 
perform a t-test to test for a difference between the mean number of sick days for the 
first and third branches and the mean number of sick days for branch 2.  Use alpha = 0.05.

(c) Write down the contrast (the linear combination of means) about which you are testing 
in part (b).  Then make up another contrast that is orthogonal to the contrast from part 
(b).  What is an advantage of having orthogonal contrasts?


TRUE-FALSE QUESTIONS:

4.  Answer True/False Concept Questions 2,4,6,7,9,10,11,12(all parts),13,15 on pages 279-280.