SPLIT BLOCK (or STRIP PLOT) homework

This is an artifical example to illustate the idea of a split block, somtimes also 
called a strip plot.
We have two types of paint to paint things on roads, such as school crossing signs, 
turn arrows, or lane stripes.  We paint a stripe of each across roads, perpendicular 
to the traffic flow, at four locations (8 paint stripes in all). After some time 
passes, we measure Y as the wear (deterioration in reflectivity of the paint) in 
2 areas on each paint stripe.  Area 2 is the area in the middle of the lane where 
few wheels pass. Area 1 is the area that the left wheels pass over, as best we 
can determine it. You can see that area really represents exposure to tires. 
Locations are our blocks.  


(1) Explain why this is not just a randomized complete block design with 4 blocks.  

(2) Explain why it is not just a split plot with paint types as whole plot 
treatments and area (which is really tire exposure) as the split plot treatment.  

(3) Input the data and run PROC MEANS as follows: 

Data paint;
do location = 1 to 4; 
do paint = 1 to 2; 
do area = 1 to 2; 
  input Y @@; 
output; end; end; end; 
cards; 
20 13 30 28
31 22 38 26
24 18 38 21
28 14 42 27
 ; 
proc means noprint; 
var Y; 
class location paint area; 
output out=out1 mean = mnY; run; 
proc print; run;  

Now using SAS code or just cutting and pasting, show the means for the 4 levels of 
location, 2 levels of paint, 2 levels of area, and of the 8 (location, paint) and 
8 (location, area) combinations. Also show the overall mean. 

(4) Now from the means you just gave, make a two way location by paint table of 
means.  Compute (by hand please) the table sum of square with 7 df, the paint sum of 
squares, and the location sum of squares.  From these, compute also a location 
by paint interaction sum of squares, again by hand.  

(5) From (4) we should be able to construct an F test for paint.  Do so, and 
give its numerator and denominator degrees of freedom. 

(6) Now add to the program above a PROC GLM treating locations as random of 
course and running the proper analysis for the situation described here.  
Include the analysis of variance table, and the proper F tests for paint, 
area, and their interaction. 

Notes:  You should be able to reproduce everything in this ANOVA table by 
hand (not collected, but you might want to check yourself on this) and you 
might want to do a PROC MIXED run just to see how that would go.  You might 
try the method=type3 option if you do this.