STAT 516 HW 4A


HAND CALCULATIONS:

1.  We will analyze the data in the following table.  The 
response variable is weight of a tomato plant in pounds, 
and Y values are given in the table for all combinations of 
the factor levels.  The factors are Fertilizer (labeled 
factor A) and Light Source (labeled factor C).  We have 3 types 
of fertilizer and 2 types of light source (lamp and sunlight).  
Each combination of factor levels had two plants assigned to it 
(i.e., there were two observations per cell).  The weights are 
as follows:

             C
        1(L)     2(S)
       ----    ------
   1    14       14
        10       13
       ----    ------
   2    13       17
A       13       13
       ----    ------
   3    16       18
        14       16
       ----    ------

Do the following by hand, SHOWING WORK.  You may check your answers 
with R if you want, but this is not necessary.

(a) Find the overall mean of the 12 plants (this is y-bar-dot-dot-dot).  
Also find the means for the six cells (these are the y-bar-i-j-dot values).

(b) Subtract the overall mean from each Y value.  Square each of 
the results, and add those squares up.  This is TSS.

(c) Subtract the corresponding cell mean from each Y value. Square 
each of the results, and add those squares up.  This is SSW.

(d) Find SS(Cells) by subtracting SSW from TSS.

(e) Find MSW and MS(Cells) by dividing by the appropriate degrees of 
freedom in this example.

(f) Find the F-ratio, and determine (at a 5% significance level) whether 
the population cell means are equal by comparing the F-ratio to the 
appropriate F value.

CONCEPT QUESTIONS

2.  Suppose we have a factorial experiment with two factors, A and C.  
Factor A has 5 levels and Factor C has 3 levels.  There are 6 observations 
for each combination of levels.  If TSS = 1128, SSA = 375, SSC = 462, and 
SSAC = 38, then:

(a) Write out the COMPLETE ANOVA table (like Table 9.4, page 456) for 
the experiment.  

(b) At a 5% significance level, is there a significant interaction between 
A and C?  Provide numerical evidence for your answer.

(c) At a 5% significance level, is there a significant difference in 
mean response across the levels of factor A?  Provide numerical evidence 
for your answer.

(d) At a 5% significance level, is there a significant difference in 
mean response across the levels of factor C?  Provide numerical evidence 
for your answer.