Question

Please answer the following stats questions.

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).

(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?)

data recognition;
input medium $ time value;
cards;
TV 5 49 
TV 5 39 
TV 10 50 
TV 10 55 
TV 15 43 
TV 15 38 
TV 20 53 
TV 20 48 
AUDIO 5 55 
AUDIO 5 41 
AUDIO 10 67 
AUDIO 10 58 
AUDIO 15 53 
AUDIO 20 85 
WRITE 5 66 
WRITE 5 68 
WRITE 10 85 
WRITE 10 92 
WRITE 15 69 
WRITE 15 62 
WRITE 20 85
;
run;

Answer 1

(a): These data considered to be unbalanced because the sample size of each category are unequal like TV sample size is 8, Audio is 6 and Write is 7.

(b): Type III SS is proper to examine this data because Type III SS gives better result for unbalanced data and unbalanced mean when sample size are unequal.