Supplementary Exercise 3.95 of IPS7e
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A study on processing of potatoes into french fries. It is of interest to 
examine whether the storage and cooking affect flavour and taste.

(a) 
The components of the experimental design are as follows:

experimental unit: batch of french fries processed in the same way
presented to the taster

response variables: ratings for colour and flavour of the fries

factors: storage (none/fresh, 1 month at room temp, 1 month refrigerated)
         cooking delay (none/immediately after slicing, 1 hour)

treatments: each of the six combinations of storage and cooking delay

The role of the tasters is discussed under (c).

(b)
As described above, the experiment is a completely randomized design
with 6 treatments from factorial combinations of two factors. We could
say it is a two-factor completely randomized design.

Randomization would consist simply in randomly assigning batches of potatoes 
(corresponding to the servings of french fries presented to the tasters)
to the six treatments. A totally random allocation would be easiest if the
total number of potatoes was known or decided in advance. If the number
of potatoes is not known, a possible alternative to a totally random
sampling (of potatoes) is a systematic random sampling (slide 2L-12, 
Exercise 3.66 of IPS7e; 3.64 of IPS6e, 3.47 of IPS5e), whereby the first 
six potatoes are randomly assigned to the 6 treatments and this pattern is 
repeated until all potatoes have been assigned.

(c)
So far the experimental design has not included any mention of the
tasting and the visual scores assigned by tasters (a taster is a person
specifically trained to detect difference in taste between different
products of the same type). Multiple tasters will be needed to ensure
adequate replication and to broaden scope of the study (if the scores
were only given by one person, the results may not be representative
for anything but this person's preferences). Each taster may be presented
with a batch of fries for each of the 6 treatments only once or multiple
times. As the scores by the same taster can be expected to be more similar
than scores from the different tasters, the tasters can be viewed as
a blocking factor. Thus, the design becomes a completely randomized two-factor 
block design.

In addition to the randomization of the potatoes, we also need to
randomize the order in which each taster is presented with the different
batches of fries. We can label the treatments 1-6 and use a random 
rearrangement of the numbers 1-6 to decide the order. For example, using
Minitab we could get the following order (for one taster; the orders should
not be the same for all tasters):

MTB > Set c1
DATA>   1( 1 : 6 / 1 )1
DATA>   End.
MTB > Sample 6 C1 c2.
MTB > Print C1 C2.
Data Display 

Row  C1  C2
  1   1   4
  2   2   2
  3   3   5
  4   4   1
  5   5   6
  6   6   3

So this taster would be presented with treatment 4 first, then treatment
2, and so on.