And one day it finally happens. Renu gives us a dazzling smile and winks at us. The Romeos are
floored and stupefied. This can't be true. Did we imagine it? It was too far fetched that all
three of us to have imagined the same thing. Our hearts turn a summersault.
Eager for more, we pause expectantly by her house the next day, and lo, pat comes the smile and
the wink. We are now positively starry eyed, and almost dance our way to college.
Strangely, Deepak looks rather thoughtful. "Come on man.. let's celebrate! She did it again"
I try to cheer him into the general loony mood. "Really?" he retorts, "But there is a little
catch. Who did she wink at? You, me or Naren?" I wake up with a start. Now, this is serious.
I too wear his brooding cap. Naren looks up and joins the gloom." Certainly, she couldn't be
winking at all three of us?". We don't bother to reply.
The smile and the wink fail to cheer us the next day. "Let's ask her upfront" I put in my two
cents. They seem to agree, but the question of who will bell the cat still remains. We MUST find
out which one of us Renu fancies.
Thinking hard, slowly but surely a game plan evolves. We decide to find out through planned experimentation.
Instead of all three walking together, we decide to go past her house in a well-planned pattern
of twos and singles.
Quickly, we put our plan into action. We already know Renu's response to all three of us walking
together. We tabulate it as below:
The next day, I stay back. Deepak and Naren walk together past her house. Much to my dismay, the
smile and the wink greet them enthusiastically. We tabulate this result as:
It's now Naren's turn to stay back. Deepak and I dutifully get the smile and the wink. Prompt in
paperwork, we put down these results too.
The data is building up, and we are all set to jump to wishful conclusions. We tell Deepak that
she's just playing games, and keep him back at home. Naren and I take a confident walk, eager to
prove our theory of Renu playing games, but are in for a shock. Renu simply does not make an
appearance. Less sure about ourselves, we tabulate this result too.
Deepak gives a laugh that love struck morons usually give, and suggests that we now walk one
person at a time.
Naren and I dutifully do our role and encounter Renu's vanishing trick. Results are dutifully tabulated.
Deepak is on cloud nine by now. He puts on his best shirt, shines his shoes, and walks past
Renu's house, chin up. He actually does walk up and down a couple of times, but Renu still fails
to appear. Naren and I take sadistic pleasure in tabulating this result.
Deepak by now looks like a deflated balloon, and Naren and I are frankly perplexed.
"What's the meaning of this? Is she trying to twist us around her little finger?" Deepak is
rightly antagonized. "Look, rather than jumping to conclusions, lets run this combination of
experiments again. At the end of all the runs, we can analyze the data and form some hypothesis",
my statistics classes have started showing effects. They both agree to the suggestion.
"I am not going on a Friday" Naren gets a sudden urge to cling to superstitions. The order in
which the runs would be carried out is decided by rolling a pair of dice, and the matter is
settled. Over the next one week, we carry out the experiments again and the results are put
We are now ready for the judgment. We consolidate the results from both the sets of runs as
We decide to analyze the results by the change in Renu's response to the presence or absence of
each of the Casanovas. Results (I discovered later that they were called effect plots in the
DOE parlance) showed as follows.
Obviously, Deepak is the clear winner. Naren and I shake Deepak's hand, wish him good luck and
go on to chase the other damsels in the neighborhood.
Much later, when I studied statistics, and Design of Experiments, did I realize that we had
performed a Factorial Experiment as we pursued Renu.
There were three Factors in this experiment. Naren, Ravi and Deepak. A factor is an independent
variable in an experiment whose state can be varied. In a planned experiment, the factors are
deliberately varied, all at a time, in a planned manner. The response is measured at every run
of such combinations. In a scientific experiment, pressure and temperature of reaction could be
two of the factors. These are varied across the experimental pattern, and the response
characteristic (such as yield of the reaction) is measured.
Each factor was evaluated at two Levels. In this case, the person being Present or Absent. A
level is a state of the factor that is deliberately varied. Experimentation is typically done at
two, or occasionally three levels for every factor. The total combination of all factors and
their levels can become too large and daunting a task if every factor is changed one at a time.
An efficient experimental design that varies multiple factors at a time can reduce the number of
runs to a great extent, still giving you enough information to be confident of the results.
Levels can be discrete like the Present/ Absent levels that our experiment had, or can be
numeric, like 80 degrees/ 100 degrees centigrade for the temperature factor in a chemical reaction.
The objective variable that you measure is the Response. You try and establish two facts by
measuring the response.
- whether there is any relationship between the change in level of each of the factors and the change in response.
- what is the size of the change in response for a change in level for each factor (sensitivity).
In our experiment, the Response was attribute type. It was expressed as whether Renu winked or
not. We could gage the size of the response by counting a favorable response to each factor at
each level. Response can be variable type, like the change in purity from 90% to 95%. In such
cases the numerical value of the response is and averaged for each level. The difference in
response is called the effect, and is expressed using an effect plot shown above.
The experiment we conducted was Balanced, since each factor at each level was evaluated at an
equal number of other factor- level combinations. A balanced experiment gives the same evaluation
advantage to each factor, and helps in removal of bias that may creep in due to unequal amount
of data for each factor-level combination.
What we achieved by rolling dice to determine the sequence of runs was Randomization. Randomization
is very important, since it gives an equal chance to all external factors to affect every run of
the experiment. A non-randomized experiment stands a great risk of external factors acting in a
systematic manner and adding 'noise' to the response.
Running two sets of the experimental runs led to Replication. Two replications gave more data, and
helped in evaluating the results with a greater confidence. More replications can make you surer
about the effects, but also add cost to the experimentation process.
What then went wrong in run no 7 and run no 14? Why didn't Renu respond to Deepak's presence?
In the first case (run 7), it was a Lurking Variable that played a role. Renu happened to have a
father who was built like a Gorilla and had a very foul temper. On the day Deepak went alone in
the first Replication, the father had confined Renu to her room for some trivial reason.
A lurking variable like Renu's father is external to the experiment, but strikes suddenly and
randomly to affect the response, and confuse the results. Anyway, what could have been a more
appropriate description of Renu's father than a 'Lurking Variable''?
In the second case (run 14) it was Renu herself who was in a foul mood, and refused to perform
as expected. After all she was human, and couldn't be expected to fall in line with statistics
all the time. This is the Experimental Error that is so often encountered in experimentation.
DOE can get more detailed when you perform ANOVA for comparing within-treatment variation with
across treatment variation, but let's save that for another day.
I was lucky to learn structured Design of Experiments early in life!
Deepak married Renu, and went ahead to become a software professional. Deepak and Renu live in
Naren is a research scientist with a world-class pharmaceutical company in Philadelphia. Early
training in Experimental Design undoubtedly prepared him for a great scientific career.
Ravi is the Managing Director of Symphony Technologies Pvt. Ltd. Do give him your feedback on this
narration at firstname.lastname@example.org .
Symphony Technologies Pvt. Ltd.,
B-4, Saket, Vidnyan Nagar, Bawdhan,
Pune 411 021, INDIA
Published: July 2002
Ravindra Khare is a Founder and Director of Symphony Technologies.
He is a qualified Mechnical and Industrial Engineer and a keen student of
Quality & Productivity Technology for the past 18 years.
He can be contacted at e-mail address: email@example.com
or through us at firstname.lastname@example.org