Design of Experiments and Statistical Process Control - Fundamentals of Industrial Chemistry: Pharmaceuticals, Polymers, and Business - page 227

of the paper correlates with the length of the flight but it does not cause it.
What is more likely is that some other variable caused the differences. Per-
haps the airflow in the two classrooms and outdoors had an effect. A likely
explanation is that I was simply getting better at making and flying paper air-
planes. Because I tested the red ones last, those are the ones that gave the best
results. This was a simple illustration of correlation versus causation. Another
example is the rooster. Each day the rooster crows and shortly thereafter the
sun rises. The crowing of the rooster correlates with the dawn but no one,
except perhaps the rooster, thinks that it is the crowing that causes the sun
to rise.
These examples seem obvious and silly but mistakes like this happen all
the time. They are just not so obvious. Imagine a scientist wishing to know
the effect of a certain variable such as temperature, agitation, solvent, or time
on reaction yield. Typically they will hold all other recognized variables as
close to constant as they can and try different levels of one variable such as
agitation to measure the effect. If the yield at low, medium, and high agitation
is 45%, 52%, and 57% respectively, they may conclude that increased agita-
tion improves yield. Just as we did with the paper airplanes, they back up the
conclusion with graphs and statistics. However, this may be a similar situation
to the paper airplanes; they are just becoming more proficient at performing
the reaction and agitation does not have an effect on yield. Perhaps the effect
is caused by some other unrecognized hidden variable such as humidity level
in the laboratory when the reaction was performed and has nothing to do with
agitation. With this approach, the scientist may never recognize this.
In another example, if the yield at low, medium, and high agitation is 45%,
47%, and 44% respectively, one may conclude that the amount of agitation
is not important. This may be correct for the temperature, solvent and time
that was used. But we can imagine that perhaps agitation is important with a
different solvent system. This effect may never be recognized when changing
variables one at a time.
Consider the contour chart of yield with temperature on the y axis and time
on the x axis (Figure 13.5). The yield varies from less than 10% to about 50%.
If we were to run experiments at a fixed time of two hours and vary the tem-
perature from 10 ∘ to 50 ∘ in 10 ∘ increments, our results might be (Figure 13.6):
And we would conclude that a temperature of about 20 ∘ C and a yield of
about 22% is optimal. However, in this example, temperature and time are
interacting variables. Notice that with this approach, we would never find the
optimal yield of about 50% which can be achieved at a temperature near 35 ∘ C
and a time of about 4 hours.
Interacting variables is just one problem that can cause someone to draw
the wrong conclusion. Another is random variation. Imagine that a reaction