Outliers and Such (In Science)

You may assume that when one tells tales taller than believable, it may be considered the product of an out-lier. This is perhaps so, but in the mysterious depths of science it usually means that one bit of information just doesn't fit. What to do?

When you run (do, conduct, etc.,) an experiment it's best to know on the front-end how you are going to handle the data. This avoids nasty surprises. Data that just wont conform to your ideas is a major problem.

My old lab partner from the Great State of California had an approach that isn't sanctioned by the powers that be, but is used more times than we wish to admit. His approach;

First - decide what the outcome of your experiments is going to be.
Second - select your experimental subjects carefully.
Third - the fewer measurements the better.
Fourth - never make an even number of measurements.
Fifth - three measurements is the ideal.
Sixth - Since two of the three will always be more in agreement with each other than the other, throw out the oddball.

See how easy it is.

Here's a set of data to test Larry's method. Granted the measurements constitute a time series so it was necessary to generate more than three points, but we assume that the investigator followed Larry's method and each point on the (to be generated graph) represents three determinations of which the scientist threw out the non-conformist and saved the other two.

In this case the ability to see as measured in diopters (the unit of refractive power of lenses, denoting the reciprocal of the focal length expressed in meters. Or in this case the accommodation of the eye to the intensity of light. One diopter being the level of light on a clear cloudless day (?))

It is obvious if one pays attention to the people about; that some are blind, some severely visually impaired, some wear glasses and some don't (regardless of age). Now how would friend Larry have handled this problem and the resulting data.
a) First, identify current thinking in the field so his paper would be published without much hassle.
b) Second, draw some conclusions.
c) Third, select ?proper? experimental subjects (patients or rats as the case might be).
d) Fourth, run the experiment, i.e., collect the data

e) Fifth, graph the data and extrapolate to the population in which he is interested. (Those 65 and older.) f) Sixth, write it up, submit and g) Seventh, graciously accept the praise and rewards. The data:

<>tr>

Age	Diopters	Diopters extrapolated	Larry's correction(d)
8	13.8	13.8	23.8
16	12.0	12.0	22.0
24	10.2	10.2	20.2
32	8.2	8.2	18.2
40	5.8	5.8	15.8
48	2.5	2.5	12.5
56	1.25	1.25	11.25
64	1.1	1.1	11.10
72	(a)	-2.151786(b)	7.8482
80	(a)	-4.153571(b)	5.8464
88	(a)	-6.155357(b)	3.8446

(a) no information available.
(b) Extrapolated values
(c) Stedman's Medical Dictionary is the source of the data.

(d) Since Larry couldn't figure out how to have negative vision, he added ten diopters to all the values. Plot the data with the "y" axis as diopters, and "x" axis as age of the individual.

The data looks simple enough until we plot it. (You?ll have to do it yourself since this program doesn't provide that capability.)

Now here's the puzzle. Note that the information comes close to fitting a straight line. But that's absurd. We know you can't have negative vision. So Larry examines the data a bit more closely for those individuals in the 40 to 64 age group. Something is going on here. It would appear that as one approaches 40, the wheels begin to fall off and sight declines much more rapid than had been projected using the earlier measurements.

But since we all don't go blind at the ripe old age of say 48, there must be accommodation(?).

What to believe? The better explanation is that these data represent averages. It's a bit like having your left hand in ice water and your right in boiling water, on average, feels pretty good (32 + 212)/2 = 122 (about right for a nice bath).

So Larry guessed right when he started; several populations, several different responses to shining bright light in peoples eyes (deer hunters have used this technique for years). And voila, he has a paper on declining vision as we age.

Now here comes the tricky part. By using "what if" in modeling, Larry can take each of the proposed (extrapolated) lines indicating age and vision decline, and make a case substantiated by his earlier data. Neat. And he doesn't even have to go looking for other subjects to test.

Three curves can be plotted and drawn when the data is extrapolated.
1) One plot shows a crash at an early date based on the data for the period from birth to 48 years of age. Extrapolate the curve and you go blind by the time you are 56.
2) The second plot shows that you will never go blind. Based on the 48 to 64 outcome, your vision will stabilize and even after you're in the grave your eyeballs will still be going strong.
3) the third plot is based on a straight line extrapolation of all the data. Bad news, blind as a bat, just like in the first extrapolation.

Only conclusion (2) above is justified. First on practical experience (you look around to see what the general public is doing). Then you select the data to support the conclusion. A bit tricky here since, actually for all the data you have collected, is all hinged on two points. Those of the age 56 and 64 group. But isn't that the two out of three strategy held by Larry? So let the presses roll.

Alas, there's another problem. Poor Larry. He discovers that the current population of mid-agers (those fifteen and older) were subjected to an experiment out of Larry's control. Seems that with the popularity of milk substitutes based on soybean protein, most in this age group were denied taurine in their diet in their early years. We now know that taurine deficiency can cause blindness or visual problems, so the practice stopped in mid 80's when taurine was added to milk replacers. (Of course, if they had nuzzled up to their mother's breast, all is well.)

What to do? Time for another experiment, and with luck another paper, or so.

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