Information Technology Reference
In-Depth Information
Variation
Variation is inherent in virtually all our observations. We would not expect
outcomes of two consecutive spins of a roulette wheel to be identical. One
result might be red, the other black. The outcome varies from spin to
spin.
There are gamblers who watch and record the spins of a single roulette
wheel hour after hour hoping to discern a pattern. A roulette wheel is,
after all, a mechanical device and perhaps a pattern will emerge. But even
those observers do not anticipate finding a pattern that is 100% determin-
istic. The outcomes are just too variable.
Anyone who spends time in a schoolroom, as a parent or as a child, can
see the vast differences among individuals. This one is tall, today, that one
short. Half an aspirin and Dr. Good's headache is gone, but his wife re-
quires four times that dosage.
There is variability even among observations on deterministic formula-
satisfying phenomena such as the position of a planet in space or the
volume of gas at a given temperature and pressure. Position and volume
satisfy Kepler's Laws and Boyle's Law, respectively, but the observations
we collect will depend upon the measuring instrument (which may be
affected by the surrounding environment) and the observer. Cut a length
of string and measure it three times. Do you record the same length each
time?
In designing an experiment or survey, we must always consider the
possibility of errors arising from the measuring instrument and from the
observer. It is one of the wonders of science that Kepler was able to for-
mulate his laws at all, given the relatively crude instruments at his disposal.
Population
The population(s) of interest must be clearly defined before we begin to
gather data.
From time to time, someone will ask us how to generate confidence inter-
vals (see Chapter 7) for the statistics arising from a total census of a popu-
lation. Our answer is no, we cannot help. Population statistics (mean,
median, 30th percentile) are not estimates. They are fixed values and will
be known with 100% accuracy if two criteria are fulfilled:
1. Every member of the population is observed.
2. All the observations are recorded correctly.
Confidence intervals would be appropriate if the first criterion is vio-
lated, because then we are looking at a sample, not a population. And if
the second criterion is violated, then we might want to talk about the con-
fidence we have in our measurements.
