Three concepts are fundamental to the design of experiments and surveys: variation, population, and sample. A thorough understanding of these concepts will prevent many errors in the collection and interpretation of data.
If there were no variation, if every observation were predictable, a mere repetition of what had gone before, there would be no need for statistics.
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% predetermined. 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, that one short, though all are the same age. Half an aspirin and Dr. Good’s headache is gone, but his wife requires 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 (the ...