Test and Proof
The term proof descended from its Latin roots (provable, probable, probare L.) meaning to test. Hence, proof is a form of inference by means of a statistical test. Statistical tests are formulated on models that generate probability distributions. Examples of probability distributions might include the binary, normal, or poisson distribution that give exact descriptions of variables that behave according to natural laws of random chance. When a statistical test is applied to samples of a population, the test determines if the sample statistics are significantly different from the assumed null-model. True values of a population, which are unknowable in practice, are called parameters of the population. Researchers sample from populations, which provide estimates of the parameters, to calculate the mean or standard deviation. If the entire population is sampled, then the sample statistic mean and distribution will converge with the parametric distribution.
Using the scientific method of falsification, the probability value that the sample statistic is sufficiently different from the null-model than can be explained by chance alone is given prior to the test. Most statisticians set the prior probability value at 0.05 or 0.1, which means if the sample statistics diverge from the parametric model more than 5 (or 10) times out of 100, then the discrepancy is unlikely to be explained by chance alone and the null-hypothesis is rejected. Statistical models provide exact outcomes of the parametric and estimates of the sample statistics. Hence, the burden of proof rests in the sample statistics that provide estimates of a statistical model. Statistical models contain the mathematical proof of the parametric values and their probability distributions.
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Famous quotes containing the words test and/or proof:
“Whenever a true theory appears, it will be its own evidence. Its test is, that it will explain all phenomena.”
—Ralph Waldo Emerson (18031882)
“If we view our children as stupid, naughty, disturbed, or guilty of their misdeeds, they will learn to behold themselves as foolish, faulty, or shameful specimens of humanity. They will regard us as judges from whom they wish to hide, and they will interpret everything we say as further proof of their unworthiness. If we view them as innocent, or at least merely ignorant, they will gain understanding from their experiences, and they will continue to regard us as wise partners.”
—Polly Berrien Berends (20th century)