by The lady tasting tea The mathematical formulations of statistics can be used to compute probabilities. Those probabilities enable us to apply statistical methods to scientific problems. In terms of the mathematics used, probability is well defined. How does this abstract concept connect to reality? How is the scientist to interpret the probability statements of statistical analyses when trying to decide what is true and what is not? … Fisher’s use of a significance test produced a number Fisher called the p-value. This is a calculated probabiity, a probability associated with the observed data under the assumption that the null hypothesis is true. For instance, suppose we wish to test a new drug for the prevention of a recurrence of breast cancer in patients who have had mastectomies, comparing it to a placebo. The null hypothesis, the straw man, is that the drug is no better than the placebo … Since [the p-value] is used to show that the hypothesis under which it is calculated is false, what does it really mean? It is a theoretical probability associated with the observations under conditions that are most likely false. It has nothing to do with reality. It is an indirect measurement of plausibility. It is not the probability that we would be wrong to say that the drug works. It is not the probability of any kind of error.
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Lars Pålsson Syll considers the following as important: Statistics & Econometrics
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The lady tasting tea
The mathematical formulations of statistics can be used to compute probabilities. Those probabilities enable us to apply statistical methods to scientific problems. In terms of the mathematics used, probability is well defined. How does this abstract concept connect to reality? How is the scientist to interpret the probability statements of statistical analyses when trying to decide what is true and what is not? …
Fisher’s use of a significance test produced a number Fisher called the p-value. This is a calculated probabiity, a probability associated with the observed data under the assumption that the null hypothesis is true. For instance, suppose we wish to test a new drug for the prevention of a recurrence of breast cancer in patients who have had mastectomies, comparing it to a placebo. The null hypothesis, the straw man, is that the drug is no better than the placebo …
Since [the p-value] is used to show that the hypothesis under which it is calculated is false, what does it really mean? It is a theoretical probability associated with the observations under conditions that are most likely false. It has nothing to do with reality. It is an indirect measurement of plausibility. It is not the probability that we would be wrong to say that the drug works. It is not the probability of any kind of error. It is not the probability that a patient will do as well on the placebo as on the drug.