is an excellent book by David Salsburg (isbn 0-8050-7143-2). As usual I'm going to quote from a few pages:
It was a summer afternoon in Cambridge, England, in the late 1920s. A group of university dons, their wives, and some guests were sitting around an outdoor table for afternoon tea. One of the women was insisting that tea tasted different depending upon whether the tea was poured into the milk or whether the milk was poured into the tea.
What I discovered working at Pfizer was that very little scientific research can be done alone.
It usually requires a combination of minds. This is because it is so easy to make mistakes.
Galton discovered a phenomenon he called "regression to the mean."
The numbers that identify the distribution are not the same type of "numbers" as the measurements.
These numbers can never be observed but can be inferred from the way in which the measurements scatter.
These numbers were later to be called parameters - from the Greek for "almost measurements."
Bliss invented a procedure he called "probate analysis." … The most important parameter his model generated is called the "50 percent lethal dose," usually referred to as the "LD-50." … The further you get from the 50 percent point, the more massive the experiment that is needed to get a good estimate.
If you are willing to settle for knowing the two parameters of a normal distribution within two significant figures, you need collect only about 50 measurements.
It is better to do mathematics on a chalkboard than on a piece of paper because chalk is easier to erase, and mathematical research is always filled with mistakes. Very few mathematicians work alone. If you are a mathematician, you need to talk about what you are doing. You need to expose your new ideas to the criticism of others.
In the deterministic approach, there is a fixed number, the gravitational constant, that describes how things fall to the Earth. In the statistical approach, our measurements of the gravitational constant will always differ from one another, and the scatter of their distribution is what we wish to establish in order to "understand" falling bodies.
No test can be powerful against all possible alternatives.
In the near disaster of American nuclear power plant at Three Mile Island power plant in Pennsylvania in the 1980s, the operators of the reactor had a large board of dials and indicators to follow the progress of the reactor. Among these were warning lights, some of which had been faulty and presented false alarms in the past. The prior beliefs of the operators were such that any new pattern of warning lights would be viewed as a false alarm. Even as the pattern of warning lights and associated dials produced a consistent picture of low water in the reactor, they continued to dismiss the evidence.
Kolmogorov called a sequence of numbers collected over time with successive values related to previous ones a "stochastic process."
is an excellent book by David Salsburg (isbn 0-8050-7143-2). As usual I'm going to quote from a few pages:
