As the dimension of the space increases, it becomes less and less possible to get good estimate of parameters. Once the analyst is out of ten- to twenty-dimensional space, it is not possible to detect anything with less than hundreds of thousands of observations. ------ Richard Bellman The true "dimensionality" of data is often no more than five. Technique: Projection Pursuit
Fisher was dealing with a deep philosophical problem-a problem that the English philosopher Bertrand Russell had addressed in the early 1930s, a problem that gnaws at the heart of scientific thought, a problem that most people do not even recognize as a problem: What is meant by "cause and effect"?Answers to that question are far from simple. Bertrand Russell showed effectively in the early 193...
Distribution-free tests: The development of nonparametric procedures Wilcoxon, Mann&Whitney, Andrei Kolmogorov&N.V.Smirnov, Herman Chernoff and I.Richard Savage Wilcoxon looked at the formulas for calculating t-tests and analysis of variance and realized that these outliers, these extreme and unusual values, greatly influenced the results, causing "Student's t-test to be smaller than it would b...
"Finding the probability of an event was exactly like finding the area of an irregular shape." ——Kolmogorov（1903-1987） Axiomization of Probability Theory, assume there is an abstract space of elementary things called events; unless we can identify Kolmogorov's abstract space, the probability statements that emerge from statistical analyses will have many different and sometimes contrary mea...
"John Maynard Keynes has pointed out that all probability are conditional. eg. the p-value that is calculated to test the null hypothesis of no treatment effect from a controlled experiment is conditional on the design of the experiment. The important aspect of conditional probability is that the probability of some given event is different for different prior conditions. It makes sense to tal...
Confidence Interval - Jersy Neyman(1894-1981) If we cannot say that the estimate is exactly correct, is there some way we can say how close the estimate is to the true value of the parameter? The answer to that question lies in the use of interval estimates. A point estimate is a single number. For instance, we might use the data from hemophiliac studies to estimate that the mean latency tim...
How he could be sure that a set of data was normally distributed if he failed to find a significant p-value when testing for normality? Whta does it mean to have a nonsignificant result in a significant test? Can we conclude that a hypothesis is true if we have failed to refute it? Fisher had addressed that question in an indirect way. Fisher would take large p-values to indicating that the d...
Recall Karl Pearson's chi square goodness of fit test. He developed it to test whether observed data fit a theoretical distribution. There really is no such thing as the chi square goodness of fit test. The analyst has available an infinite number of ways to apply the test to a given set of data. There appeared to be no criterion on how "best" to pick among those many choices. Every time t...
Hypothesis, or significance, testing is a formal statistical procedure that calculates the probability of what we have observed, assuming that the hypothesis to be tested is true. When the observed probability is very low, we conclude that the hypothesis is not true. One important point is that hypothesis testing provides a tool for rejecting a hypothesis. In the case above, this is the hypot...
Before the statistical revolution, the "things" with which science dealt were either the measurements made or the physical events that generated those measurements. With the statistical revolution, the things of science became the parameters that governed the distribution of the measurements. In the earlier deterministic approach, there was always the belief that more refined measurements woul...
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