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Politics : Sharks in the Septic Tank -- Ignore unavailable to you. Want to Upgrade?

To: epicure who wrote (74822)	9/15/2003 12:23:01 PM
From: epicure	Respond to of 82486

This seemed like the best summation I've seen so far. Expresses how people in the sciences really use the terms. : I will attempt to explain these definitions, though sometimes this is better done in conversation (I am willing to talk this through with anyone who phones). In science, a theory is a broad explanation of how a system works. The hypothesis is the outcome I expect on a specific phenomenon. Example: Galileo and Gravity Theory: Gravity imparts the same acceleration on all objects regardless of weight Hypothesis: If I drop a light object and a heavy object from the top of the Tower of Pisa, both will hit the ground at the same time. Now I run the experiment suggested by the hypothesis. Note that if I drop a stone and a feather, they will fall at different rates, due to air resistance on the feather. I may need to adjust my theory and hypothesis to account for air resistance, or I could go to the moon (where there is a vacuum) and perform the experiment (one of the Apollo missions really did this). Note that Galileo's assumption was that air resistance = 0. If you choose your objects carefully (both relatively dense and the same shape), I can run the experiment on earth and get the "right" answer. In statistics, the usual hypotheses are that two data sets are either the same or different. The "null" hypothesis is that the two data sets are the same (the difference between the means is zero for example). Statisticians usually use the null hypothesis due to the Type I and Type II errors. I can usually calculate the alpha error for the false alarm rate of declaring the two data sets are different, when they actually are the same. However, to calculate the beta error (failing to detect a difference when one exists) is much more difficult. This is because there are many possibilities for "how different" the data sets are. I usually have to talk about "given the two data sets differ by X, the probability I will declare them to be the same is P(X)." This can be shown on an "operating characteristic" curve for any statistical test, plotting X vs. P(X). Note for a given construction of a test, attempts to reduce the beta error will force an increase in the alpha error and vice versa. Adjusting your household smoke detector to alarm at a more sensitive level will decrease the beta error (reducing the probability that a real fire will occur, but the detector will not alarm), but increasing the alpha error (increasing the false alarm rate). The "null" hypothesis is that your house is not burning down. Dr. Deming was strongly against tests of hypotheses, because you lump the two data sets into two numbers which are then compared against some "significance level". The time distribution of the data series are lost. Rather than asking "is the CY 1997 value of this performance indicator significantly higher than the CY 1996 value at an alpha error of 10% [note the null hypothesis is that CY 1997 = CY 1996]", make a control chart. This maintains the time series, and perhaps CY 1996 and CY 1997 are the same, but the last quarter of CY 1997 was different. Does this help? - Steve Prevette 509-373-9371 steven_s_prevette@rl.gov deming.eng.clemson.edu