Tom,
You are absolutely wrong! Statistics are never ever wrong. Statistics are the perfect predictors. The problem is that what people call statistics are not statistics. What people call statistics are just people making up conclusions and saying that they are statistics. These people making up the statistics, your professor included, are just using the word statistics. They do not even know what a statistic is.
When you say that the smaller the data set the less reliable the results, you are wrong again. The mean (one type of statistic) of a data set is always reliable, even with only 1 element. As a matter of fact we could define the mean of the null data set as null and we would not need any data to have a "reliable" mean. Now if we tried to draw a conclusion about the mean of the whole population from a small sample, we could not be very confident of the population mean accuracy.
The problem that we are having is not with statistics. The problem is that people are making predictions and calling them statistics. This is not how conclusions should be drawn from the numbers (statistics). To draw any conclusions from statistics, a statistical hypotheses and its' alternative need to be presented. The statistics are then used to show via a p.d.f. (probability density function), within a specific degree of confidence, whether we can conclude that the hypothesis is true and if it is not then the alternate hypothesis is true.
When someone says that the statistics say something, ask them, what exactly is the hypothesis, the alternative, the p.d.f. and what is the degree of confidence. If they can not answer these questions, they are not using statistics. They are just using the word statistics to make you think that they are using statistics.
Along with the word statistics these same non statisticians like to use "Proof by Intimidation". Proof by Intimidation consists of laughing at you, calling you stupid and ignorant and sometimes belittling your whole family. Anecdotes may be brought up at this time to help confirm the proof. You will not find this type of proof in any math book but it is the most commonly used of all of the proofs.
I wanted to give an actual example but figured that it would take a couple of hours. It is so much easier to just bypass the math when making statements.
Sorry for the long diatribe, but it is the most accurate statistical discussion that has been posted yet.
Does anyone know yet what a statistic is?
Many years ago a professor told me, "There are three kinds of liars. There are liars, damn liars, and statisticians." Hopefully everyone will get a good grin out of that and not take offense as it was certainly not aimed at anyone on the list. (It is a true anecdote.) The point is one must be careful when using statistics. Statistics can be meaningful when dealing with large data sets. When attempting to evaluate data and derive trends the smaller the data set the less reliable the results. When you take a statistical trend, derived from a large group, and attempt to apply it to an individual it might or might not be accurate for that individual. Caveat emptor. One other parting thought: Logic is a method of reasoning whereby one can reach an incorrect conclusion, but with confidence. (I may have said that before. Sometimes I suffer from CRS; Can't Remember.....Stuff.)
Tom Gourley
-- Lorn H. 'Feathers' Olsen, MAA, DynaComm, Corp. LNC2, O-320-D1F, 1,200 hrs, N31161, Y47, SE Michigan
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