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Proportions & Means Tests (fwd)
Posted:
Feb 2, 1997 3:02 PM


 Forwarded message from AlCoons@aol.com 
Since you do not need the standard dev of the population for inferential statistics when using proportions my students can do their own real world experiments without knowing the tdistribution.
Al
 End of forwarded message from AlCoons@aol.com 
Only if "inferential statistics" = "hypothesis tests". I think many people would like to put the primary emphasis on estimating a parameter (with an error estimate called a "confidence interval"). There are statistical reasons for doing this. There is also the fact that the logic of estimation is much more straightforward than the logic of hypothesis testing, and it is easier to teach from the simpler to the more complex.
Inference for proportions involves the binomial distribution, but using a binomial table for inference is MUCH harder than using a ttable. If n is large you can approximate the binomial with the normal distribution (though you can approximate the tdistribution even better!). To treat binary data this way you have to code it as 0s and 1s. Your sample will NEVER look normally distributed. Indeed, most textbooks do not even show the data for proportions, and tacitly push students toward the worst crime of all: not examining the data! In these ways the situation with proportions is ATYPICAL of other inference situations. For that reason, I hesitate to do it FIRST because then it becomes the paradigm. And what you do in practice is many more steps away from the theory that underlies what you are doing. If you explain any of this, there are a lot MORE things that need explaining. I think these more than offset not needing to learn to read the ttable. The traditional way around this is the old distinction between "large sample" and "small sample" inference. For "large" samples, the t and z values are indistinguishable, so you can use z even when sigma is unknown. The problem with that too is that it involves one more level of approximation, and obscures what is really going on mathematically: t is correct when sigma is estimated from the sample data, z when sigma is known, regardless of sample size. You are relying on this approximation when you use z for proportions; if you are willing to do that, why not use z for other means? (The tricks for proportions work only because the proportion is the mean of the 01 data, and hence the theory for means applies to proportions as a special case.)
On the other hand, these are just my opinions, and I am going out on a limb by disagreeing with someone who has made as large a contribution to this list as Al Coons has.
_   Robert W. Hayden   Department of Mathematics /  Plymouth State College MSC#29   Plymouth, New Hampshire 03264 USA  *  Rural Route 1, Box 10 /  Ashland, NH 032179702  ) (603) 9689914 (home) L_____/ hayden@oz.plymouth.edu fax (603) 5352943 (work)



