Re: Student's t vs. z tests
I can't help but be reminded of learning to ride a bicycle. 99.% of people ride one with two wheels (natch!) - but many children do start to learn with training wheels.. Alan dennis roberts wrote: > > the fundamental issue here is ... is it reasonably to expect ... that when > you are making some inference about a population mean ... that you will > KNOW the variance in the population? > > i suspect that the answer is no ... in all but the most convoluted cases > ... or, to say it another way ... in 99.99% (or more) of the cases where we > talk about making an inference about the mean in a population ... we have > no more info about the variance than we do the mean ... ie, X bar is the > best we can do as an estimate of mu ... and, S^2 is the best we can do as > an estimate of sigma squared ... > > this is why i personally don't like to start with the case where you assume > that you know sigma ... as a "simplification" ... since it is totally > unrealistic > > start with the realistic case ... even if it takes a bit more "doing" to > explain it > > = > Instructions for joining and leaving this list and remarks about > the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ > = -- Alan McLean ([EMAIL PROTECTED]) Department of Econometrics and Business Statistics Monash University, Caulfield Campus, Melbourne Tel: +61 03 9903 2102Fax: +61 03 9903 2007 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Student's t vs. z tests
dennis roberts wrote: > > the fundamental issue here is ... is it reasonably to expect ... that when > you are making some inference about a population mean ... that you will > KNOW the variance in the population? No, Dennis, of course it isn't - at least in the social sciences and usually elsewhere as well. That's why I don't recommend teaching this (recall my comments about "dangerous scaffolding") to the average life-sciences student who needs to know how to use the test and what it _means_, but not the theory behind it. In the case of the student with some mathematical background, who may actually need to do something theoretical with the distribution one day (and may actually have the ability to do so) I would introduce t by way of Z. A rough guide; If this group of students know what a maximum-likelihood estimator is, and have been or will be expected to derive, from first principles, a hypothesis test or confidence interval for (say) a singleton sample from an exponential distribution, then they ought to be introduced by way of Z. If not, then: (a) don't do it at all, or (b) put your chalk down and talk your way through it as an Interesting Historical Anecdote without giving them anything to write down. Draw a few pictures if you must. Or (c) give them a handout with "DO NOT USE THIS TECHNIQUE!" written on it in big letters. (I've tried all four approaches, as well as the wrong one.) -Robert Dawson = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Student's t vs. z tests
the fundamental issue here is ... is it reasonably to expect ... that when you are making some inference about a population mean ... that you will KNOW the variance in the population? i suspect that the answer is no ... in all but the most convoluted cases ... or, to say it another way ... in 99.99% (or more) of the cases where we talk about making an inference about the mean in a population ... we have no more info about the variance than we do the mean ... ie, X bar is the best we can do as an estimate of mu ... and, S^2 is the best we can do as an estimate of sigma squared ... this is why i personally don't like to start with the case where you assume that you know sigma ... as a "simplification" ... since it is totally unrealistic start with the realistic case ... even if it takes a bit more "doing" to explain it = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Student's t vs. z tests
Jon Cryer wrote: > > These examples come the closest I have seen to having a known variance. > However, often measuring instruments, such as micrometers, quote their > accuracy as a percentage of the size of the measurement. Thus, if you > don't know the mean you also don't know the variance. You do if you log-transform... -Robert Dawson = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Student's t vs. z tests
At 1:18 PM -0500 23/4/01, Jon Cryer wrote: >These examples come the closest I have seen to having a known variance. >However, often measuring instruments, such as micrometers, quote their >accuracy as a percentage of the size of the measurement. Thus, if you >don't know the mean you also don't know the variance. Certainly many measurements do have errors that are best given as a percent of the reading. In such cases, the error usually is a "constant" percent, not a constant absolute amount. To put it another way, the log of the readings has a normally distributed error that is independent of the reading. So you should perform all your analyses on the log-transformed variable, and express all your outcomes as percent differences or changes. Otherwise your analyses are riddled with non-uniform error (heteroscedasticity). Will = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Student's t vs. z tests
These examples come the closest I have seen to having a known variance. However, often measuring instruments, such as micrometers, quote their accuracy as a percentage of the size of the measurement. Thus, if you don't know the mean you also don't know the variance. Jon Cryer At 09:28 AM 4/23/01 -0400, you wrote: >> Date: Fri, 20 Apr 2001 13:02:57 -0500 >> From: Jon Cryer <[EMAIL PROTECTED]> >> >> Could you please give us an example of such a situation? >> >> ">Consider first a set of measurements taken with >> >a measuring instrument whose sampling errors have a known standard >> >deviation (and approximately normal distribution)." > >Sure. Suppose we use an instrument such as a micrometer, electronic >balance or ohmmeter to measure a series of similar items. (For >concreteness, suppose they are components coming off a mass production >machine such as a screw machine.) As long as the measuring instrument >isn't broken, we don't have to conduct an extensive series of repeated >measurements every time we use it to determine its error variance with a >part of the given conformation. Normality is also reasonably likely under >those circumstances. > >Slightly more sophisticated version of the same: Supposed the operating >characteristics of such a machine can be characterized by slow drift (due >to tool wear, heat expansion of machine parts, settings that gradually >shift, etc.) plus independent random noise that is approximately normal. >It is plausible in that setting that the variance of measurements on a >short series of parts would be fairly constant. (I'm not just making >this up; it's consistent with my own experience in my former career as a >machinist.) Again, you don't have to calibrate the error variance of the >"measurement" (in this case, average measurement of several successive >parts to estimate the current system mean) every time you do it. > > = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: ANCOVA vs. sequential regression
It's also called a test of homogeneity of regression slopes, but it is really just a an interaction. There is also a test of parallelism in profile analysis which tends to confuse the issue. I sometimes wonder if it is worth it to try and give all these tests names. An interaction is always a test of parallel lines whether it is factoral anova, ancova, regression, or profile analysis. At 01:40 AM 4/22/01 GMT, you wrote: >Paul Swank <[EMAIL PROTECTED]> wrote: >: I agree. ... > >It's usually called a test of parallelism. The Ancova test is a test of >separation only if the lines are parallel > > >= >Instructions for joining and leaving this list and remarks about >the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ >= > Paul R. Swank, PhD. Professor & Advanced Quantitative Methodologist UT-Houston School of Nursing Center for Nursing Research Phone (713)500-2031 Fax (713) 500-2033 soon to be moving to the Department of Pediatrics UT Houston School of Medicine = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Student's t vs. z tests
> Date: Fri, 20 Apr 2001 13:02:57 -0500 > From: Jon Cryer <[EMAIL PROTECTED]> > > Could you please give us an example of such a situation? > > ">Consider first a set of measurements taken with > >a measuring instrument whose sampling errors have a known standard > >deviation (and approximately normal distribution)." Sure. Suppose we use an instrument such as a micrometer, electronic balance or ohmmeter to measure a series of similar items. (For concreteness, suppose they are components coming off a mass production machine such as a screw machine.) As long as the measuring instrument isn't broken, we don't have to conduct an extensive series of repeated measurements every time we use it to determine its error variance with a part of the given conformation. Normality is also reasonably likely under those circumstances. Slightly more sophisticated version of the same: Supposed the operating characteristics of such a machine can be characterized by slow drift (due to tool wear, heat expansion of machine parts, settings that gradually shift, etc.) plus independent random noise that is approximately normal. It is plausible in that setting that the variance of measurements on a short series of parts would be fairly constant. (I'm not just making this up; it's consistent with my own experience in my former career as a machinist.) Again, you don't have to calibrate the error variance of the "measurement" (in this case, average measurement of several successive parts to estimate the current system mean) every time you do it. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
