Re: Artifacts in stats: (Was Student's t vs. z tests)
"Robert J. MacG. Dawson" wrote: > > > Alan McLean wrote: > The p value is a direct measure of 'strength of evidence'. > > and Lise DeShea responded: > > > > I disagree. The p-value may be small when a > > study has enormous power yet a small effect size. > A p-value by itself doesn't say much. > > I don't think there's actually a contradiction > here, provided that "strenth of evidence" [against the > null hypothesis] is not misunderstood to mean > "strength of evidence for the conclusion you are > trying to draw", this latter rarely being the literal > denial of the null hypothesis. > > -Robert Dawson There is certainly no contradiction. A small p value indicates that the effect (whatever its size!) is (probably) valid. (Use the word 'genuine' if you prefer.) The effect may be too small to be of much use, but that is a very different question. Alan -- 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: Artifacts in stats: (Was Student's t vs. z tests)
> Alan McLean wrote: The p value is a direct measure of 'strength of evidence'. and Lise DeShea responded: > > I disagree. The p-value may be small when a > study has enormous power yet a small effect size. A p-value by itself doesn't say much. I don't think there's actually a contradiction here, provided that "strenth of evidence" [against the null hypothesis] is not misunderstood to mean "strength of evidence for the conclusion you are trying to draw", this latter rarely being the literal denial of the null hypothesis. -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: Artifacts in stats: (Was Student's t vs. z tests)
Alan McLean wrote: > ... In general, I emphasise the use of p values - in > many ways it is a more natural way than using critical values to carry > out a test. The p value is a direct measure of 'strength of evidence'. I disagree. The p-value may be small when a study has enormous power yet a small effect size. A p-value by itself doesn't say much. Lise DeShea, Ph.D. Educational and Counseling Psychology University of Kentucky [EMAIL PROTECTED] = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Artifacts in stats: (Was Student's t vs. z tests)
I agree - although students do need tables in (written) exams... But we use a computer program called Tuteman in our teaching and testing, so the natural way to find critical values or p-values is via the computer - we use Excel mainly. In general, I emphasise the use of p values - in many ways it is a more natural way than using critical values to carry out a test. The p value is a direct measure of 'strength of evidence'. Alan "Paul W. Jeffries" wrote: > > Robert Dawson said that one of his approaches to dealing with z test is to > treat it as a historical anecdote. I like that approach and must give it > a try. > > But this approach made me think about artifacts in statistics. What are > list members views on teaching students to use tables. In the computer > age, tables are an anachronism. The vast majority of students will never > use a t table. They will just rely on the computer to print the p value. > And those rare students that might want to check something on a table will > probably be the ones who know enough stats so that they can quickly figure > out how to read a table. Does fussing with tables get in the way of > students' understanding hypothesis testing or do tables help? > > I am interested to hear the views of list members. > > Paul W. Jeffries > Department of Psychology > SUNY--Stony Brook > Stony Brook NY 11794-2500 > > = > 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/ =
Artifacts in stats: (Was Student's t vs. z tests)
Robert Dawson said that one of his approaches to dealing with z test is to treat it as a historical anecdote. I like that approach and must give it a try. But this approach made me think about artifacts in statistics. What are list members views on teaching students to use tables. In the computer age, tables are an anachronism. The vast majority of students will never use a t table. They will just rely on the computer to print the p value. And those rare students that might want to check something on a table will probably be the ones who know enough stats so that they can quickly figure out how to read a table. Does fussing with tables get in the way of students' understanding hypothesis testing or do tables help? I am interested to hear the views of list members. Paul W. Jeffries Department of Psychology SUNY--Stony Brook Stony Brook NY 11794-2500 = 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
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: 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/ =
Re: Student's t vs. z tests
Alan: I don't understand your comments about the estimation of a proportion. It sounds to me as if you are using the estimated standard error. (Surely you are not assuming a known standard error.) You are presumably, also using the normal approximation to the binomial (or perhaps the hypergeometric.) To do so requires a "large" sample size in which case it doesn't matter whether you use the normal or t distribution. Both would be acceptable approximations. (and both would be approximations.) So what is your point? Once more I think you need to separate the issues of what statistic to use and what distribution to use. Jon At 01:10 PM 4/20/01 -0400, you wrote: >(This note is largely in support of points made by Rich Ulrich and >Paul Swank.) > snip > >Now consider estimation of a proportion. Using the information that the >data consist only of 0's and 1's, and an approximate value of the >proportion, we can calculate an approximate standard error more >accurately (for p near 1/2) than we could without this information. The >interval based on the usual variance formula p(1-p) and the z >distribution is therefore better than the one based on the t >distribution. This is why (as Paul pointed out) everybody uses z >tests in comparing proportions, not t tests. The same applies to >generalizations of tests of proportions as in logistic regression. > >snip > > Alan Zaslavsky > Harvard Med School > > > >= >Instructions for joining and leaving this list and remarks about >the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ >= > > = 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
Alan: 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)." Jon At 01:10 PM 4/20/01 -0400, you wrote: >(This note is largely in support of points made by Rich Ulrich and >Paul Swank.) > >I disagree with the claim (expressed in several recent postings) that >z-tests are in general superseded by t-tests. The t-test (in simple >one-sample problems) is developed under the assumption that independent >observations are drawn from a normal distribution (and hence the mean and >sample SD are independent and have specific distributional forms). >It is widely applicable because it is fairly robust against violations >of this assumptions. > >However, there are also situations in which the t-test is clearly >inferior to a z-test. Consider first a set of measurements taken with >a measuring instrument whose sampling errors have a known standard >deviation (and approximately normal distribution). In this case, with >a few observations (let's say 1 or 2, if you want to make it very clear), >the z-based procedure that uses the known SD will give much more useful >tests or intervals than a t-based procedure (which estimates the SD from >the data at hand). > >snip> > Alan Zaslavsky > Harvard Med School > > > >= >Instructions for joining and leaving this list and remarks about >the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ >= > > = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Student's t vs. z tests
(This note is largely in support of points made by Rich Ulrich and Paul Swank.) I disagree with the claim (expressed in several recent postings) that z-tests are in general superseded by t-tests. The t-test (in simple one-sample problems) is developed under the assumption that independent observations are drawn from a normal distribution (and hence the mean and sample SD are independent and have specific distributional forms). It is widely applicable because it is fairly robust against violations of this assumptions. However, there are also situations in which the t-test is clearly inferior to a z-test. Consider first a set of measurements taken with a measuring instrument whose sampling errors have a known standard deviation (and approximately normal distribution). In this case, with a few observations (let's say 1 or 2, if you want to make it very clear), the z-based procedure that uses the known SD will give much more useful tests or intervals than a t-based procedure (which estimates the SD from the data at hand). Now consider estimation of a proportion. Using the information that the data consist only of 0's and 1's, and an approximate value of the proportion, we can calculate an approximate standard error more accurately (for p near 1/2) than we could without this information. The interval based on the usual variance formula p(1-p) and the z distribution is therefore better than the one based on the t distribution. This is why (as Paul pointed out) everybody uses z tests in comparing proportions, not t tests. The same applies to generalizations of tests of proportions as in logistic regression. On the pedagogical issue, if you want to motivate the z-test all you need is the formula for the variance of the mean and the fact (accepted without proof in an elementary course) that a mean of normals is normal. To get to the t-distribution you need all of this and also have to talk about the sampling distribution of the SE estimate in the denominator and how they combine to give yet another distribution which is free of the mean and the nuisance parameter (a fact that depends on subtle properties of the normal). One could take the cynical view that most intro students will get neither of these, but short of that, the Z seems easier to motivate. When I taught out of Moore and McCabe, I usually tried to give some motivation along these lines for the Z test/interval, and then when I got to the t I waved my hands and said "when we estimate the variance instead of knowing it in advance, the intervals have to be spread out a bit more as shown in this table". Alan Zaslavsky Harvard Med School = 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
I agree. I normally start inference by using the binomial and then then the normal approximation to the binomial for large n. It might be best to begin all graduate students with nonparametric statistics followed by linear models. Then we could get them to where they can do something interesting without taking four courses. At 01:28 PM 4/19/01 -0500, you wrote: >Why not introduce hypothesis testing in a binomial setting where there are >no nuisance parameters and p-values, power, alpha, beta,... may be obtained >easily and exactly from the Binomial distribution? > >Jon Cryer > >At 01:48 AM 4/20/01 -0400, you wrote: >>At 11:47 AM 4/19/01 -0500, Christopher J. Mecklin wrote: >>>As a reply to Dennis' comments: >>> >>>If we deleted the z-test and went right to t-test, I believe that >>>students' understanding of p-value would be even worse... >> >> >>i don't follow the logic here ... are you saying that instead of their >>understanding being "bad" it will be worse? if so, not sure that this >>is a decrement other than trivial >> >>what makes using a normal model ... and say zs of +/- 1.96 ... any "more >>meaningful" to understand p values ... ? is it that they only learn ONE >>critical value? and that is simpler to keep neatly arranged in their mind? >> >>as i see it, until we talk to students about the normal distribution ... >>being some probability distribution where, you can find subpart areas at >>various baseline values and out (or inbetween) ... there is nothing >>inherently sensible about a normal distribution either ... and certainly i >>don't see anything that makes this discussion based on a normal >>distribution more inherently understandable than using a probability >>distribution based on t ... you still have to look for subpart areas ... >>beyond some baseline values ... or between baseline values ... >> >>since t distributions and unit normal distributions look very similar ... >>except when df is really small (and even there, they LOOK the same it is >>just that ts are somewhat wider) ... seems like whatever applies to one ... >>for good or for bad ... applies about the same for the other ... >> >>i would be appreciative of ANY good logical argument or empirical data that >>suggests that if we use unit normal distributions and z values ... z >>intervals and z tests ... to INTRODUCE the notions of confidence intervals >>and/or simple hypothesis testing ... that students somehow UNDERSTAND these >>notions better ... >> >>i contend that we have no evidence of this ... it is just something that we >>think ... and thus we do it that way >> >> >> >>= >>Instructions for joining and leaving this list and remarks about >>the problem of INAPPROPRIATE MESSAGES are available at >> http://jse.stat.ncsu.edu/ >>= >> >> > ___ >--- | \ >Jon Cryer, Professor [EMAIL PROTECTED] ( ) >Dept. of Statistics www.stat.uiowa.edu/~jcryer \\_University > and Actuarial Science office 319-335-0819 \ * \of Iowa >The University of Iowa dept. 319-335-0706 \/Hawkeyes >Iowa City, IA 52242 FAX319-335-3017 |__ ) >--- V > >"It ain't so much the things we don't know that get us into trouble. >It's the things we do know that just ain't so." --Artemus Ward > > >= >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
They are more than just related. One is a natural extension of the other just as chi-square is a natural extension of Z. With linear models, one can begin with a simple one sample model and build up to multiple factors and covariates using the same basic framework, which I find easier to make sense of logically and easier to teach. At 01:58 AM 4/19/01 -0300, you wrote: > > >Paul Swank wrote: >> >> However, rather than do that why not right on to F? Why do t at all when you can do anything with F that t can do plus a whole lot more? > > Because the mean, normalized using the hypothesized mean and the >observed standard deviation, has a t distribution and not an F >distribution. I am aware that the two are algebraically related,(and >simply) but trying to get through statistics with only one table (or >only one menu item on your stats software) seems pointless - like trying >to do all your logic with NAND operations just because you can. > > -Robert Dawson > 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
I agree. I still teach the t test also because of this, but at the same time I realize that what goes around, comes around, so what we are doing is ensuring that we will continue to see t tests in the literature. However, I find linear models easier to teach (once I erase the old stuff from their memories) than the basic inference course. It is so much more logical. At 12:41 AM 4/20/01 -0400, you wrote: >At 10:39 AM 4/19/01 -0500, Paul Swank wrote: >>However, rather than do that why not right on to F? Why do t at all when >>you can do anything with F that t can do plus a whole lot more? > > >don't necessarily disagree with this but, i don't ever see in the >literature in two group situations comparing means ... F tests done ... > >so, part of this has to do with educating students about what they will see >in the journals, etc. > > > 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
Paul Swank wrote: > > However, rather than do that why not right on to F? Why do t at all when you can do >anything with F that t can do plus a whole lot more? Because the mean, normalized using the hypothesized mean and the observed standard deviation, has a t distribution and not an F distribution. I am aware that the two are algebraically related,(and simply) but trying to get through statistics with only one table (or only one menu item on your stats software) seems pointless - like trying to do all your logic with NAND operations just because you can. -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 10:39 AM 4/19/01 -0500, Paul Swank wrote: >However, rather than do that why not right on to F? Why do t at all when >you can do anything with F that t can do plus a whole lot more? don't necessarily disagree with this but, i don't ever see in the literature in two group situations comparing means ... F tests done ... so, part of this has to do with educating students about what they will see in the journals, etc. = 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
However, rather than do that why not right on to F? Why do t at all when you can do anything with F that t can do plus a whole lot more? At 10:58 PM 4/19/01 -0400, you wrote: >students have enough problems with all the stuff in stat as it is ... but, >when we start some discussion about sampling error of means ... for use in >building a confidence interval and/or testing some hypothesis ... the first >thing observant students will ask when you say to them ... > >assume SRS of n=50 and THAT WE KNOW THAT THE POPULATION SD = 4 ... is: if >we are trying to do some inferencing about the population mean ... how come >we know the population sd but NOT the mean too? most find this notion >highly illogical ... but we and books trudge on ... > >and they are correct of course in the NON logic of this scenario > >thus, it makes a ton more sense to me to introduce at this point a t >distribution ... this is NOT hard to do ... then get right on with the >reality case > >asking something about the population mean when everything we have is an >estimate ... makes sense ... and is the way to go > >in the moore and mccabe book ... the way they go is to use z first ... >assume population is normal and we know sd ... spend alot of time on that >... CI and logic of hypothesis testing ... THEN get into applications of t >in the next chapter ... > >i think that the benefit of using z first ... then switching to reality ... >is a misguided order > >finally, if one picks up a SRS random journal and looks at some SRS random >article, the chance of finding a z interval or z test being done is close >to 0 ... rather, in these situations, t intervals or t tests are almost >always reported ... > >if that is the case ... why do we waste our time on z? > > > >At 08:52 PM 4/18/01 -0300, Robert J. MacG. Dawson wrote: >>David J Firth wrote: >> > >> > : You're running into a historical artifact: in pre-computer days, >> using the >> > : normal distribution rather than the t distribution reduced the size >> of the >> > : tables you had to work with. Nowadays, a computer can compute a t >> > : probability just as easily as a z probability, so unless you're in the >> > : rare situation Karl mentioned, there's no reason not to use a t test. >> > >> > Yet the old ways are still actively taught, even when classroom >> > instruction assumes the use of computers. >> >> The z test and interval do have some value as a pedagogical >>scaffold with the better students who are intended to actually >>_understand_ the t test at a mathematical level by the end of the >>course. >> >> For the rest, we - like construction crews - have to be careful >>about leaving scaffolding unattended where youngsters might play on it >>in a dangerous fashion. >> >> One can also justify teaching advanced students about the Z test so >>that they can read papers that are 50 years out of date. The fact that >>some of those papers may have been written last year - or next- is, >>however, unfortunate; and we should make it plain to *our* students that >>this is a "deprecated feature included for reverse compatibility only". >> >> -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/ >>= > >_ >dennis roberts, educational psychology, penn state university >208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED] >http://roberts.ed.psu.edu/users/droberts/drober~1.htm > > > >= >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/ =
