Re: Student's t vs. z tests
Hi On Fri, 20 Apr 2001, dennis roberts wrote: > At 10:58 AM 4/20/01 -0500, jim clark wrote: > > What does a t-distribution mean to a student who does not > >know what a binomial distribution is and how to calculate the > >probabilities, and who does not know what a normal distribution > >is and how to obtain the probabilities? > > good question but, NONE of us have an answer to this ... i know of NO data > that exists about going through various different "routes" and then > assessing one's understanding at the end Just a couple of comments. (1) Not having specific evidence on a pedagogical question does not mean that any approach is just as justified as any other approach. We should base our practice on what information is available, appreciating its possible limitations (e.g., personal experience, cognitive models of concept learning, general principles of teaching, principles of task analysis, logic, feedback from students, ...). Only the very naivest sort of crude empiricism would dictate that specific findings are the only worthwhile factors in a science-based practice. (2) In general I suspect that there is much evidence supportive of a task-analytic approach to teaching mathematics, although I have not looked at the literature for many years. That is, mathematics, perhaps more than many other areas, requires a sensitivity to the kinds of prior knowledge presumed by the new knowledge to be acquired. > to say that we know that IF we want students to learn about and understand > something about t and its applications ... one must: > > 1. do binomial first ... > 2. then do normal > 3. then do t > > is mere speculation Only if you completely devalue many years of experience teaching a subject matter, a background in cognitive and educational psychology, the possibility that there might be certain logical entailments involved among the topics, and so on. Your statement makes it sound as though one is equally justified to promote any of the 3! = 6 possible permutations of all 3 tasks + the 3x2! = 6 permutations of 2 tasks + the 3 possible single tasks (+ the 1 possible 0 tasks, if one wants to be comprehensive). > without some kind of an experiment where we try various combinations and > orderings ... and see what happens to student's understandings, we know not > of what we assert (including me) This is just too nihilistic a view of knowledge and teaching. There are certain constraints. For example, one normally expects that learning the alphabet is better done before learning words. Would you want an experiment before concluding that presenting the calculus of statistics is probably not the best approach to intro stats in non-mathematical disciplines? > off the top of my head, i would say that one could learn alot about a t > distribution studying it ... are you suggesting that one could not learn > about calculating probabilities within a t distribution without having > worked and learned about calculating probabilities in a normal distribution? > as far as i know, the way students learn about calculating probabilities is > NOT by any integrative process ... rather, they are shown a nice drawing of > the normal curve, with lines up at -3 to +3 ... with values like .02, .14, > .34 ... etc. within certain whole number boundaries under the curve, and > then are shown tables on how to find areas (ps) for various kinds of > problems (areas between points, below points, above points) > > if there is something real high level and particularly intuitive about > this, let me know. you make it sound like there is some magical "learning" > here ... some INductive principle being established ... and, i don't see it Of course you left off my starting point. For the binomial distribution, students can readily be shown how to actually calculate the probabilities in the sampling distribution. They do not have to take it purely on faith. Then when we move to the normal or t or F or whatever, we can say that these distributions are produced by more sophisticated mathematical techniques that are beyond our capabilities, but _analogous_ to what students did for the binomial. This is the foundation (with its own foundation in an adequate understanding of probability and counting principles). The normal distribution is the bridge between this foundation and the t-distribution (then F, whatever). I can't speak for other disciplines, but at least in psychology and education, it is probability worth noting that an understanding of the normal distribution is valuable in and of itself, irrespective of its role in hypothesis testing. Examples of normal distributions would occur in testing (e.g., understanding different test score transformations, such as T-scores, computed percentiles, and the like), in understanding certain transformations (e.g., of skewed reaction time distributions), and in perception (e.g., d-prime measures of sensitivity). > i don't see one whit of difference b
t's vs. z's
It has been interesting as a student currently learning about t's versus z's to read all of the dialogue on this matter in the archives. I'm in an interesting position because for my masters degree over 18 years ago, I learned this material without the use of computer technology. Thus as a very nontraditional shall we say, doctoral student in the year 2001, I decided I needed to take this level statistics again . Certainly as I have affirmed my suspicions, the technology is different but the basic material is the same. For me both back then and now, what has been really helpful is the following: 1. honest explanations as to why we are learning something, whether it be to help us understand the next more complex concept, or to directly use the one we are learning. It does help when the snstructor says directly to me at least, "It will be rare that you use this but it will be helpful to you to understand it because it will help you learn hte next thing." 2. very practical problem demonstration in class, taking the time to go through each step of the problem solving process and why we are doing it that way. It especially helps for me if it is a "human type" problem rather then a "blood gas" problem or a "milligrams of sodium in substances" problem, but that is most likely because I am a professional counselor and the research I am interested in conducting in the future is a human behavior problem. I've also appreciated the respectful attitude I've sensed while reading your differing opinions and comments. Lois Ehrmann = 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
William B. Ware <[EMAIL PROTECTED]> wrote: : sequential/hierarchical regression as you note below... however, ANCOVA : has at least two assumptions that your situation does not meet. First, it : assumes that assignment to treatment condition is random. Second, it : assumes that the measurement on the covariate is independent of : treatment. That is, the covariate should be measured before the treatment : is implemented. Thus, I believe that you should implement the : hierarchical regression... but I'm not certain what question you are They aren't assumptions but they do affect interpretations. either way is ANCOVA which will answer a question. Write the model comparison and you'll see that. Whether it's the question you want to answer is another = 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've joined this one at the fag end. I'm with Dennis Roberts. The way I would put it is this: the PRINCIPLE of a sampling distribution is actually incredibly simple: keep repeating the study and this is the sort of spread you get for the statistic you're interested in. What makes it incredibly simple is that I keep well away from test statistics when I teach stats to biomedical researchers. I deal only with effect (outcome) statistics. I even forbid my students and colleagues from putting the values of test statistics in their papers. Test statistics are clutter. The actual mathematical form of any given sampling distribution is incredibly complex, but only the really gifted students who want to make careers out of statistical research need to come to terms with that. The rest of us just plug numbers into a stats package or spreadsheet. I'm not sure what would be a good sequence for teaching the mathematical forms. Binomial --> normal --> t is probably as good as any. Will = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
IT SCHOLARSHIPS
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Central Limit Theorem Proof using MGF
I am trying to get a better understanding of the proof for the central limit theorem which uses the MGF. Can anyone direct me to some resources that will lead me through this proof step by step? Thanks. Dave J. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
