Re: teaching statistical methods by rules?
Alan McLean wrote, among other things: On the other hand, a body of knowledge can be thought of as a set of 'rules'. I think you are concentrating on the information in what is learned and ignoring the format. This works for computers, which learn in only one format (memory), but not for people, for which memory is just one format. My argument: For the sake of example, suppose I want to teach students how to tie their shoes. I could observe what I do and create a verbal description. I could teach students this verbal description, and they could memorize it. I could test them on their ability to remember this information. A student who could remember it probably could tie their shoes. My students might end up knowledge roughly the same information as me, but their knowledge wouldnt be stored in their brains the same way it is stored in mine. I have a connected series of motor movements built into my brain as a habit. And these different storage formats have different implications. My students would be good at verbal descriptions, but probably not so fast at actually tying their shoes. Now to reality. Research on implicit learning has suggested that people can learn something without being able to report what they have learned. Presumably, they have no conscious knowledge of what they have learned. In my published opinion, there are three types of implicit knowledge, with habits being just one. Combined with conscious knowledge, that makes four different types of learning. The format in which something is learned has implications. One is for memory. Research suggests that implicit learning is retained much longer than explicit learning. Another is for usage. Obviously, for verbal report, conscious knowledge is far superior than any other type of knowledge. But the other types of learning probably are probably better for other types of performance. For example, in one study, we either gave subjects implicit knowledge of a rule or explicitly taught them a collection of rules. The subjects with implicit knowledge could use the information in an identification task better than they could report it. The subjects with conscious knowledge could report the rules better than they could use them. The hardest type of learning to describe or define is what I call mental models, and what often corresponds to what people call understanding. For example, you have a mental model of your spouse (or friend). You can use this mental model to predict what your spouse or friend will do. You can also try to use this mental model to verbally describe your spouse or friend, but that isn't a natural use of the mental model and that format of learning isn't that good for verbal report. Someone adept at statistics would have a mental model of standard deviation, the t-test, statistical testing, etc. Teaching students rules or formulas does not develop mental models. Bob F.
Re: teaching statistical methods by rules?
Sorry to get so close to "off topic" but: There are persistent rumours that the U.S. Air Force, which has a massive educational system, including teacher-training, does a far and away better job of "education" than the "public school system." You don't have to be outstandingly intelligent to join the Air Force, either, and it seems to be able to cope with a wide variety of students. a) are the rumours false? b) if not, is the success a function of subject matter rather than their approach to teaching, and hence presumably inapplicable to teaching Statistics? I am not, nor have I ever been, in the Air Force, and hence I am unable to shed any light on the matter, but for DECADES I have been picking up rumours that something about their educational system WORKS. -- "I would predict that there are far greater mistakes waiting to be made by someone with your obvious talent for it." Orac to Vila. [City at the Edge of the World.] --- R.W. Hutchinson. | [EMAIL PROTECTED]
Re: teaching statistical methods by rules?
With all this discussion about methods and rules I thought that this question might be appropriate: Has anyone tried using "Comprehending Behavioral Statistics" by Russell T. Hurlburt, Brooks Cole, 1994 (that I saw) It seems to be the usual sort of intro stat text, but with a twist. He makes a large point of showing students how to "eyeball" a dataset and by doing this to be able to extract the parameters with a fairly high degree of accuracy. For each parameter he describes a technique to use, or sometimes a couple of alternate techniques to use. His claim is that the typical method that authors have been using results in students grinding away with calculators for tens of minutes and when they get a resulting number they often have no idea whether it is right or have any feel for what that number really represents. He does include all the usual formulas, he hasn't abandoned them. But he claims that the "eyeball" method can be done much more quickly and that allows him to have many many more such exercises done in class, allows students of differing skill levels to all work with some reward on such problems, etc. I was considering trying some of the ideas out and thought I would ask for opinions before subjecting students to one more questionable idea. Thanks ---== Posted via Newsfeeds.Com, Uncensored Usenet News ==-- http://www.newsfeeds.com The Largest Usenet Servers in the World! --== Over 73,000 Newsgroups - Including Dedicated Binaries Servers ==-
Re: teaching statistical methods by rules?
Yep!! As you say: "Why are people so obsessed with T and Z? " Perhaps it would be even better (easier?) to focus on F since F(df1,df2) = t^2(df2) (Reminder: when using a t-table, the p-values usually involve ONE-TAIL and when using the F-table, the p-values involve TWO-TAILS ) Example: The critical-value of t for probability of p = .05 at t(18) = 1.734 The critical-value of F for probability of p = .10 at F(1,18) = (1.734)^2 = 3.01 :-) -- Joe * Joe Ward Health Careers High School * * 167 East Arrowhead Dr 4646 Hamilton Wolfe* * San Antonio, TX 78228-2402San Antonio, TX 78229 * * Phone: 210-433-6575 Phone: 210-617-5400* * Fax: 210-433-2828 Fax: 210-617-5423 * * [EMAIL PROTECTED]* * http://www.ijoa.org/joeward/wardindex.html * - Original Message - From: [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Sunday, December 19, 1999 4:44 PM Subject: Re: teaching statistical methods by rules? | In article [EMAIL PROTECTED], | [EMAIL PROTECTED] says... | | snip | | On the other hand, a body of knowledge can be thought of as a set of | 'rules'. The important thing is that this set is constructed by the | individual, so our aim should not be to teach statistics as a set of | rules, but in such a way that each student can develop his or her own | set of rules. They won't be the same for all, and they will different | from the teacher's, but they hopefully will work. (If you like, this is | a defintion of a 'good student' - one who manages to construct a | successful set of rules for each subject. | | | It's either undergraduate students in Australia are much smarter than those | living in the United States or you live on a different planet. The last time I | taught an undergraduate introductory statistics class, some students couldn't | even do fractions and simple algebra. Can you expect them to develop their own | rules? | | Why are people so obsessed with T and Z? When the degrees of freedom exceeds | say 30, the difference between T and Z is practically negligible. You can use T | or Z in such a case. However, the P-value from Z is easier to compute. | | -- | Tjen-Sien Lim | [EMAIL PROTECTED] | www.Recursive-Partitioning.com | | Get your free Web-based email! http://recursive-partitioning.zzn.com | |
Re: teaching statistical methods by rules?
[EMAIL PROTECTED] wrote: In article [EMAIL PROTECTED], [EMAIL PROTECTED] says... snip On the other hand, a body of knowledge can be thought of as a set of 'rules'. The important thing is that this set is constructed by the individual, so our aim should not be to teach statistics as a set of rules, but in such a way that each student can develop his or her own set of rules. They won't be the same for all, and they will different from the teacher's, but they hopefully will work. (If you like, this is a defintion of a 'good student' - one who manages to construct a successful set of rules for each subject. It's either undergraduate students in Australia are much smarter than those living in the United States or you live on a different planet. The last time I taught an undergraduate introductory statistics class, some students couldn't even do fractions and simple algebra. Can you expect them to develop their own rules? My comment above has nothing to do with students' 'smartness' or with their level of skill (two different things!) It is simply a way of describing what learning is. Why are people so obsessed with T and Z? When the degrees of freedom exceeds say 30, the difference between T and Z is practically negligible. You can use T or Z in such a case. However, the P-value from Z is easier to compute. Your interpretation of 'practically negligible' is different from mine, that's all. And with a computer, the p-value for t is exactly as easy to compute as the p-value for z. Regards, Alan -- Tjen-Sien Lim [EMAIL PROTECTED] www.Recursive-Partitioning.com Get your free Web-based email! http://recursive-partitioning.zzn.com -- Alan McLean ([EMAIL PROTECTED]) Acting Deputy Head, Department of Econometrics and Business Statistics Monash University, Caulfield Campus, Melbourne Tel: +61 03 9903 2102Fax: +61 03 9903 2007
Re: teaching statistical methods by rules?
Tjen-Sien Lim asks:
Why are people so obsessed with T and Z? When the degrees of freedom
exceeds
say 30, the difference between T and Z is practically negligible. You can
use T
or Z in such a case. However, the P-value from Z is easier to compute.
With appropriate tables or software, the P-value from Z is *not* any
easier to compute.
I don't think most of us here are "obsessed with T and Z" but, rather,
concerned by others' obsession with it. I see it as a needless confusion
and a waste of time. Moreover, it has been observed that the meme tends to
mutate in the wild from harmless superstition ("I should use Z when n30")
to actual error ("Anybody who uses t with n30 is wrong.")
*Instructors* should consider this as a pedagogical matter; the question
should ideally never arise in the classroom. Unfortunately, many textbooks
and instructors in other courses sow the seeds of this silly little
anachronism, and it may be necessary to weed them out.
-Robert Dawson
Re: teaching statistical methods by rules?
Herman Rubin wrote:
Robert Frick [EMAIL PROTECTED] wrote:
Jerry Dallal wrote:
Robert Frick wrote:
I know it is hard to make statistics fun, but FOLLOWING
RULES IS NEVER
FUN. Not in math, not in games, nowhere.
In math and in games, following rules isn't just fun,
IT'S THE LAW. In fact, you can't have fun unless
you follow them. :-)
Well, technically, most real rules tell you what not to do -- they
usually don't tell you what to do, because that isn't fun.
This is well put. The rules describe what is allowed, but
not which of the allowed possibilities to perform.
I can't help but feel we're using the word "rules" in different ways.
Any time you learn a new game, the first thing you learn is the rules,
a mix of can and can't do. ("The batter shall take his position within
the lines of the batter's box". The batter shall not have his entire
foot touching the ground completely oytside the lines of the batter's
box...") One of the reasons I enjoy mathematics
so much is that it is rule based. You follow the rules, you get to
someplace new. These new locations reached by following the rules are
called "publications". :-) 'Couse, that's also what makes it
tautological!
Happy holidays to all!
Re: teaching statistical methods by rules?
On 20 Dec 1999, Don Taylor wrote in part: Has anyone tried using "Comprehending Behavioral Statistics" by Russell T. Hurlburt, Brooks Cole, 1994 (that I saw) It seems to be the usual sort of intro stat text, but with a twist. He makes a large point of showing students how to "eyeball" a dataset and by doing this to be able to extract the parameters with a fairly high degree of accuracy. Sounds refreshing. Might even convey, sort of subliminally, the notion that accuracy (or precision) is something one might be interested in... snip, description of Hurlburt's approach I was considering trying some of the ideas out and thought I would ask for opinions before subjecting students to one more questionable idea. There are hardly any ideas worth considering that aren't questionable. Won't hurt students to have "one more questionable idea" to work with. They get plenty as it is, and usually without much concern for their "questionability" on the part of their mentors. Occupational hazard. Live with it. -- Don. Donald F. Burrill [EMAIL PROTECTED] 348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED] MSC #29, Plymouth, NH 03264 603-535-2597 184 Nashua Road, Bedford, NH 03110 603-471-7128
Re: teaching statistical methods by rules?
In article [EMAIL PROTECTED], Robert Frick [EMAIL PROTECTED] wrote: Jerry Dallal wrote: Robert Frick wrote: I know it is hard to make statistics fun, but FOLLOWING RULES IS NEVER FUN. Not in math, not in games, nowhere. In math and in games, following rules isn't just fun, IT'S THE LAW. In fact, you can't have fun unless you follow them. :-) Well, technically, most real rules tell you what not to do -- they usually don't tell you what to do, because that isn't fun. This is well put. The rules describe what is allowed, but not which of the allowed possibilities to perform. In bridge, the language of the bidding is very prescribed, but you almost always have choices as to what you can bid. On the other hand, the prescription to bid 1NT with a balanced hand and 15-17 points tells you what to do, but is not a real rule of the game. Instead, it is a rule the experts constructed so that the game wouldn't be fun. Ha ha, they really constructed the rule so that people could play better bridge. Destroying the game is an unintended byproduct. In math, aren't students often taught algorithms for solving problems? Again, no fun. Yes, this is a mistake. They are given many rules in linear algebra, which are all special cases of what is known in logic as the rule of equality. But these rules only state what processes are allowed. The introduction of formal algorithms added nothing but glitz to algebra. The ones often given as rules for solving, such as Cramer's rule, or inversion of a matrix by determinants, are essentially useless in most situations. These are rules, of the type given for special situations in statistics. Of course, most real problems in statistics are not of this special type. Bob F. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
Re: teaching statistical methods by rules?
Jerry Dallal wrote: Robert Frick wrote: I know it is hard to make statistics fun, but FOLLOWING RULES IS NEVER FUN. Not in math, not in games, nowhere. In math and in games, following rules isn't just fun, IT'S THE LAW. In fact, you can't have fun unless you follow them. :-) Well, technically, most real rules tell you what not to do -- they usually don't tell you what to do, because that isn't fun. In bridge, the language of the bidding is very prescribed, but you almost always have choices as to what you can bid. On the other hand, the prescription to bid 1NT with a balanced hand and 15-17 points tells you what to do, but is not a real rule of the game. Instead, it is a rule the experts constructed so that the game wouldn't be fun. Ha ha, they really constructed the rule so that people could play better bridge. Destroying the game is an unintended byproduct. In math, aren't students often taught algorithms for solving problems? Again, no fun. Bob F.
Re: teaching statistical methods by rules?
Robert Frick wrote (I've rearranged the points a little) - If you give students rules to memorize, they will surely forget them. ... But your best student will just remember half the rules -- and by that, I mean half of each rule. ... This, I have to disagree with as a point of fact. Many students are very good at memorizing rules. Too good, in fact; they substitute it for thinking and expect to get good marks if they do enough of it. The best way I know of discouraging this is to permit them to bring (limited) notes to tests. But there is a difference between memorizing rules and following rules. It can be argued - in the same way that any objective and nonstochastic decision-making process yields a "rejection region" - that any objective and nonstochastic procedure for statistical analysis of data yields a "set of rules". The task of the educator is to put some structure onto this so that they can be learned efficiently. *Some* parts are best deduced as needed; others are not. Realistically, few students - especially those who are not training to be statisticians - will be able to decide for themselves what to do in every situation. There are a lot of rules which are a matter of convention. People expect to know what the whiskers in a boxplot mean and where the parts of an ANOVA table are to be found. There are also "defensive" rules such as "don't worry about the z test for the mean", "never bother with the preparatory F test before a t test", and so on. These are there for two reasons: firstly, students or ex-students who found out that there was such a thing as an F test for equal variance. and knew that the pooled t test assumed equal variance might well - unless their intuition was excellent - decide that that was what it was for. More realistically, they might come across a book or semilearned colleague who recommended the practice. The point is that few of our students are ever going to learn enough about statistics that they can make sensible decisions for themselves on all of these matters. Yes, we'd like them to; no, they won't. If you had a student who learned and applied the rules, people would say that the student was mindlessly following rules and couldn't think for him/herself. Huh? Referee's report: " page 3, line 15-25: The author's use of ANOVA here, in a situation where the assumptions of normality and homoscedasticity are (as shown in the accompanying boxplot) well justified, shows a great lack of originality. Some other technique must be substituted. Page 4, line -5: The degrees-of-freedom calculation is performed in a highly standard way,and the answer apears to be correct. Please do something about this." [And - as Harry Chapin might have put it- the young researcher said: "Roses are red, and green leaves are green; there's no need to see them any other way than the way they always have been seen..."] I know it is hard to make statistics fun, but FOLLOWING RULES IS NEVER FUN. Not in math, not in games, nowhere. I can't think of anything to say that makes the case *for* the necessity of a certain number of rules better than that. -Robert Dawson
Re: teaching statistical methods by rules?
Dale Berger wrote: How about this one: The sampling distribution of the mean is likely to be approximately normal with a sample of at least 30 cases IF the population is roughly symmetrical with no extreme outliers. Diagnosis: Plot the data, plus use whatever information is available about the population distribution. What do you think? Cheers, Dale Berger That's essentially what I tell my students and back it up with pictures like those in Freedman, Pisani and Purves. I hedge a little on the 30. It's more like starting to feel comfortable at 30, relaxed at 60, and not a care in the world at 100, provided they (as has become the class slogan), "Show me the data!"
Re: teaching statistical methods by rules?
The question is: If you don't teach by rules, what will you use? In the Elementary Statistics course I used to teach, I had several different objectives. 1) Students should develop arithmetic reliability. 2) Students should learn how they can be tricked by statistical wizardry. 3) Students should learn how to understand what is written by responsible statisticians. In the Applied Statistics course, my objectives were different. 1) Students should learn to read and evaluate the professional literature in their discipline. 2) Students should learn to apply the basic ideas of statistical description and inference: estimation, simple hypothesis testing, regression, etc. 3) Students should learn that their experience is limited and gain the confidence to consult a professional statistician. In the Mathematical Statistics course, my objectives were primarily mathematical, not statistical. Statistics was seen as a technology built on the foundations of the infinitesimal and finite difference calculus. Different strokes for different folks!
Re: teaching statistical methods by rules?
Robert Frick wrote: I know it is hard to make statistics fun, but FOLLOWING RULES IS NEVER FUN. Not in math, not in games, nowhere. In math and in games, following rules isn't just fun, IT'S THE LAW. In fact, you can't have fun unless you follow them. :-)
Re: teaching statistical methods by rules?
"Richard A. Beldin, Ph.D." wrote: The question is: If you don't teach by rules, what will you use? In the Elementary Statistics course I used to teach, I had several different objectives. 1) Students should develop arithmetic reliability. 2) Students should learn how they can be tricked by statistical wizardry. 3) Students should learn how to understand what is written by responsible statisticians. FWIW, here are the vision and mission statements for my one year course offered to students in the School of Nutrition Science and Policy and Tufts. Students receive them on the first day of class and I demand they hold me to them! VISION STATEMENT Every student will find Nutrition 209 to be one of the most valuable and enjoyable course ever taken. MISSION STATEMENT Every student who takes Nutrition 209 will gain the statistical skills necessary to be productive in the fields of nutrition science and policy. In particular, each student will have the statistical skills needed to read and produce technical reports and to read and contribute to the published literature. Each student will understand the basic principles and techniques of study design and data analysis. Each student will learn the appropriate use of common statistical procedures and will be able to perform the necessary calculations by using standard statistical program packages. Each student will gain the ability to determine whether the techniques taught in this course are appropriate for analyzing a particular set of data, to apply those techniques to the data, and to write a summary of findings from the analyses.
Re: teaching statistical methods by rules?
There has been a side note to "rules" concerning z -- On 13 Dec 1999 13:58:31 -0800, [EMAIL PROTECTED] (Robert Dawson) wrote: Exactly... An example - we've been using Devore Peck, which unfortunately introduces the Z test for the mean, supposedly for pedagogical reasons but without nearly a strong enough indication of this. A lot of students infer a rule "if n30 use z rather than t" despite my repeated statements that Z is NEVER a better test for the mean under circumstances they are likely to encounter [in psychology]. snip If you *never* wanted z, that might call for a different rule. But you find z (or its square, chisquare) actually in use in the large-sample versions of tests on ranks or dichotomies -- the variance meets that necessary requirement for having z instead of t; that is, it has a "KNOWN" variance. For data consisting of dichotomies or ranks, the total variance is known in advance, though there is a question of what to do with ties. Indeed, the F-test might work better than another formula for estimating the "exact" variance when there are a lot of ties, but the known-variance version of ANOVA can use chisquared instead of F -- If you have a small enough N, the distinction can matter. But the direction of error if you use F is on the conservative side, so doing various ANOVAs on ranks, as an alternative to exact testing, is a handy tool to know about. Even though the exact test might be available. Teaching? I think it is good have EXAMPLES available, to go along with rules. Perhaps you want examples that just skirt the rules, too. I keep thinking that I want to internalize the best set of rules and examples by browsing 3 or 4 books on the particular topic, in addition to seeing a few examples by Monte Carlo.. But I can't do that myself, for every topic. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html
Re: teaching statistical methods by rules?
- Original Message -
From: Jerry Dallal [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Thursday, December 16, 1999 10:08 AM
Subject: Re: teaching statistical methods by rules?
Robert Dawson wrote:
Jerry Dallal wrote:
The problem for
me
with the statement "Z is NEVER a better test for the mean under
circumstances they are likely to encounter [in psychology]" is that it
reads like an indictment
It is. The last thing students in Intro Stats need is one more red
herring.
If I'm reading you properly ("NEVER"; it is an indictment),
Not an indictment of the approximation, but of the idea that there is
some n at which one *ought* to _stop_using_t_ and start using Z. There is
simply no reason for this extra complication unless Z works *better*, and it
never does.
then
one of the important rules students are to get from your course is
that there is a critical distinction between the percentiles of the t
distribution and the standard normal distribution when talking about
means of large samples.
Not at all. The approximation is, of course, an excellent one. I tell
the students that, and it is implicit in the use of any sanely-devised t
table (one that does not have rows/columns for 61, 62, ..., 733, ...
degrees of freedom).
The lack of a critical distinction is itself a sufficient condition for "Z
over 30" to be a waste of time, and for the superstition that it is somehow
wrong to use t for large samples to be just that - a superstition.
I guess we'll have to agree to disagree on this one. I hope
I'm not misstating your case.
Myself, I hope we *can* agree that there are no circumstances where
Z-with-s is a better test than t; that the rule
"use t for the mean"
is preferable - mainly on the grounds of simplicity and elegance - to
"use t for the mean unless n is over 30 in which case you may use z";
and that it is preferable on the grounds of factual accuracy to
"use t for the mean unless n is over 30 in which case you must use z".
A final point: Getting across - in the face of the psychology texts saying
the opposite that are sometimes quoted to me by students - that the Central
Limit Theorem does not magically start working exactly at n=30 is hard
enough. Assigning *other* magical powers to n=30 just reconfounds the
confusion.
-Robert Dawson
Re: teaching statistical methods by rules?
I happened to have a vehement and probably radical opinion on this. One of my sayings: "Ironically, our educational system is ideally suited to teaching computers and ill-suited to teaching human beings." If you are going to program a computer to do statistics, tell the computer rules to follow. If you give students rules to memorize, they will surely forget them. If you had a student who learned and applied the rules, people would say that the student was mindlessly following rules and couldn't think for him/herself. But your best student will just remember half the rules -- and by that, I mean half of each rule. I know it is hard to make statistics fun, but FOLLOWING RULES IS NEVER FUN. Not in math, not in games, nowhere. There are advantages to teaching rules. Most students like it. They certainly understand that method of teaching. They just won't learn anything. Bob F. EAKIN MARK E wrote: I just received a review which stated that statistics should not be taught by the use of rules. For example a rule might be: "if you wish to infer about the central tendency of a non-normal but continuous population using a small random sample, then use nonparametrics methods." I see why rules might not be appropriate in mathematical statistics classes where everything is developed by theory and proof. However I teach statistical methods classes to business students. It is my belief that if faculty do not give rules in methods classes, then students will infer the rules from the presentation. These student-developed rules may or may not be valid. I would be intested in reading what other faculty say about rule-based teaching depending on whether you teach theory or methods classes. Mark Eakin Associate Professor Information Systems and Management Sciences Department University of Texas at Arlington [EMAIL PROTECTED] or [EMAIL PROTECTED]
Re: teaching statistical methods by rules?
Dear Colleagues, I think it would help to draw a distinction between iron-clad rules and rules-of-thumb. Perhaps we can agree that it is generally not a good idea to teach students iron clad rules for making statistical decisions, especially if they do not understand the logic behind the rules. On the other hand, with experience we all develop rules of thumb that allow practical short cuts. If we can teach the logic behind the rules of thumb and the conditions under which the rules of thumb are likely to be valid and when they may fail, students can learn to use the rules of thumb effectively. It might be interesting to look at some of our favorite rules of thumb and see where they are likely to hold and where they are likely to fail (and how we can do diagnoses to tell the difference). How about this one: The sampling distribution of the mean is likely to be approximately normal with a sample of at least 30 cases IF the population is roughly symmetrical with no extreme outliers. Diagnosis: Plot the data, plus use whatever information is available about the population distribution. What do you think? Cheers, Dale Berger - Original Message - From: Robert Frick [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Thursday, December 16, 1999 8:14 PM Subject: Re: teaching statistical methods by rules? I happened to have a vehement and probably radical opinion on this. One of my sayings: "Ironically, our educational system is ideally suited to teaching computers and ill-suited to teaching human beings." If you are going to program a computer to do statistics, tell the computer rules to follow. If you give students rules to memorize, they will surely forget them. If you had a student who learned and applied the rules, people would say that the student was mindlessly following rules and couldn't think for him/herself. But your best student will just remember half the rules -- and by that, I mean half of each rule. I know it is hard to make statistics fun, but FOLLOWING RULES IS NEVER FUN. Not in math, not in games, nowhere. There are advantages to teaching rules. Most students like it. They certainly understand that method of teaching. They just won't learn anything. Bob F. EAKIN MARK E wrote: I just received a review which stated that statistics should not be taught by the use of rules. For example a rule might be: "if you wish to infer about the central tendency of a non-normal but continuous population using a small random sample, then use nonparametrics methods." I see why rules might not be appropriate in mathematical statistics classes where everything is developed by theory and proof. However I teach statistical methods classes to business students. It is my belief that if faculty do not give rules in methods classes, then students will infer the rules from the presentation. These student-developed rules may or may not be valid. I would be intested in reading what other faculty say about rule-based teaching depending on whether you teach theory or methods classes. Mark Eakin Associate Professor Information Systems and Management Sciences Department University of Texas at Arlington [EMAIL PROTECTED] or [EMAIL PROTECTED]
Re: teaching statistical methods by rules?
Robert Dawson wrote: Exactly... An example - we've been using Devore Peck, which unfortunately introduces the Z test for the mean, supposedly for pedagogical reasons but without nearly a strong enough indication of this. A lot of students infer a rule "if n30 use z rather than t" despite my repeated statements that Z is NEVER a better test for the mean under circumstances they are likely to encounter [in psychology]. Of course, if they are cutting lectures that day they won't hear the warning... Okay, I'll bite. Why?
Re: teaching statistical methods by rules?
Robert Dawson wrote: Exactly... An example - we've been using Devore Peck, which unfortunately introduces the Z test for the mean, supposedly for pedagogical reasons but without nearly a strong enough indication of this. A lot of students infer a rule "if n30 use z rather than t" despite my repeated statements that Z is NEVER a better test for the mean under circumstances they are likely to encounter [in psychology]. Of course, if they are cutting lectures that day they won't hear the warning... Okay, I'll bite. Why? Recall that "the" z test for the mean is actually two often-confused tests. The first, the "Z test with sigma", involves exact prior knowledge of sigma. This is an artificial situation very unlikely to arise if the variation is intrinsic to what is being measured. If the variation comes from a separate source (eg, instrumentation) it is possible that one might know sigma but not mu - but this is more of an engineering scenario, and probably oversimplified even then. The "Z test with s" is nothing but an unnecessary approximation of the t distribution for n1 degrees of freedom by the z distribution. The most that can be said for it is that if n is large it is not wrong by very much. However: -inasmuch as the outcomes, p values, or confidence intervals obtained differ from those of the t procedures, the z outcomes are wrong and the t procedures are right. Z is never mathematically better. -Students need to learn how to use both tables anyhow. Using "z above thirty" does not reduce the amount students need to learn. If they are using a stats package the same principle applies. For this and the next two reasons, z is never pedagogically better. Caveat: Old fashioned t tables fashioned after the tradition the Church of the Holy 5% make it hard to compute p values that are not round numbers. See Devore Peck's 3rd edition, or my article "Turning the Tables - a t-table for Today" in JSE a couple years ago, for alternatives. -The test-selection decision process is made more complicated if the "z over thirty" rule is added, not less so. -Students tend to somehow twist the "z over thirty" rule around to say (to them) "t is incorrect over thirty". This could be embarrassing to them in later life (eg, if they were refereeing a paper and demanded that the author change a t test to a z test). -Robert Dawson
RE: teaching statistical methods by rules?
Hello Robert and All -- Please forgive the intrusion of a lurker in a domain above my pay grade, as it were, but I have a slight question... The "Z test with s" is nothing but an unnecessary approximation of the t distribution for n1 degrees of freedom by the z distribution. The most that can be said for it is that if n is large it is not wrong by very much. It would seem to me that more than this most can be said. If my reading of the central limit theorem is up to snuff, I should be able to use the "Z test with s" without an underlying assumption of the normality of the parent population, required for the t. I am not etching n = 30 in stone, here -- but there is _some_ large n that will make the underlying sampling distribution of the mean sufficiently close to normal to justify the "Z with s." So how far off base is my understanding? -- Chris Chris Olsen George Washington High School 2205 Forest Dr. S.E. Cedar Rapids, IA 52403 (319)-398-2161 [EMAIL PROTECTED]
RE: teaching statistical methods by rules?
i would highly recommend a paper by ken brewer ... titled: behavioral statistics textbooks: source of myths and misconceptions, Journal of Educational Statistics .. Fall, 1985, V 10, #3, pp 252-268 ... for an excellent discussion of the CLT At 12:20 PM 12/15/99 -0600, Olsen, Chris wrote: Hello Robert and All -- It would seem to me that more than this most can be said. If my reading of the central limit theorem is up to snuff, I should be able to use the "Z test with s" without an underlying assumption of the normality of the parent population, required for the t. I am not etching n = 30 in stone, here -- but there is _some_ large n that will make the underlying sampling distribution of the mean sufficiently close to normal to justify the "Z with s." -- 208 Cedar Bldg., University Park, PA 16802 AC 814-863-2401Email mailto:[EMAIL PROTECTED] WWW: http://roberts.ed.psu.edu/users/droberts/drober~1.htm FAX: AC 814-863-1002
Re: teaching statistical methods by rules?
I thought there was a chance it would hinge on "better". Since it was "never" that got the emphasis, I thought I'd ask. The problem for me with the statement "Z is NEVER a better test for the mean under circumstances they are likely to encounter [in psychology]" is that it reads like an indictment. While technically correct in some sense, the use of percentiles of the standard normal distribution in place of those from the t distribution for large samples doesn't make much (any?) difference, so the NEVER rule struck me as unnecessary overkill. In fact, in place of the precise 0.05 two-sided critical value of 1.96, many people use 2, which is the critical value for a t with 60 d.f. However: -inasmuch as the outcomes, p values, or confidence intervals obtained differ from those of the t procedures, the z outcomes are wrong and the t procedures are right. Z is never mathematically better. I would think that for percentiles of the t distribution to be more right than percentiles of the standard normal distribution for large degrees of freedom, underlying normality would be critical. However, I haven't done any formal study of this and will defer to anyone who has. Caveat: Old fashioned t tables fashioned after the tradition the Church of the Holy 5% make it hard to compute p values that are not round numbers. So maybe z is sometimes better? In fact, it's hard to imagine circumstances where anyone dealing with real data will not be using a computer, if only to establish an audit trail. Since software insists on using t, the question is moot for all practical purposes.
Re: teaching statistical methods by rules?
Chris Olsen wrote: It would seem to me that more than this most can be said. If my reading of the central limit theorem is up to snuff, I should be able to use the "Z test with s" without an underlying assumption of the normality of the parent population, Yes, as an unnecessary approximation, required for the t. and no. The utility of either test for non-normal populations depends on the central limit theorem and related results. "Z with s" relies on the same assumptions about the sampling distribution of s and mu that the t test does. I am not etching n = 30 in stone, here Good... There are distributions (ie, the normal distributions) for which n=1 suffices. There are distributions (eg. lottery prizes) for which n=1 is too small. If t won't work for a population, z-with-s won't either. but there is _some_ large n that will make the underlying sampling distribution of the mean sufficiently close to normal to justify the "Z with s." No - at least not if you mean "there is some large n independent of the distribution..." -RJMD
Re: teaching statistical methods by rules?
Jerry Dallal wrote: The problem for me with the statement "Z is NEVER a better test for the mean under circumstances they are likely to encounter [in psychology]" is that it reads like an indictment It is. The last thing students in Intro Stats need is one more red herring. Caveat: Old fashioned t tables fashioned after the tradition the Church of the Holy 5% make it hard to compute p values that are not round numbers. So maybe z is sometimes better? Under certain artificial "desert island" scenarios, yes. But: In fact, it's hard to imagine circumstances where anyone dealing with real data will not be using a computer, if only to establish an audit trail. A new and different motive grin Since software insists on using t, the question is moot for all practical purposes. No, MINITAB (frinstance) will use Z if you insist. (And a pistol will shoot you in the foot if you point it there pull the trigger.) But it is rarely the right thing to do. -Robert Dawson
