And, please forgive my disorganized blowout following.
Though I most often do not behave arrogantly, I volunteer to be the one
who shouts out that this is SIMPLE, and should not be made difficult:
If you are travelling, your choice of transportation depends on where you
are going. If your car is your choice today, you may use ship tomorrow.
We have to use the tools appropriate for the task at hand, and if a task needs
a certain tool, we have to use it. If persons are more comfortable with other
tools, not appropriate for the task, and we are to learn them how to deal with
the task, what should we do? What would the carpenter or the smith do? Let the
apprentice continue to use what he knew how to use at the start of learning
period?
In _any subject_ we have to teach the tools of the trade. Adequate
communication is one of the needs we can _never_ sacrifice on at any level
in any subject if our students shall be able to do work on which someone
depends. Adequate precicion may be everyday language outside our subject,
but should not be so inside the subject. What is adequate should be
evaluated by looking at possible consequences (worst case) if we are
misunderstood. If we are to use the knowlege of our subject professionally,
people should be able to trust our competence, and so relaxed precicion
requirements are no to be tolerated. (Of cource reaching precicion will take
work and time, and I see that there is a problem with curricula
underestimating the work.)
And so, we have to live with the fact that _all subjects_, when treated at a
certain level, demands a welldefined terminology delivering the necessary
precicion, but demanding work to be learned. If the car mechanic didn't know
more words for car parts (precicely defined) than I do, he would have
problems ordering what he needed, and evaluating the time for my car repair
would transform into a textbook problem. But he don't use these words at home
at the dinner table (I hope.)
If we dress for snow and storm one day, it doesnt have to be so every day. We
have to be able to comfortably change clothes (and language) after determining
what is required. People studying psychology and sociology do so when
switching between their professional and their everyday terminology. I am a
bit surpriced if students studying statistics should not.
Of course, communication with people outside the subject is important, and so
the difference between meaning of same word inside and outside subject
terminology should be emphasized in teaching. 'Expected value', given by
Herman, is a nice example, given by Herman. Independence is another.
Students do understand the concept content, but behave strange whenever their
everyday definition surfaces and kills the formal definition (which should of
cource NOT be given the antididactical way through an equation!!!).
The example I first use in teaching communication importance is from my
getting my driver licence. I was so angry about the questions that I nearly
didn't get the licence (because I refused to write that my car was four times
heavier when travelling at double speed -- and later refused to accept my
error and learn this fact. Now I understand that this might be effective
communication. What I still do not accept is that the person evaluating me did
not have the knowlege to appreciate an understanding a bit less primitive. He
did not behave profecionally, because of inadequate knowlege.)
So:
What we should _never_ compromice on is the fight for adequate precicion in
communication. What we are to communicate, on the other hand, may be debated.
Example:
I have (as have others) come to the conclucion that if my nonmath students are
to appreciate statistics 5 years after they have left me, they should
learn it in such a way that it does not evaporate with the math when they
leave school. (Not to be misunderstood: I love math. Pure math, not
statistics, is my subject. But I accept realities.) Necessary precicion of
communication may be achieved by other means than math (although not as
beautiful in the case of probability and statistics, but this is another
matter: Beautiful for whom?)
And so my nonmath students should learn to use statistics as I learn to drive
my car. I do not have to be a mechanic ( knowing mechanical details = knowing
mathematical development of method.) But I certainly have to know when, and
how to brake. This is concidered appropriate by me as a driver because I
understand the _concequences_ if the car does not stop (= Demonstrate by cases
concequences of wrong model in statistics).
Now, if I as a driver may drive safely without being a mechanic, I also have
to understand my limitations. I have to know that I am to stay on ordinary
roads, and not approach Sahara. If I was to go there, or taking my car other
unusual places, I _should_ be equipped with a lot more tools, be a pretty good
mechanic, or have one beside me.
It all is very reasonable outside statistics. Why should it be complicated
inside?
Oh, I am sorry. I am lowering the level of this group by being emotional, and
talking to knowlegable people the way I use to talk to my students.
But I think what I say is important, and this is my usual way
to get it through. So the message is not cancelled.
And, I am not writing an article, so I do not reread what I have written, to
condece it. It just is my lunch table chat to friends in a group which I enjoy
very very much.
Please forgive me.
Jan Gunnar
----------------------------------------
In article <38j20a$gbl@b.stat.purdue.edu> hrubin@b.stat.purdue.edu (Herman
Rubin) writes:>From: hrubin@b.stat.purdue.edu (Herman Rubin)
>Subject: Re: Seeking...understanding...
>Date: 25 Oct 1994 08:42:34 -0500
>In article <9410242134.AA04026@landfair.math.ucla.edu>,
>James Hilden-Minton <jhilden@math.ucla.edu> wrote:
>>Forwarded message:
>>> From edstat-l@jse.stat.ncsu.edu Fri Oct 21 05:36 PDT 1994
>>> Reply-To: RDAWSON@HUSKY1.STMARYS.CA
>>> I agree with James Hilden-Minton that the use of "likely"
>>> that I made was not a statistically valid comparison. The main point
>>> that I was trying to make was that "probable" isa word with an exact
>>> technical meaning that we should expect everybody doing anything with
>>> statistics or probability to use correctly. This is *not* the sense
>>> in which "probable" and "likely" are synonyms - as colloquial words
>>> whose meaning, to most people, is not the statistician's definition
>>> of probability.
>>We should recognize that meaning is not to be identified with definition.
>>For example, what it means to be sick is what we experience when we are
>>ill, and this meaning of sickness may have little to do with a physician's
>>definition of sickness. Likewise, the meaning of life is not the definition
>>of life, but in my opinion it has more to do with our experience of life
>>than with our intellectual ability to articulate a pithy definition.
>This occurs in everything else as well. The intuitive words "long"
>and "slow" need to be made precise to to anything with them. Also,
>"natural" language is very imprecise; this is a very good reason why
>it is necessary to use precise mathematical notation. Unfortunately,
>many, if not most, of those taking beginning statistics courses are
>not only not conversant in mathematics (the choice of words is deliberate)
>but many have even been brainwashed against it. I am not all that sure
>about some of the textbood writers. :-)
>>> That colloquial meaning is also, unfortunately, muddled. It
>>> seems to refer to a mathematically inconsistent concept which is, at
>>> the same time, both a measure of what one should bet on and of how well
>>> the evidence fits the theory. I'm not suggesting for a moment that we
>>> should try to make this the basis of statistics. It's muddy thinking and
>>> it has to go when students start to learn probability.
>We must face the unpleasant fact that most ordinary concepts are muddled
>and inconsistent. But even the Egyptian architects, and the Sumerian
>merchants, and the early Greek philosophers, realized that precise
>communication was necessary. One could not tell one worker on the
>pyramid to put in a small block of limestone, and another a large block,
>etc., and get the pyramid built. It was necessary to quantify.
>So the idea of a linear scale for length and time was developed.
>It was much later that the idea of a linear scale for probability
>emerged. Just as the ancients realized that construction required
>a more precise scale for length than crude visual observation, those
>who started the mathematical field of probability recognized that
>the same was true here, and that the words "probable" and "likely"
>and "improbable" and "unlikely" had different and inconsistent
>meanings in ordinary language, just as "large" and "small" have.
>What makes things harder in probability is that one cannot get
>measurements of probability which have the type of accuracy of
>measurements of length and time.
> ......................
>>> However, we should understand that we are using the word with a
>>> meaning that is not what our students are used to - we are not just
>>> making their old meaning of the word a little more precise for them. In
>>> class, the word "probability" has a new meaning that they have to learn.
>>> Therefore, perhaps we should treat the word like other exact technical
>>> terms, and try not to use near-synonyms for variety. Algebraists don't
>>> alternately refer to the "field" and the "meadow" of real numbers, after
>>> all.
>>Algebraists have little need or ability to communicate their theories to
>>people who are not mathematicians. In field theory, algebraist are not
>>intending to define what a meadow is. They don't seem to be interested
>>in any empirical objects, only theoretical constructs. That's just
>>fine for algebraists.
>>However, there is a great need for statisticians to communicate their ideas
>>to the masses, and they should develop the ability to do so. It stikes me
>>as cynical to suggest that students be instructed to discard the social
>>meaning and personal experience of probability for an abstract, technical
>>definition.
>This is not the case; those who understand algebraic notation, without
>which precise communication is essentially impossible, can learn, if
>the ideas, rather than just the manipulations, are presented, that
>something like this is what a precise formulation of the loose meaning
>of probability must be. It is not hard to convince them that the model
>chosen is the only one which meets certain criteria. Length could be
>defined on a logarithmic scale; there are reasons why it is not. The
>same holds for the linear scale for probability.
>This leads to a form of double-speak: The statistician speaks
>>of probability with a peculiar meaning while the masses hear of probability
>>with some other unrelated meaning, but only the indoctrinated know the
>>esoteric meaning. This is not communication in any healthy sense. Chance,
>>likelihood, risk, uncertainty, bias, probability, reliability, odds, these
>>are all words that the people use and experience.
>People use these, but do NOT experience them. They do not experience
>length, either. That people cannot "intuit" probability ACCURATELY does
>not mean that sloppiness should prevail. That people cannot accurately
>tell which of two rods at different distances is longer is no reason not
>to have a formal notion of length. That people cannot accurately compare
>durations is no reason not to have a formal notion of time.
>It is the task of the
>>theoretician to give an account which is faithful to the use and meaning
>>of these expressions. The theoretician must show how specific formulations
>>are useful interpretations of their pre-analytical experiences.
>There are some words which are ill-chosen. One of them is "expectation";
>this is not something to be expected. The expected number of A's in a
>course is not 4.6; the expected number of children in a family is not 2.3.
>Another one is "significance"; it has nothing whatever to do with the
>practical importance of the difference. But odds to a horse-player
>(if he knows what he is doing) and to a probabilist are the same; he
>should bet on a horse if his odds are better than the ones quoted for
>payoff, and not otherwise.
>--
>Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
>Phone: (317)494-6054
>hrubin@stat.purdue.edu (Internet, bitnet)
>{purdue,pur-ee}!snap.stat!hrubin(UUCP)