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
