when we discuss things like power, beta, type I error, etc. ... we often
show a 2 by 2 table ... similar to
null true null false
retain correct type II, beta
reject type I, alpha power
i think that we need a bit of overhaul to this typical way of doing things ...
1. each cell needs to have a name ... label ... that reflects the
consequence of the decision (retain, reject) that was made
i propose something along the lines of
null true null false
retain type I correct, 1C type II error, 2E
reject type I error, 1E type II correct, 2C
then, we have names or symbols for probabilities attached to each cell
null true null false
retain WHAT NAME/SYMBOL FOR THIS?? beta
reject alpha power
DOES ANYONE HAVE SOME SUGGESTION AS TO HOW THE UPPER LEFT CELL MIGHT BE
REFERRED TO via A SYMBOL??? OR, SOME NAME THAT IS DIFFERENT FROM POWER BUT
... STILL GIVES THE FLAVOR THAT A CORRECT DECISION HAS BEEN MADE (better
than making an error)?
2. i think it would be helpful to first identify each cell with a
distinctive label ... describing the decision (correct, error) and ... the
type ... 1 or 2
3. i think it would be helpful to have a system where there are names for
EACH cell (why should the poor upper left be "left" out in the cold??) ...
FIRST ... then some OTHER name/symbol for the probability associated with
that cell
confusions that might be avoided would be like:
a. saying type II error is the same as beta ...
b. saying that power is NOT a name for a decision but, rather, THE
probability of making some particular decision
we have special names for errors of the first and second kind .... type I
and type II ... and we have symbols of alpha and beta to represent their
associated probabilities
we have power which is supposed to be the probability of making a certain
kind of decision ... but, no special name for THAT cell like we have given
to differentiate the two kinds of errors one can make ...
any support out there to try to right this somewhat ambiguous ship?
==============================================================
dennis roberts, penn state university
educational psychology, 8148632401
http://roberts.ed.psu.edu/users/droberts/drober~1.htm
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