On 4 Jan 2001 20:53:04 -0800, [EMAIL PROTECTED] (Will Hopkins)
wrote:
> Rich, thanks for those comments. I have a few remarks in reply.
(me) >
> >If you have a criterion (reaction time, etc.) where you average dozens
> >or hundreds of observations to make a point to be analyzed, the
> >"effect size" is magnified by averaging. That is, if you can change
> >an average by .01, that fraction is a lot bigger fraction of the
> >between-Subject variance (of averages) than it is of the
> >between-trial variance.
WIll >
> Effect size in experiments or cross-sectional studies is the change
> or difference in the mean of something expressed as a fraction or
> multiple of the between-subject standard deviation. As such, it is
> not biased by sample size. Some people erroneously use the standard
> deviation of the change score or of the residuals in experiments, or,
> as Rich appears to be suggesting, the standard error of a mean. Is
> that what you mean, Rich? I don't quite follow you. Between-trial
> variance is not an issue here.
Are you following a prescription from somewhere?
Are you saying that "effects" are only "effects" if they are
between-Subject? (In your book, what are they called, otherwise?)
In my use of ANOVA terms, I can have an experiment with single
subjects, and other subjects as replication; where the "effect size"
would certainly be based on between-trial variance. When there are
hundreds of trials, it will almost assuredly be more robust to
generate means (to crunch down the serial correlation), and then I
will be dealing with the SE of a mean.
At the other end, I can have Group-effects where there's no such thing
as a useful "between-subject" variance. If the subjects are scored
0/1, then what is useful is the SD of a group. Generally speaking,
the "effect size" is most sensible in terms of the error of the ANOVA
- however that might be defined. But you need to be more flexible if
you are contrasting results from several analyses, with various error
terms.
< snip, some >
> I think I've resolved this question with a colleague. We likened the
> heritability of a given trait, for example, jump height, to the
> relationship between that trait and some other explanatory variable,
> such as leg length. The R^2 for leg length explaining jump height
> might be 0.36. Now, 0.36 is a gross underestimate of the effect of
> leg length on jump height.
... well, no, from what you say, it is the estimate of the *variance*
which is what happens to be additive. It is a "gross underestimate"
(apparently) if you are trying to get the regression coefficient. For
this particular thing.
> We should use root(0.36), i.e. 0.60,
> because, if you experimentally change leg length by one standard
> deviation with growth hormone during development, or if you move from
> one individual to another who differs by one standard deviation in
> leg length, you will find that jump height changes or differs on
> average by 0.60 of a standard deviation for jump height. Trust me,
> it's true. 0.60 is large on Cohen's scale, whereas 0.36 is moderate.
- I will mention again, if you are not talking "behavioral science,"
Cohen offers no assurances for the relevance of his scale.
> Now let's bring in heritability. For the sake of simplicity, let's
> assume leg length is entirely inherited and is the only inherited
> factor explaining jump height. Therefore we would find that the H^2
> for inheritance explaining jump height is 0.36. So we should
> interpret H, but not H^2, when we talk about magnitude of
> heritability, and we should do it in the following way: there is
> some variable, the values of which are determined by heredity, such
> that a change in one standard deviation of the variable results in a
> change of 0.6 standard deviations in jump height. Of course, there
> are lots of variables contributing to jump height, but you can
> combine them into one composite virtual variable for the sake of
> understanding what H means.
My recent problems with H have to do with assessing the RANGE of
natural variability, especially in humans, when it is expressed across
generations.
Coefficients H are fairly sizable for heritance of height and IQ.
How do you use data in Japan,
where heights for men are rather homogeneous right now at 175 cm, and
they were also homogeneous in 1940 at 150 cm? - For most purposes,
you don't need and don't want that "between generation" effect, but
you should respect it because you do need it for other purposes.
IQ, it seems to me lately, must be more like an "attitude" than
something that is narrowly, genetically determined. The population
SDs are about 16 points (by definition), but the tests have had to be
rescaled repeatedly since the 1940s to accommodate a world-wide
increase in measured IQ of about 0.5 SD per generation.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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