Hi all.
This debate seems to be moving away from presenting statistics as such but
is touching on some important distinctions in statistical language!
I have always understood measures of association as assuming no causal
relationship and only providing (or attempting to provide) an indication of
the extent to which variables are observed to move in the same or opposite
direction ie strength. Thus the formulae for bivariate measures are
symmetric in X and Y. Test of association based on sample data may indicate
a non-zero level of association in the population, which may be weak or
strong. I agree that the significance level at which the null hypothesis is
rejected (if that is the outcome) has no bearing on the strength of the
observed association.
Regression, on the other hand, does assume a particular causality.
Bivariate f
formulae are not symmetric in X and Y. However, in a manner similar to
association, the significance level at which the null hypothesis of a zero
slope coefficient may be rejected has no bearing on the size of the impact
that a unit change in the explanatory variable will have on the dependent.
There are many cases in statistical consultancy where a highly significant
effect is found which, operationally, is meaningless to the client company
because of its very small impact.
Chris Webber
Director, ASQM Consultancy Unit
Faculty of Computing, Engineering and Mathematical Sciences
University of the West of England
Coldharbour Lane
Bristol BS16 1QY
Tel: +44 (0)117 32 83140 (office)
+44 (0)7979 547 932 (mobile)
Fax: +44 (0)117 32 82734
www.cems.uwe.ac.uk/asqm
The views expressed are those of the sender and do not necessarily represent
those of the University.
----- Original Message -----
From: "Paul Spicker" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Sunday, November 06, 2005 3:23 PM
Subject: Re: How should we present statistics?
> I have to apologise for using a word (slope) that caused more confusion
than
> it clarified; I dashed off the initial message in between teaching
sessions
> and clearly didn't say what I'd intended.
>
> The point I wanted to make was that statistical significance is not what
> most people mean by strength of association. Take, for example, the
> relationship between price and quantity on a demand curve. The
correlation
> between observed variables might be perfect, but the quantity demanded
could
> be almost inelastic to price.
>
> Strength of association means, as I wrote, that "changes in one variable
> have an appreciably large impact on the other." What is "appreciably
> large" is a value judgment, not a mathematical one. If, for example, you
> want to argue that violence on TV is strongly associated with violent
> activity in the community, you'd need to show not just that one goes up or
> down in line with the other, but that a lot of violence on TV leads to a
lot
> of violent activity. If a lot of violence on TV leads only to a little
> extra violence in the community, that would show some association, and it
> could have a statistical correlation at a very significant level (it
depends
> e.g. on how big the sample is), but it would not be a strong association
in
> the sense I've just used. The value judgment comes in because what we
think
> of as "a lot" or "a little" seems to be based in our evaluation of their
> relative importance, rather than any testable numerical criteria, such as
> proportionate change.
>
> I'm not sure I understand all of Ray's points. I don't understand, for
> example, why correlation is descriptive and regression is judgmental. I
> can't share the view that statisticial significance doesn't matter at
all -
> it's the main way we compare the outcomes of non-parametric tests. I
> suspect, though, that we share a mistrust of cavalier user of
"significance"
> as a way of describing the relationship between variables.
>
> Paul Spicker
>
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