Newsgroups: sci.psychology
From: mgreen@cs.toronto.edu (Marc Green)
Subject: re: Psychology and statistics
Organization: Department of Computer Science, University of Toronto
Date: 25 Aug 92 19:32:55 GMT

schabert@samish.Stanford.EDU (Vernon Schabert) writes:

|> Statistics should be avoided if possible. Anybody who thinks that
|> statistics are "objective" knows very little about statistical theory
|> or its history.  Any use of statistics requires a host of assumptions,
|> not only about things like underlying distributions and metric
|> properties of the data, but about interpretation.

-Yes and no.  Most Gaussian (normal-theory) statistical models make
-many assumptions about the distribution of one's data, but many
-nonparametric techniques exist that make fewer assumptions about data.
-Also, statistical tests are often robust to violation of some of their
-assumptions.  

The key words here are "fewer" and "often."

-If you've examined your data before modeling them with
-statistical procedures, you should know whether your data fit the
-assumptions of the model, and thus how much you should trust your
-modeled results.

Many of the required assumptions cannot be discerned simply by looking
at the data: the metric properties, for example.

-Assumptions about interpretation are completely in the hands of the
-researcher.  Statistics should support a researcher's interpretation
-of data, but should not assume the role of interpretation themselves.
-Unfortunately, many psychologists forget this.

The problem is that there is no clear interpretation of the numbers in
any statistical formula. How can an experimenter use statistics to
interpret data when the numbers in the statistical formalism have no
clear meaning?  Blindly applying a formalism to a set of data is not
going to produce "objective" or meaning ful results. The concepts in
the formalism have to be interpreted. Most researchers (implicitly)
assume that probabilities reflect the "long run frequency"
interpretation. But this is based on a number of assumptions, none of
which has been validated. 

|> The use of statistics has other problems too. It usually means
|> averaging subjects together. It is easy to get "results" which do not
|> reflect any individual subject and it is easy to miss secondary
|> effects. 

-A statistic is an estimate of a parameter from a population.  Why
-someone would use statistics to reflect the qualities of a particular
-individual is not completely clear.  Statistical models allow us to
-generalize about a population, provided the sample is truly reflective
-of the population.  If one wants to know about a particular

If 10 subjects score 100 and 10 score 200 then the poulation mean is
150. Does this reflect the population? Hardly. This is obviously an
exaggerated example, but reflects a common problem in using statistics.

|> Statistics are used as a means of control. But they are not a
|> substitute for experimental control, and too often, this is exactly
|> how statistics are used. The best experiments use a few subjects with
|> tight experimental control.

-Again, yes and no.  Statistics are used as an arbitrary yet objective
-method by which to support arguments made by the researcher.

But statistics are not objective. See Fine.

-Statistical modeling itself has nothing to do with control; both

Huh? The whole purpose of statistics is to partial out the effects of
variability due to uncontrolled variables. 

-rigorously controlled experimental studies and loosely bounded
-correlational data can be modeled by statistical methods.  Control,
-like interpretation, is completely in the hands of the researcher.

Huh? Science is the art of making controlled observations. Most of an
experimenters technical training is in learning how to properly
control studies. Control is about the only thing that is in the
researchers hands.

-Lack of control means that relationships should be interpreted as
-relationships, and nothing more.  When other pote

Huh? Lack of control means that effects cannot be attibuted with
certainty to the independent variable. 

Marc Green
Trent University

Newsgroups: sci.psychology