From: tarkkone@klaava.Helsinki.FI (Lauri Tarkkonen)
Newsgroups: sci.math.stat
Subject: Re: What are P and reliability in factor analysis.
Date: 11 Apr 92 08:22:58 GMT
Organization: University of Helsinki

In <5425@kielo.uta.fi> csmani@arovuokko.uta.fi (Marko Niinim{ki) writes:

>Hello, and sorry 'bout this simple question.

>I'm using factor analysis only in order to find out whether these factors
>are plausible. The program I use (Survo) is quite unknown everywhere except 
>in Finnish universities. 

Survo module FACTA uses the same Maximum Likelihood algorithm that is 
used for example in the more known program EFAP II, made by K.G. J|reskog,
and the method is quite same as used by any statistical package appluing
the maximum likelihood method.

By the way, Your assesment about the distribution of survo is innaccurate.
From the a bit over 1000 copies sold, only one third is in the univeristies,
two thirds is sold to the market outside the universities. 

>The communality-values (h^2) for each variable are high, but in addition to
>these the program gives more information, notably "P" and reliablity (reliability
>being high, 0.94....).
>So, I wonder if I can conclude from either of these that the number of factors
>I'm using (or actually, the number of factors mentioned in literature concerning
>this ergonomy-method) in the analysis is sufficient. 

The P-value refer to the probability of the log-likelihood.  Briefly explained
you can say that your null hypothesis claims that the number of factors you
have choosen is sufficient and your alternative hypothesis is that any number
of factors bigger than the present is correct. The high P-value tells you
that, there is no reason to reject your null-hypothesis.

The reliability used by J|reskog is the Tucker-Lewis coefficient of relia-
bility and the general meaning of it is to give the reliability of the 
facroe solution as such. The implementation of the coefficient is biased
and you easily end up with reliabilities over unity. I would say that the
Tucker-Lewis approach to the reliability problem has some shortcomings.
I would not recommend the use of it. 

>I also suppose there is a sort of "common communality", some indicator that 
>tells how much of values of variables can be explained by the factors. I 
>would like to know what, in statistics, this is called and if it can be 
>derived from some of the information given (either h^2-values, P or 
>reliablity).

The reliability is in a way a function of communality, because you divide
the variation of a observed variable to the variation caused by the factors
(true scores in true score theory) and measurement errors. The realiability
af a measuremet scale is the proportion of the variance of the scale caused
by the factors (true scores).

To more specific elaboration of the problem i refer to
Lauri Tarkkonen: On reliability of composite scales, publisher Finnish
Statistical Society, 1987. ISBN 951-95421-0-8. c/o  Panula, Tilastokeskus
tel 90-17341.

- Lauri Tarkkonen

>Greets,
>Marko
>-- 
>Marko Niinimaki, Tutkimusapulainen/Research assistant, 
>Tyosuojeluhallitus/Ministry of Labour Protection, Tampere, Finland
>csmani@uta.fi / C=fi ADMD=Fumail PRDM=inet O=uta S=csmani
>Addr: Satamakatu 5 c 77, 33200 Tampere, Finland  Phone: (358-31-) 22 99 32
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