hello again. i'm just gonna be nit-picky because i like you and not because i'm trying to be mean. otherwise i'd just let your thread sink into the depths of oblivion.

Uses & grats. These are the dependent variables. 59 5-point Likert-type items that have been put through factor analysis resulting in 12 factors with eigenvalues > 1.

bad rule for extracting factors. it is well-known that it extracts more factors than it should and its susceptible to things like the number of variables in the dataset. so like say you have a scale that has 100 items and one that has 10, but they all only have a 1-factor structure. the eigenvalue>1 rule would select more factors from the first scale for no other reason that it has more items and a bigger covariance/correlation matrix.

the most accurate methods to indicate the number of factors to extract are computer-based, monte carlo simulation methods. particularly one that is called Parallel Analysis. this is what is recommended by the literature.

for a very easy-to-use web-based app to do parallel analysis on your data click here:

http://ires.ku.edu/~smishra/parallelengine.htm
for a more in-depth discussion (but still accesible to the non-initiated in the secret mysteries and dark arts of psychometric analysis) click here:

http://pareonline.net/pdf/v12n2.pdf
The first question I have a handle on; I ran a one-way ANOVA using the factor analysis scores and the three scenarios, and that worked like a charm.

bad move again. it is well-known that using factor scores as if they were observed scores in analyses meant for observed data (so multiple regression, ANOVA, etc.) results in biased parameter estimates and spurious signifiance. a more in-depth discussion would be:

Tucker, L. (1971). Relations of factor score estimates to their use. Psychometrika, 36, 427–436.

Shevlin, M., Miles, J. N. V., & Bunting, B. P. (1997). Summated rating scales: A Monte Carlo investigation

of the effects of reliability and collinearity in regression models. Personality and Individual Differences,

23, 665–676

the main problem, however, stems from the fact that factor-scores are not invariant to rotations. if you find a factor analysis solution that fits your data decently and extract factor scores to do some multiple regression/ANOVA analysis type i can just as easily use the same factor solution, rotate it until i get a different set of scores and do an analysis that might contradict yours, using the

*same* data and the

*same* factors. this is referred to as the 'factor indeterminacy problem' (which is actually a collection of problems) but the easier one to grasp is this one, which starts by the fact that there are an infinite number of factor rotations that fit the data equally well.

if you want to play in latent-variable land (so factors form factor analysis) you would need to do Structural Equation Modelling (SEM).

The other two questions are where I'm getting a little stuck. For #2, you can't do a one-way ANOVA using a continuous independent variable, so would it make sense to break subjects up into quartiles and just run the ANOVA as if the continuous variable was four groups? Or is there a better way?

As for #3, I'm not sure what test at all that would be. Any recommendations?

i'm not sure if you know this or not (some people do, some people don't). ANOVA *is* regression. it just happens to be a very constrained type of regression where all the predictors are categorical. there is nothing that would prevent you from doing a similar analysis if you just conveniently code your predictors (you know... dummy coding, effects coding, all that stuff) to handle categorical/nominal data, leave the continuous data as it is and fit it like a linear model. i won't go into the details as for why discretizing a continuous variable is not a good idea... but, trust me on this one, it is not.

then again this is solely contingent on the statistical expertise of the people who will review your work. i'm pretty sure you can do outrageously wrong things in your field (which i believe is media/communication studies, right?) and nobody would bat an eyelash