# Factor analysis or just stick with compare means?

I would be grateful if somebody could assist me with the questions below This is for my dissertation (I am relatively new to SPSS and indeed to statistics).

I have a small set of cases (N=41) of companies who took my questionnaire. There are 2 5-point Likert scale sets of questions: - one set is intended to determine whether the company uses performance measurement for a cost advantage strategy or a differentiation strategy (8 questions) - one set is intended to measure if the company finds performance measurement useful (6 questions) The companies have already been classified in the high (Hi) performers and low (Lo) performers.

I have computed the mean scores for each group and was able to compare the means using the t-test for the two groups (Hi/Lo).

I also did a factor analysis, decided on two factors for the 1st set (KMO=0.74) and one for the second and ended up with factor scores as variables. These range from say -2.6 to +1.3. Now I do not know what I can do with these results.

I would really like to be able to determine that if a company scored high on the second set of questions (Usefulness) and high say on the cost advantage scale that this company used performance measurement for cost advantage strategy. Sort of a usefulness scale "enhancing" the other two (if this makes sense).

I would then be able to find out if the high performer group follows a particular strategy or not (same for the low performers).

Could regression or correlation do that?

Nic

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First, if the measure of performance is really numeric and was classified into high vs. low by someone, it would be better if you could get the original measure. You could then do linear regression using that measure as the dependent variable and the two factor scores as independent variables. You might want to include the interaction between them, as well.

If "high" and "low" are all you can get, then you can do something very similar except you will need to use logistic regression rather than linear regression.

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Peter, thanks for the reply. The measure of performance is from a subjective point of view (in the upper 10%, upper 25% down to the lower 10%...5 point) –  Nic Sep 28 '12 at 10:20
Oh, in that case, probably the thing to do is ordinal logistic regression. –  Peter Flom Sep 28 '12 at 10:23
Peter I really appreciate your replies. I can argue that the hi performers are the ones responded in the upper 10% and all others lo performers. Thus having two groups lo/hi. What about the problem " Sort of the usefulness scale "enhancing" the other two (if this makes sense)." ?? –  Nic Sep 28 '12 at 10:34
In general, it is better to have more groups than fewer and to do ordinal than binary logistic. By cutting it into two groups you are saying the bottom 90% are all alike. That rarely makes sense, but it might in your situation. –  Peter Flom Sep 28 '12 at 10:38
Also, I just noticed you have only 41 companies. In that case, the top 10% would be 4 companies. That is too few - any analysis would risk being overfit. Probably best, in this case, is quartiles of 10 companies (with one group having 11). With two IVs that's still a bit overfit, but not too horrendous. –  Peter Flom Sep 28 '12 at 10:40
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Given what Peter has said and what he and the OP said in comments, I think the categories should just be assumed to be correct and do the analysis from there. I don't see exactly why a factor analysis was conducted. A test of difference between the means of the two groups may be informative but since it is the average of Likert scale variables which are ordinal in nature a nonparametric test such as the rank sum test might be more appropriate.

I agree with Peter that a logistic regression using the repondents individual average Likert score from the first set of questions and the same average Likert score for the second set of questions could be used as covariates for predicting the group. The importance of these variables in the model might address your question.

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I thought that the factor analysis would produce scores that can then be used as nominal in the subsequent analysis. –  Nic Sep 28 '12 at 11:50
How would you go about Logistic regression in SPSS? and how to interpret it? I put in the dependent the performance scale, and in the factors the 8 likert items? and in the covariate the 6 likert items? –  Nic Sep 28 '12 at 11:59