Dear Rekha,  The suggestion given concerning converting to z-score is correct because a z-score avoids the problems of unequal units encountered in percentile ranks. Also, you should state the alternative hypothesis (not the null).  

I disagree with Stephen because Likert scales are treated as interval measure, therefore,  the suggestion of a z-score is appropriate. Here, the reference is total score. I believe Stephen is confusing Likert item with Likert scale. I have culled the document below from JALT Testing & Evaluation SIG Newsletter of March 2011, p11. I agree with his reference to B. 

"With regard to Likert scales -

1. Likert scales are totals or averages of answers to multiple Likert items.

2. Likert scales contain multiple items and are therefore likely to be more reliable than single

items.

3. Naturally, the reliability of Likert scales should be checked using Cronbach alpha or another

appropriate reliability estimate.

4. Likert scales contain multiple items and can be taken to be interval scales so descriptive

statistics can be applied, as well as correlational analyses, factor analyses, analysis of

variance procedures, etc. (if all other design conditions and assumptions are met).

Dear Rekha

I agree with both the above. The issue is transformation. Even though you consider likert scale, theoretically as a continuous data (most do't agree), you can go for transformation. The issue is interpretation of the analysis. Moreover, based on your explanation, it seems a case of multiple regression, B as dependent variable. Even, if you have conducted an controlled experimenter for the data you can go for ANOVA.

Regards

Rekha, 

First and foremost congratulations on being done with your data collection! you are almost there. 

Opinion data on a 5-point scale is interval data. To say that there is no meaningful values between 1 and 2 is erroneous and antiquated. It derived from Steven's (1951), but this has been counter argued by Borgatta and Bohrnstedt(1980) and many others. Studies by Gaito (1980) suggest treating scales as ordinal or interval lead to the same conclusions regardless of using parametric or non-parametric analysis. In your paper, if you feel like you need to justify the interval treatment I would suggest citing a more up-to-date view of Likert scales such as Morgan (2006) or Vaske (2008). 

As an example, grades are given in a categorical fashion (A,B,C,D, F). However as you aggregate them, they become interval data. A student with a 3.9 GPA did better in school than did a student with a 3.2 GPA. The same is true when you perform additive composite scales, and this is done on a regular basis in social psychology and sociology. 

Z-scoring these data is not an issue and may lead to a better performance in the CFA. Please understand that as you transform them your results will be based on z-scores rather then on the original scale. This is fine, but some readers may find that the z-score is not intuitive. You can address this by being clean in your reporting and discussion. Can see a CFA that I published recently to see the methods that I used 

Good luck to you in your efforts. 

Cordially, 

______________________________________________________________________

Loren Chase, PhD 

Article Measurement of Wildlife Value Orientations Among Diverse Aud...

Data Measurement of Wildlife Value Orientations Among Diverse Aud...

Excellent comments by Loren! I am very  impressed.

Thanks and GIg 'em! I proposed under the century tree!

To Rekha's question: z-score is just a linear transformation of the original scores, so no impact on distributions, correlations, (standardized) mean differences, and so on (agree with Stephen and others).  The only salient feature is that unstandardized and standardized coefficient estimates should be the same (since you'd be standardizing all of the variables)...not unlike using correlations as input vs. covariance matrix. in CFA

However, to touch on the "what-the-heck strength of data do I have when people respond to items using an ordinal response scale?" question, Likert's 1932 monograph, A Technique for the Measurement of Attitudes (see link below) is worth a look.  He showed that his integer scored response scale (e.g., 1 = "Strongly disapprove," 2 = "Disapprove," 3 = "Uncertain," 4 = "Approve," 5 = "Strongly approve") values correlated so highly those derived from more complex scaling methods (that did imply interval strength, normality, and independence), that there was no compelling reason to bite off the more complex methods. 

Yes, Likert's method refers to using scores from summated scales, not the individual items.  You'll find, however, numerous instances in the literature wherein people have used a single such item score as the variate of interest.

Finally, I agree with Stephen that CFA doesn't necessarily sound like your best option. From your hypotheses, it seems that a path model, with either partial or full mediation ("D" is the mediator of A, C), could more directly help evaluate your questions.

http://www.voteview.com/pdf/Likert_1932.pdf