I'm trying to understand the relationship between pregnancy experience and well-being through my research. I've used 2 scales; one of Pregnancy Experience Scale (PES) (20 items) with 4 points Likert scale and the other of Well-being (5 items) with 6 points Likert scale. My sample size is 101. Since the item responses are in ordinal data I was planning for Spearman's Correlation. What are the other alternatives and possibilities for further analysis (like Pearson Correlation, Linear regression, Multiple Regression)?
N.B:
1. Can the total scores be considered as continuous data?
2. Can Pearson Product Moment Correlation be done, as the data is skewed (there is no normality)
3. Is it required to convert raw scores of both scales to Z-scores?
(Info. For PES there are 6 different scores: Hassles Frequency, Hassles Intensity, Uplift Frequency, Uplift Intensity, Frequency (hassles by uplifts), Intensity (hassles by uplifts))
1. No. Specifically with ordinal data we don't know what the gaps between scale items represent. Summing items or averaging doesn't get round this unless we assume that the gaps are evenly spaces with respect to a continuous scale plus random error. However, under certain circumstances this might not be terrible as an assumption - especially with a validated scale. But ideally one would treat scale items as ordinal. This is more plausible if the scale items are distributed somewhat unimodally without marked skew.
2. Yes. You can calculate it. There is no assumption about normality inherent in calculation Pearson's r. The assumptions of normality relate to inference, but you can also use bootstrapping. Of course other correlation approaches or alternative parametric models (e.g., ordinal logistic regression) might be better in terms of statistical power etc. in some contexts. Even with a standard linear model the assumption is about the residuals of the model are drawn from a normal distribution - not the individual variables.
3. I don't think that's helpful. It sometimes used with ranks to convert them to z scores to increase statistical power, but I can see any value for a Pearson correlation. This is because the Pearson correlation is the slop of a regression of two variables X when both are z scored.
For this I would consider just using an ordinal correlation such as Kendall's tau, Spearman's rho or gamma. That assumes you are just interest in the relationship between the two. You could compare this to Pearson's r. Often they are very similar - but if they are very different that's an indication that bivariate normality does not hold and the ordinal correlation is superior. For more complex model as I'd consider ordinal regression or a an ordinal structural equation model.
The right option would be using polychoric correlation; you can hand compute if you need to. Statistical software will process the data; however, it's not correct to use Pearson for ordinal data (unless your Likert scale is greater than 8).
No, its not better econometric techniques for your model.
Regards,
D. Eastern Kang Sim I agree that the polychoric correlation is an important option to consider for ordinal data. This is probably the preferred choice if you are OK assuming an underlying latent variable with a normal distribution. If not tau, Spearman's rho or gamma are ordinal measures with weaker assumptions.
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