Reporting the relationship between variables: correlation or regression?

Question

I'm doing my dissertation in Accounting and I developed a questionnaire to test certain hypotheses on the relationship between independent variables and a dependent variable. All were measured on a 5-point Likert scale. I am using SPSS to analyse the data. The variables are all non-normal (I used Kolmogorov-Smirnov test) and so I will be using Spearman correlation to test the relationships.

I was wondering whether this is enough? Should I use some form of regression as well? And if I do, do I still include the Spearman results? Do studies usually include both?

I have not studied any statistics so this is quite new to me.

Answer 1

This can't be answered by us, only by you. But I can give you the information you need to make the decision.

In correlation (whether Spearman or Pearson) we are looking at the relationship between two variables. Neither is dependent or independent - they are treated equally.

In regression (of any sort) one variable is the dependent variable and one or more are independent. The measurement of the dependent variable is critical. If it was measured on a 5 point Likert scale, then you probably need ordinal logistic regression.

Which to choose? Since you say you have a dependent variable, that indicates regression. But if you are new to statistics you might not be able to run and interpret an ordinal logistic regression, so you might have to hire a consultant.

Answer 2

To report the relashionship between variables, you may prefer a scatterplot. As part of the Royal Society of Chemistry's Analytical Methods Committee, Prof Brian Ripley used to write short expository notes for ANALYST. The note entitle "Uses (Proper and Improper) of Correlation Coefficients", which appeared in ANALYST, SEPTEMBER 1988, VOL. 113 1469, is pertinent to your questions. In particular, the abstract says:

The statistical concept of a correlation coefficient r is frequently misused in 
interpreting analytical data. In particular, a large value of r does not indicate a 
linear relationship between two measurements; this is demonstrated graphically. For many 
of the problems for which a correlation coefficient is used it would be better to 
present a scatterplot.

While the most useful summary of the relationship between the x and y measurements is often a scatterplot, many would like a more objective measure of linearity than visual inspection of a scatterplot. This raises at least two questions: What is the proper use of a correlation coefficient? and How do we assess linearity?, both of which are addressed in Ripley's report.