11 December 2020 — The following essay is taken verbatim from a posting I made to the discussion forum for a class in my Doctor of Business Administration program at Keiser University.

Sometimes, but not always, variables of interest in survey studies depend on each other (Alreck, 2019). As Figure 1a shows, this sets up two kinds of relationship: causality and correlation. Causality is the stronger of the two. It means that variable A, called the independent variable, has whatever value it happens to have because of extraneous factors, but variable B gets its value because of variable A’s value. Mathematically, we symbolize this relationship as A → B, which means “A implies B.” If extraneous things change A’s value, variable B’s value will change as a result.

Correlation, however, is weaker. It just means that both A and B generally change similarly. Figure 1b shows one possible way this can happen. In this instance, not only there is a causal relationship between A and B, there is also a causal relationship between A and C. In such a case, there will also be a correlation between B and C, but no causal relationship between them. If researchers include questions about only B and C, but fail to ask about A, they will miss the most important part of the relationship.

Simple statistical analysis can thus show correlation, but cannot show causation (Alreck, 2019). For example simple scatter plots can show cross-correlations between variables, and even show degrees of correlation (Weiss, 2012). They cannot, however, prove that there is a causal relationship between them (Alreck, 2019). That requires some outside information (Bekiros & Sweeney, 2018). Essentially, an understanding of the system under study must be available to ensure that all relavant variables have been observed (Coetzee & Erasmus, 2017).

Figure 2 shows a more complicated web of interrelationships between variables. A second independent variable D appears that also affects the value of variable C, but not that of B. In this case, B is still closely correlated with A, but A’s correlation with C is less close because D variations also affect C. To find causation in such situations, use factorial ANOVA (Steinberg, 2008).

References

Alreck, P. L. (2019). Survey research handbook (3rd ed.). McGraw-Hill Education.

Bekiros, S., Sjö, B., & Sweeney, R. J. (2018). Pitfalls in cross‐section studies with integrated regressors: A survey and new developments. Journal of Economic Surveys, 32(4), 1045–1073.

Coetzee, P., & Erasmus, L. J. (2017). What drives and measures public sector internal audit effectiveness? Dependent and independent variables. International Journal of Auditing, 21(3), 237–248.

Steinberg, W. J. (2008). Statistics Alive! Sage Publications.

Weiss, N.A. (2012). Elementary Statistics (8th ed.) Addison Wesley.