The Correlational

Author

David Huron

The Correlational Study

Correlational studies aim to identify linkages or relationships between things. We say two things are correlated when there is some sort of connection or association between them. For example, music with a fast tempo tends to be louder than music with a slow tempo. Although there are exceptions to this, in general, there is a correlation between tempo and dynamic level.

A correlational study involves collecting at least two different sets of measurements, and determining whether there is any relationship between the two sets. When we suspect that two measures are correlated, we should plot the measures, with one measure on the horizontal axis, and the other measure on the vertical axis. For example, we might plot the average dynamic level against the average tempo. Each point will represent a single musical work.

The degree of correlation can be expressed using a numerical correlation coefficient. Correlation coefficients range between -1 and +1. A correlation of +1 means a perfect positive correlation: as one measure increases, the corresponding measure also increases. Conversely, a correlation of -1 means a perfect negative correlation: as one measure increases, the corresponding measure decreases.

An example of a strong positive correlation would be +.89. An example of a moderate positive correlation would be +.65. An example of a weak positive correlation would be +.21. Similarly, strong, moderate, and weak negative correlations would simply reverse the sign from positive to negative. If there is little or no meaningful relationship between two sets of measures, the correlation will tend to be near zero—or where the correlation coefficient (of whatever value) is deemed not to be statistically significant. (Refer to our later discussion.)

A common type of correlational study is the survey (although many surveys are descriptive or measurementive rather than correlational). For example, a survey might reveal that people with high incomes are more likely to prefer jazz than country music, or that social conservatives are less likely to enjoy sad music. Once again, correlational studies say nothing about causation: they simply suggest that certain relationships exist.

  1. Correlational studies may or may not be hypothesis-driven. When there is no a priori hypothesis, the study is said to be an exploratory correlational study.
  2. Correlational studies always involve at least two sets of measurements.
  3. A common type of correlational study is the survey or questionnaire.

An Example

Both formal field observations and formal experiments have shown that males tend to prefer slower dance tempos than females. What accounts for this sex-related difference in preference? One possibility is that males and females prefer different styles of music. For example, women are more likely to prefer (generally fast) dance music, whereas men are more likely to prefer (slower) rock music. However, the difference in tempo preference is evident even when women and men are allowed to “tune” their own preferred dance tempo using a drum machine programmed to produce a simple back beat rhythm of alternating bass and snare drums.

Sofia Dahl and David Huron (2007) considered an alternative hypothesis that dance tempo might be correlated with body morphology. Dancing is essentially stylized bouncing, and like any oscillating system, the optimum rate of bouncing might be expected to depend on physical aspects of the moving body—such as height and weight.

Accordingly, Dahl and Huron had participants tune a drum machine to their preferred dance tempo, and then afterwards made a series of morphological measures, including the person’s height and weight. The graph below shows a scatterplot for 30 participants. Each point plots the preferred dance tempo (in beats per minute) against the average length of the persons’s two legs (in centimeters). As can be seen, there is a general trend downward: people with longer legs tend to prefer slower tempos. The correlation coefficient is a moderate -.67.

Body weight was found to produce a somewhat weaker correlation of -.38. That is, heavier people tend to prefer slower dance tempos.

Reference

Sofia Dahl & David Huron (2007). The influence of body morphology on preferred dance tempos. In: Proceedings of the International Computer Music Conference. Copenhagen, Denmark, Vol. 2, pp. 1-4.

Dahl, S., Huron, D., Brod, G., & Altenmüller, E. (2014). Preferred dance tempo: Does sex or body morphology influence how we groove? Journal of New Music Research, pp. 1-10.