Correlation analysis of continuous emotional response to music: Correcting for the effects of serial correlation

Abstract

Publications of research concerning continuous emotional responses to music are increasing. The developing interest brings with it a need to understand the problems associated with the analysis of time series data. This article investigates growing concern in the use of conventional Pearson correlations for comparing time series data. Using continuous data collected in response to selected pieces of music, with two emotional dimensions for each piece, two falsification studies were conducted. The first study consisted of a factor analysis of the individual responses using the original data set and its first-order differenced transformation. The differenced data aligned according to theoretical constraints better than the untransformed data, supporting the use of first-order difference transformations. Using a similar method, the second study specifically investigated the relationship between Pearson correlations, difference transformations and the critical correlation coefficient above which the conventional correlation analysis remains internally valid. A falsification table was formulated and quantified through a hypothesis index function. The study revealed that correlations of undifferenced data must be greater than 0.75 for a valid interpretation of the relationship between bivariate emotional response time series data. First and second-order transformations were also investigated and found to be valid for correlation coefficients as low as 0.24. Of the three version of the data (untransformed, first-order differenced, and second-order differenced), first-order differenced data produced the fewest problems with serial correlation, whilst remaining a simple and meaningful transformation.

Get full access to this article

View all access options for this article.

References

Beran

, & Mazzola

(1999). Analysing musical structure and performance: A statistical approach. Statistical Science, 14, 47–79.

Box

G. E. P.

, & Jenkins

G. M.

(1976). Time series analysis: Forecasting and control (Rev. ed.). San Francisco: Holden-Day.

Campbell

D. T.

, & Stanley

J. C.

(1963). Experimental and quasi-experimental designs for research. Chicago: Rand McNally.

Fredrickson

W. E.

(1997). Elementary, middle, and high school perceptions of tension in music. Journal of Research In Music Education, 45, 626–35.

Fredrickson

W. E.

(1999). Effect of musical performance on perception of tension in Gustav Hoist's first suite in E-flat. Journal of Research in Music Education, 47, 44–52.

Frego

R. J. D.

(1999). Effects of aural and visual conditions on response to perceived artistic tension in music and dance. Journal of Research in Music Education, 47, 31–43.

Gabrielsson

, & Juslin

P. N.

(1996). Emotional expression in music performance: Between the performers intention and the listener's experience. Psychology of Music, 24, 68–91.

Gibbons

J. D.

(1993). Nonparametric Measures of Association. Newbury Park: Sage.

Gorsuch

R. L.

(1983). Factor analysis (2nd ed). Hillsdale, NJ: Erlbaum.

10.

Gottman

J. M.

(1981). Time-series analysis: A comprehensive introduction for social scientists. Cambridge: Cambridge University Press.

11.

Hamilton

J. D.

(1994). Time series analysis. Princeton, NJ: Princeton University Press.

12.

Heinlein

C. P.

(1928). The affective characters of the major and minor modes in music. Journal of Comparative Psychology, 8, 101–42.

13.

Howell

D. C.

(1997). Statistical methods for psychology (4th ed.). Belmont, CA: Duxbury.

14.

Krumhansl

C. L.

(1996). A perceptual analysis of Mozart's Piano Sonata K. 282 - segmentation, tension, and musical ideas. Music Perception, 13, 401–32.

15.

Krumhansl

C. L.

(1997). An exploratory study of musical emotions and physiology. Canadian Journal of Experimental Psychology, 51, 336–52.

16.

Krumhansl

C. L.

(1998). Topic in music: An empirical study of memorability, openness, and emotion in Mozart's String Quintet in C major and Beethoven's String Quartet in A Minor. Music Perception, 16, 119–34.

17.

Madsen

C. K.

, & Fredrickson

W. E.

(1993). The experience of musical tension: A replication of Nielsen's research using the continuous response digital interface. Journal of Music Therapy, 30, 46–63.

18.

Madsen

C. K.

(1997). Emotional response to music as measured by the two-dimensional CRDI. Journal of Music Therapy, 34, 187–99.

19.

Madsen

C. K.

(1998). Emotion versus tension in Haydn's Symphony No. 104 as measured by the two-dimensional continuous response digital interface. Journal of Research In Music Education, 46, 546–54.

20.

Madsen

C. K.

, Brittin

R. V.

, & Capperella-Sheldon

D. A.

(1993). An empirical investigation of the aesthetic response to music. Journal of Research In Music Education, 41, 57–69.

21.

Mooney

C. Z.

(1997). Monte Carlo Simulation. Thousand Oaks: Sage.

22.

Nielsen

F. V.

(1983). Oplevelse of musikalsk spending (the experience of musical tension). Copenhagen: Akademisk Forlag.

23.

Radocy

R. E.

, & Boyle

J. D.

(1988). Psychological foundations of musical behaviour (2nd ed.). Springfield, IL: Charles C. Thomas.

24.

Schubert

, & Dunsmuir

(1999). Regression modelling continuous data in music psychology. In Yi

S. W.

(ed.), Music, Mind, and Science (pp. 298–352). Seoul: Seoul National University Press.

25.

Schubert

(1999a). Measuring emotion continuously: Validity and reliability of the two-dimensional emotion-space. Australian Journal of Psychology, 51, 154–65.

26.

Schubert

(1999b). Measurement and Time Series Analysis of Emotion in music. Unpublished doctoral dissertation, University of New South Wales, Sydney.

27.

Schubert

(2001). Continuous measurement of self-report emotional response to music. In Juslin

P. N.

, and Sloboda

J. A.

(eds), Music and emotion: Theory and research (pp. 393–414). New York: Oxford University Press.

28.

Sloboda

J. A.

, & Lehmann

A. C.

(2001). Tracking performance correlates of changes in perceived intensity of emotion during different interpretations of a Chopin Piano Prelude. Music Perception, 19, 87–120.

29.

Stanovich

K. E.

(1998). How to Think Straight about Psychology (5th ed.). New York: Longman.