A Statistical Method for Comparing Aggregate Data Across A Priori Groups

Abstract

This article introduces a new method for statistically comparing pairs of aggregate data series. Aggregate data series refers to a set of values, each of which is averaged or otherwise aggregated across respondents. The motivating problem is the comparison of aggregate proximity matrices, such as those obtained from pile sort exercises. The standard approach to this problem uses the nonparametric, permutation-based quadratic assignment program (QAP) technique. However, the null distribution that QAP is based on is inappropriate for comparing subsamples of a data set and may lead to misleading conclusions. The new method can yield different results than QAP, results more in line with researchers' intuition. Furthermore, the method can be applied to a variety of data types beyond those appropriate for QAP.

Get full access to this article

View all access options for this article.

References

Boster, J. 1987. Agreement between biological classification systems is not dependent on cultural transmission. American Anthropologist 89:914–920.

Boster, J. , and J. C. Johnson . 1989. Form or function: A comparison of expert and novice judgments of similarity among fish. American Anthropologist 91:866–889.

Carroll, J. D. 1972. Individual differences and multidimensional scaling. In Multidimensional scaling: Theory and applications in the behavioral sciences. Vol. 1. Theory, edited by R. N. Shepard , A. K. Romney , and S. Nerlove , 105–155. New York: Seminar.

Edgington, E. S. 1969. Approximate randomization tests. Journal of Psychology 72:143–149.

Faust, K. , and A. K. Romney . 1985. The effect of skewed distributions on matrix permutation tests. British Journal of Mathematical and Statistical Psychology 38:152–160.

Fisher, R. A. 1934. The logic of inductive inference (with discussion). Journal of the Royal Statistical Society A 98:39–54.

Garro, L. C. 1986. Intracultural variation in folk medical knowledge: A comparison between curers and noncurers. American Anthropologist 88:351–370.

Good, P. 1994. Permutation tests: A practical guide to resampling methods for testing hypotheses. New York: Springer-Verlag.

Hubert, L. J. , and J. Schultz . 1976. Quadratic assignment as a general data analysis strategy. British Journal of Mathematical and Statistical Psychology 29:190–241.

10.

Jang, H. , and G. A. Barnett . 1994. Cultural differences in organizational communication: A semantic networks analysis. Bulletin de Methodologie Sociologique 44:31–50.

11.

Johnson, K. E. , C. B. Mervis , and J. S. Boster . 1992. Development changes in the structure of the mammal domain. Developmental Psychology 28:74–83.

12.

Krackhardt, D. 1986. A caveat on the use of the quadratic assignment procedure. Unpublished manuscript.

13.

Krackhardt, D. 1987. Cognitive social structures. Social Networks 9:104–134.

14.

Mantel, N. 1967. The detection of disease clustering and a general regression approach. Cancer Research 27 (2): 209–220.

15.

Noreen, E. 1989. Computer intensive methods for testing hypotheses: An introduction. New York: Wiley.

16.

Romney, A. K. , S. Weller , and W. Batchelder . 1986. Culture as consensus: A theory of culture and informant accuracy. American Anthropologist 88 (2): 313–338.

17.

Weller, S. C. 1984. Cross-cultural concepts of illness: Variation and validation. American Anthropologist 86:341–350.

18.

Weller, S. C. , and A. K. Romney . 1988. Systematic data collection. Beverly Hills, CA: Sage.