Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T09:03:52.588Z Has data issue: false hasContentIssue false
  • English
  • Français

Simple Bayesian Inference for Qualitative Political Research

Published online by Cambridge University Press:  04 January 2017

Jack Buckley
Jack Buckley*
Affiliation:
Department of Educational Research, Measurement, and Evaluation, Boston College, Lynch School of Education, 336E Campion Hall, Chestnut Hill, MA 02467. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In political science and related disciplines in the social and behavioral sciences, there exists an unfortunate de facto divide between qualitative and quantitative empirical research. Sometimes this divide is purely a function of training and disciplinary socialization, but often it reflects a valid dispute over the philosophical foundations of inquiry. I argue here that the Bayesian approach to quantitative empirical modeling is an amenable starting point for building a rapprochement between qualitative and quantitative research, and I introduce as an example a straightforward model that allows for the Bayesian estimation of the difference between means of very small samples with unknown and possibly unequal variances. I then extend this approach to consider nonnormal variates, informative priors, and a multivariate test of the difference of means useful for the researcher who is interested in determining whether two small samples are different on several dimensions simultaneously.

Type
Research Article
Information
Political Analysis , Volume 12 , Issue 4: Special Issue on Bayesian Methods , Autumn 2004 , pp. 386 - 399
Copyright
Copyright © Society for Political Methodology 2004 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Behrens, W. A. 1929. “Ein Betrag zur Fehlenberechnung bei wenigen Beobachtungen (A Contribution for Error Computation When There Are Few Observations).” Landwirtschaftliche Jahrbucher 68: 807–837.Google Scholar
Bennett, B. M. 1951. “Note on a Solution of the Generalized Behrens-Fisher Problem.” Annals of the Institute of Statistical Mathematics 2: 87–90.Google Scholar
Buston, K. 1997. NUD*IST in Action: Its Use and Usefulness in a Study of Chronic Illness in Young People. (Available from http://www.socresonline.org.uk/2/3/6.html.)CrossRefGoogle Scholar
Carlin, Bradley P., Chaloner, Kathryn, Church, Timothy, Louis, Thomas A., and Matts, John P. 1993. “Bayesian Approaches for Monitoring Clinical Trials with an Application to Toxoplastic Encephalitis Prophylaxis.” Statistician 42: 355–367.Google Scholar
Chaloner, K., Church, T., Louis, T. A., and Matts, J. P. 1993. “Graphical Elicitation of a Prior Distribution for a Clinical Trial.” Statistician 42: 341–353.Google Scholar
Christensen, W. F., and Rencher, A. C. 1997. “A Comparison of Type I Error Rates and Power Levels for Seven Solutions to the Multivariate Behrens-Fisher Problem.” Communications in Statistics—Simulation and Computation 26(4): 1251–1273.Google Scholar
Congdon, P. 2001. Bayesian Statistical Modeling. Chichester, UK: Wiley.Google Scholar
Denzin, N. K. 1978. The Research Act: A Theoretical Introduction to Sociological Methods, 2nd ed. New York: McGraw-Hill.Google Scholar
Desrosières, A. 1998. The Politics of Large Numbers, trans. Naish, C. Cambridge, MA: Harvard University Press.Google Scholar
Drass, K. 1980. “The Analysis of Qualitative Data: A Computer Program.” Urban Life 9: 332–353.Google Scholar
Geweke, J. 1992. “Evaluating the Accuracy of Sampling-Based Approaches to Calculating Posterior Moments.” In Bayesian Statistics 4, eds. Bernardo, J. M., Berger, J. O., Dawid, A. P., and Smith, A. F. M. Oxford: Clarendon, pp. 169–193.Google Scholar
Gill, J., and Walker, L. D. 2003. “Elicited Priors in Bayesian Model Specifications with an Application to Comparative Politics.” Unpublished manuscript.Google Scholar
Greene, J. C. 2000. “Understanding Social Programs through Evaluation.” In Handbook of Qualitative Research, eds. Denzin, N. K. and Lincoln, Y. S. Thousand Oaks, CA: Sage, pp. 981–1000.Google Scholar
Greene, J. C., and Caracelli, V. J. 1997. “Defining and Describing the Paradigm Issue in Mixed-Method Evaluation.” In New Directions for Evaluation, Advances in Mixed-Method Evaluation: The Challenges and Benefits of Integrating Diverse Paradigms, No. 74, eds. Greene, J. C. and Caracelli, V. J. New York: Jossey-Bass, pp. 5–17.Google Scholar
Haney, Walt, Russell, Mike, and Bebell, Damien. Forthcoming. “Drawing on Education: Using Drawings to Study and Change Education and Schooling.” Harvard Educational Review.Google Scholar
Heidelberger, P., and Welch, P. D. 1983. “Simulation Run Length Control in the Presence of an Initial Transient.” Operations Research 21: 1109–1144.Google Scholar
Hesse-Biber, S. 1995. “Unleashing Frankenstein's Monster? The Use of Computers in Qualitative Research.” In Studies in Qualitative Methodology, Volume 5: Computing and Qualitative Research, ed. Burgess, R. G. London: JAI, pp. 25–41.Google Scholar
Hotelling, H. 1931. “The Generalization of Student's Ratio.” Annals of Mathematical Statistics 2: 360–378.Google Scholar
James, G. S. 1954. “Tests of Linear Hypotheses in Univariate and Multivariate Analysis When the Ratios of the Population Variances Are Unknown.” Biometrika 41: 19–43.Google Scholar
Johnson, R. A., and Weerahandi, S. 1988. “A Bayesian Solution to the Multivariate Behrens-Fisher Problem.” Journal of the American Statistical Association 83: 145–149.Google Scholar
Kelle, U. 1997. “Theory-Building in Qualitative Research and Computer Programs for the Management of Textual Data.” (Available from http://www.socresonline.org.uk/2/2/1.html)CrossRefGoogle Scholar
Kim, S. 1992. “A Practical Solution to the Multivariate Behrens-Fisher Problem.” Biometrika 79: 171–176.CrossRefGoogle Scholar
King, G., Keohane, R. O., and Verba, S. 1994. Designing Social Inquiry: Scientific Inference in Qualitative Research. Princeton, NJ: Princeton University Press.Google Scholar
Krishnamoorthy, K., and Thomson, J. 2004. “A More Powerful Test for Comparing Two Poisson Means.” Journal of Statistical Planning and Inference 119(1): 23–35.Google Scholar
LeCompte, M. D. 1978. “Learning from Work: The Hidden Curriculum of the Classroom.” Anthropology and Education Quarterly 9: 22–37.Google Scholar
LeCompte, M. D., and Preissle, J. 2003. Ethnography and Qualitative Design in Educational Research, 2nd. ed. San Diego, CA: Academic.Google Scholar
Lee, P. M. 1997 (1981). Bayesian Statistics: An Introduction, 2nd ed. London: Arnold.Google Scholar
Lincoln, Y. S., and Guba, E. G. 1985. Naturalistic Inquiry. Thousand Oaks, CA: Sage.Google Scholar
Lins, G. C. N., and de Souza, Campello F. M. 2001. “A Protocol for the Elicitation of Prior Distributions.” Paper presented at the Second International Symposium on Imprecise Probabilities and their Applications, Ithaca, NY.Google Scholar
McCall, G. J. 1969. “Data Quality Control in Participant Observation.” In Issues in Participant Observation: A Text and Reader, eds. McCall, G. J. and Simmons, J. L. Reading, MA: Addison-Wesley, pp. 128–141.Google Scholar
Patii, V. H. 1965. “Approximations to the Behrens-Fisher Distribution.” Biometrika 52: 267–271.Google Scholar
Pollard, W. E. 1986. Bayesian Statistics for Evaluation Research: An Introduction. Beverly Hills, CA: Sage.Google Scholar
Przyborowski, J., and Wilenski, H. 1940. “Homogeneity of Results in Testing Samples from Poisson Series.” Biometrika 31: 313–323.Google Scholar
Reichardt, C. S., and Cook, T. D. 1979. “Beyond Qualitative Versus Quantitative Methods.” In Qualitative and Quantitative Methods in Evaluation Research, ed. Cook, T. D. Thousand Oaks, CA: Sage, pp. 7–32.Google Scholar
Richards, L. 1995. “Transition Work! Reflections on a Three-Year NUD*IST Project.” In Studies in Qualitative Methodology, Volume 5: Computing and Qualitative Research, ed. Burgess, R. G. London: JAI, pp. 105–140.Google Scholar
Robinson, G. K. 1976. “Properties of Student's t and of the Behrens-Fisher Solution to the Two-Means Problem.” Annals of Statistics 4: 963–971.CrossRefGoogle Scholar
Scheffé, H. 1970. “Practical Solutions of the Behrens-Fisher Problem.” Journal of the American Statistical Association 64: 1501–1508.Google Scholar
Spetzler, C. S., and von Holstein, Stael C.-S. 1975. “Probability Encoding in Decision Analysis.” Management Science 22: 340–358.CrossRefGoogle Scholar
Stevens, S. S. 1946. “On the Theory of Scales of Measurement.” Science 103: 677–680.Google Scholar
Stevens, S. S. 1951. “Mathematics, Measurement, and Psychophysics.” In Handbook of Experimental Psychology, ed. Stevens, S. S. New York: Wiley, pp. 1–49.Google Scholar
Subrahmaniam, K., and Subrahmaniam, K. 1973. “On the Multivariate Behrens-Fisher Problem.” Biometrika 60: 107–111.Google Scholar
Weitzman, E. A. 2000. “Software and Qualitative Research.” In Handbook of Qualitative Research, eds. Denzin, N. A. and Lincoln, Y. S. Thousand Oaks, CA: Sage, pp. 803–820.Google Scholar
Welch, B. L. 1937. “The Significance of the Difference between Two Means When the Population Variances Are Unequal.” Biometrika 29: 350–360.Google Scholar
Welch, B. L. 1947. “The Generalization of ‘Student's’ Problem When Several Different Population Variances Are Involved.” Biometrika 34: 28–35.Google Scholar
Wilcox, R. R. 1989. “Adjusting for Unequal Variances When Comparing Means in One-Way and Two-Way Fixed Effects ANOVA Models.” Journal of Educational Statistics 14: 269–278.Google Scholar
Yao, Y. 1965. “An Approximate Degrees of Freedom Solution to the Multivariate Behrens-Fisher Problem.” Biometrika 52: 139–147.Google Scholar
Supplementary material: File

Buckley supplementary material

Supplementary Material

Download Buckley supplementary material(File)
File 3.1 KB