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Comparing Discrete Distributions: Survey Validation and Survey Experiments

Published online by Cambridge University Press:  04 January 2017

Kishore Gawande ,
Gina Yannitell Reinhardt ,
Carol L. Silva  and
Domonic Bearfield
Kishore Gawande*
Affiliation:
Bush School of Government, Texas A&M University, College Station, TX 77843-4220
Gina Yannitell Reinhardt
Affiliation:
Bush School of Government, Texas A&M University, College Station, TX 77843-4220 e-mail: [email protected]
Carol L. Silva
Affiliation:
Center for Applied Social Research, Department of Political Science, University of Oklahoma, 455 W. Lindsey, Room 205, Norman, OK 73019-2001 e-mail: [email protected]
Domonic Bearfield
Affiliation:
Bush School of Government, Texas A&M University, College Station, TX 77843-4220 e-mail: [email protected]
*
e-mail: [email protected] (corresponding author)
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Abstract

Field survey experiments often measure amorphous concepts in discretely ordered categories, with postsurvey analytics that fail to account for the discrete attributes of the data. This article demonstrates the use of discrete distribution tests, specifically the chi-square test and the discrete Kolmogorov—Smirnov (KS) test, as simple devices for comparing and analyzing ordered responses typically found in surveys. In Monte Carlo simulations, we find the discrete KS test to have more power than the chi-square test when distributions are right or left skewed, regardless of the sample size or the number of alternatives. The discrete KS test has at least as much power as the chi-square, and sometimes more so, when distributions are bi-modal or approximately uniform and samples are small. After deriving rules of usage for the two tests, we implement them in two cases typical of survey analysis. Using our own data collected after Hurricanes Katrina and Rita, we employ our rules to both validate and assess treatment effects in a natural experimental setting.

Type
Regular Articles
Information
Political Analysis , Volume 21 , Issue 1 , Winter 2013 , pp. 70 - 85
Copyright
Copyright © The Author 2013. Published by Oxford University Press on behalf of the Society for Political Methodology 

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Footnotes

Authors' note: We appreciate Matt Henderson's valuable assistance with coding the Internet-based survey. We thank Elisabeth Gerber, Jennifer Jerit, Jason Barabas, Janet Box-Steffensmeier, Andrew Sobel, Gary Miller, Randall Calvert, Andrew Martin, and Itai Sened for helpful comments. The editor, R. Michael Alvarez, and an anonymous referee suggested revisions that improved the article significantly. For replication data, code, and instructions, see Gawande et al. (2012). Supplementary materials for this article are available on the Political Analysis website.

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