PsychologicalReports, 2006,98,865-869.
O Psychological Reports 2006
RESAMPLING PROBABILITY VALUES FOR DIFFERENCES BETWEEN T W O INDEPENDENT INDICES OF ORDINAL VARIATION AND CONSENSUS ' JANIS E. JOHNSTON, KENNETH J. BERRY, AND PAUL W. MIELKE, JR. Colorado State Unzivevsity Summary.-A permutation method is presented to calculate resampling probability values for differences between two independent indices of ordinal variation and consensus.
It is sometimes important in psychological research to measure the difference between two independent indices of variability, or the complement, two independent indices of consensus. While tests of the difference between two independent measures of variability computed on interval/ratio level data, i.e., variance, are common, no analogous test exists for the difference between two independent measures of variation computed on ordinal level data, i.e., variation. A common application is the analysis of differences among Likert scale responses between two independent samples. For example, it may be of interest to test for differences in consensus, i.e., agreement, between cognitive and social psychologists on the issue of the continuity hypothesis, i.e., representations of the positive integers are part of innate cognition endowment (Gelman & Gallistel, 1978). Berry and Mielke (1992a) extended the index of qualitative variation (IQV) to yield a measure of variation for ordered categories, the index of ordinal variation (IOV). Berry and Mielke (199213) detailed properties of the index of ordinal variation and compared it to Leik's measure of ordinal variation, LOV (1966). Berry, Johnston, and Mielke (2005) introduced the complement of the index of ordinal variation, the index of ordinal consensus (IOC), and described resampling permutation procedures for the index of ordinal variation (consensus), yielding one-sided approximate probability (P) values under the null hypothesis (Ho) that the ordinal variation (consensus) in the population is zero. The measures of ordinal variation and consensus presented by Berry and Mielke (1992a, 1992b) and Berry, et a/. (2005) were limited to single samples. In this paper, two independent samples are considered, and a permutation method is provided to compute resampling probability values for differences between two independent indices of ordinal variation and the corresponding indices of consensus. 'Address correspondence to J. E. Johnston, Department of Sociolo y, Colorado State University, Fort Collins, CO 80523-1784 or e-mail (
[email protected]~ostate.e&). DO1 10.2466DR0.98.3.865-869
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J. E. JOHNSTON, ET AL.
MEASURE Consider one sample of N objects. If c predefined, fixed, mutually exclusive categories are ordered from 1 to c with frequencies n l , . . . , n, where
then the index of ordinal variation is defined as
where V=
C n i n j ( j - i) , t
