Parameter Estimation Using Asymptotic Analogy

• Published in: European conference on research methodology for business and management studies p. 380
• Main Author: Stacey, Anthony
• Format: Conference Proceeding
• Language: English
• Published: Kidmore End Academic Conferences International Limited 01.06.2012
• Subjects: Agreements; Algorithms; Asymptotic methods; Attitudes; Beliefs; Correlation; Expected values; Inferences; Likert Scales; Parameter estimation; Population; Rating Scales; Researchers; Sample variance; Sampling; Sampling error; Simulation; Software; Standard deviation; Statistical Analysis; Statistical inference; Studies
• ISSN: 2049-0968; 2049-0976

Conventional analysis of quantitative research data calculates sample statistics from which population parameters and characteristics are inferred. As a result of using ordinal response scales, much quantitative research data is subject to discretisation error. This error compounds the well-recognised and quantifiable sampling error, but is generally overlooked. Discretisation error results in unreliable estimates of population parameters such as means, standard deviation, correlation coefficients and the like. Hypothesis tests and other inferences are similarly affected. It will be demonstrated in this paper that the magnitude of discretisation error may be substantial. A novel methodology will be presented that completely eliminates discretisation error by treating ordinal data as strictly ordinal, and avoiding incorrectly attributing a numeric property to an ordinal response scale. In its generic form, the asymptotic analogy methodology involves the creation of a numerical (agent based) simulation model of individuals' attitudes, perceptions, opinions, thoughts, feelings, beliefs or judgements. The initial input parameters of the model are completely arbitrary. Summary statistics are calculated for the simulation model corresponding to the research sample statistics. The input parameters of the model are then incrementally adjusted using a goal seeking algorithm which minimises the differences between the sample statistics and the summary statistics for the numerical model. The numerical model is thus asymptotically calibrated to the observed research data. Two examples of parameter estimation using asymptotic analogy will be presented. In the first exposition of the methodology, the means and standard deviations of verbal ordinal (Likert-type) survey data will be estimated by fitting normal distributions to the raw categorical data. The second illustration of the methodology will demonstrate the analysis of rank-ordered survey data, thereby resolving a frustrating and intractable problem for quantitative researchers. Apart from the obvious theoretical benefits of eliminating discretisation error, the methodology has the practical benefit of not requiring technical statistical software because the modelling can be implemented using readily available desktop spread sheet software. [PUBLICATION ABSTRACT]