Journal ArticleDOI
Parametric statistics and levels of measurement : factorial designs and multiple regression
Mark L. Davison,Anu Sharma +1 more
TLDR
In general, for factorial designs, an analysis of variance of the observed variable Y cannot be used to draw inferences about main effects and interactions on the latent variable θ even when the standard normality and equality of variance assumptions hold as mentioned in this paper.Abstract:
Let Y be a continuous, ordinal measure of a latent variable θ. In general, for factorial designs, an analysis of variance of the observed variable Y cannot be used to draw inferences about main effects and interactions on the latent variable θ even when the standard normality and equality of variance assumptions hold.read more
Citations
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Journal ArticleDOI
Item Response Theory and Clinical Measurement
Steven P. Reise,Niels G. Waller +1 more
TL;DR: It is concluded that there are notable differences between cognitive and clinical measures that have relevance for IRT modeling and future research should be directed toward a better understanding of the metric of the latent trait and the psychological processes that lead to individual differences in item response behaviors.
Journal ArticleDOI
The new rules of measurement.
TL;DR: A large family of diverse item response theory models are now available to apply to an assortment of measurement tasks as mentioned in this paper, such as rating scales, partial credit scoring, and rating scales.
Journal ArticleDOI
Is the selection of statistical methods governed by level of measurement
TL;DR: In this article, the authors present a new paradigm using experimental mathematics to examine the claims made in the levels of measurement controversy, which is referred to as monte carlo simulation, and demonstrate that the approach advocated in this paper is linked closely to representational theory.
Journal ArticleDOI
Self-esteem and threats to self: Implications for self-construals and interpersonal perceptions
TL;DR: Differences in independent and interdependent self-construals statistically accounted for differences in likability and personality perceptions of high and low self-esteem people after threat.
Journal ArticleDOI
Statistics and the theory of measurement
TL;DR: One general conclusion is that the domains of applicability of the two major theories are typically different, and it is this which helps apparent contradictions to be avoided in most practical applications.
References
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Book
Introduction to Mathematical Statistics
TL;DR: In this article, the authors present a list of common distributions of probability and distribution of likelihood for Bayesian models. But they do not discuss the relation between distributions and normal models.
Book
A course in probability theory
TL;DR: This edition of A Course in Probability Theory includes an introduction to measure theory that expands the market, as this treatment is more consistent with current courses.
Book
Finite Mixture Distributions
Brian Everitt,David J. Hand +1 more
TL;DR: In this paper, the authors propose a method to estimate the parameters in normal mixture distributions. But this method is not suitable for counting the number of components in a mixture and cannot be used to detect mixtures of binomial distributions.