Document Detail

Variance matters: the shape of a datum.
MedLine Citation:
PMID:  19429214     Owner:  NLM     Status:  MEDLINE    
In the quantitative analysis of behaviour, choice data are most often plotted and analyzed as logarithmic transforms of ratios of responses and of ratios of reinforcers according to the generalized-matching relation, or its derivatives such as conditional-discrimination models. The relation between log choice ratios and log reinforcer ratios has normally been found using ordinary linear regression, which minimizes the sums of the squares of the y deviations from the fitted line. However, linear regression of this type requires that the log choice data be normally distributed, of equal variance for each log reinforcer ratio, and that the x (log reinforcer ratio) measures be fixed with no variance. We argue that, while log transformed choice data may be normally distributed, log reinforcer ratios do have variance, and because these measures derive from a binomial process, log reinforcer ratio distributions will be non-normal and skewed to more extreme values. These effects result in ordinary linear regression systematically underestimating generalized-matching sensitivity values, and in faulty parameter estimates from non-linear regression to assume hyperbolic and exponential decay processes. They also lead to model comparisons, which assume equal normally distributed error around every data point, being incorrect. We describe an alternative approach that can be used if the variance in choice is measured.
Michael Davison; Douglas Elliffe
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Publication Detail:
Type:  Journal Article     Date:  2009-01-31
Journal Detail:
Title:  Behavioural processes     Volume:  81     ISSN:  1872-8308     ISO Abbreviation:  Behav. Processes     Publication Date:  2009 Jun 
Date Detail:
Created Date:  2009-05-11     Completed Date:  2009-07-15     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  7703854     Medline TA:  Behav Processes     Country:  Netherlands    
Other Details:
Languages:  eng     Pagination:  216-22     Citation Subset:  IM    
Psychology Department, The University of Auckland, Auckland, New Zealand.
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MeSH Terms
Data Interpretation, Statistical*
Discrimination (Psychology) / physiology
Models, Psychological*
Models, Statistical*
Regression Analysis

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