Failure of additivity in bisection of length

Anderson, Norman H.

doi:10.3758/bf03199682

“…And, there are numerous cases in which relative preferences are not decomposable into component attitudes at all. For example, intransitive relative preferences, violating unidimensionality, have been demonstrated repeatedly (e.g., Bar-Hillel & Margalit, 1988;Birnbaum, 1992;Shafir, Osherson, & Smith, 1990;Tversky, 1969) as have sub-or super-additivity (Anderson, 1977). Also, Hsee, Loewenstein, Blount, and Bazerman (1999) identified circumstances in which most participants preferred object A to object B when considered separately, while B was preferred to A in a relative comparison.…”

Section: Relative Preference ≠ Additive Differencementioning

confidence: 97%

Faulty assumptions: A comment on Blanton, Jaccard, Gonzales, and Christie (2006)

Nosek¹,

Narayanan²

2016

Preprint

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Blanton, Jaccard, Gonzales, and Christie (BJGC, 2006) assert that the Implicit Association Test (IAT) imposes a model that portrays relative preferences as the additive difference between single attitudes. This assertion is misplaced because relative preferences do not necessarily reduce to component attitudes. BJGC also assume that the IAT conditions represent two indicators of the same construct. This assumption is incorrect, and is the cause of their poor-fitting models. The IAT, like other experimental paradigms, contrasts performance between interdependent conditions, and cannot be reduced to component parts. This is true whether calculating a simple difference between conditions, or using the IAT D score. D – an individual effect size that is monotonically related to Cohen's d – codifies the interdependency between IAT conditions. When their unjustified psychometric assumptions are replaced with plausible assumptions, the models fit their data very well, and basis for their poor-fitting models becomes clear.

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“…And, there are numerous cases in which relative preferences are not decomposable into component attitudes at all. For example, intransitive relative preferences, violating unidimensionality, have been demonstrated repeatedly (e.g., Bar-Hillel & Margalit, 1988;Birnbaum, 1992;Shafir, Osherson, & Smith, 1990;Tversky, 1969) as have sub-or superadditivity (Anderson, 1977). Also, Hsee, Loewenstein, Blount, and Bazerman (1999) identified circumstances in which most participants preferred object A to object B when considered separately, while B was preferred to A in a relative comparison.…”

Section: Statementioning

confidence: 98%

Faulty assumptions: A comment on Blanton, Jaccard, Gonzales, and Christie (2006)

Nosek

¹

,

Narayanan

²

2007

Journal of Experimental Social Psychology

View full text Add to dashboard Cite

Blanton, Jaccard, Gonzales, and Christie (BJGC, 2006) assert that the Implicit Association Test (IAT) imposes a model that portrays relative preferences as the additive difference between single attitudes. This assertion is misplaced because relative preferences do not necessarily reduce to component attitudes. BJGC also assume that the IAT conditions represent two indicators of the same construct. This assumption is incorrect, and is the cause of their poor-fitting models. The IAT, like other experimental paradigms, contrasts performance between interdependent conditions, and cannot be reduced to component parts. This is true whether calculating a simple difference between conditions, or using the IAT D score. D -an individual effect size that is monotonically related to Cohen's dcodifies the interdependency between IAT conditions. When their unjustified psychometric assumptions are replaced with plausible assumptions, the models fit their data very well, and basis for their poor-fitting models becomes clear.Blanton, Jaccard, Gonzales, and Christie (2006; hereafter "BJGC") criticize relative measurement and the use of difference scores for comparing experimental conditions. This article makes two points: (1) BJGC are too quick to dismiss the value of relative measurement and mistakenly suggest that relative attitude measures are necessarily reducible to component evaluations; and (2) BJGC misperceive the Implicit Association Test (IAT; Nosek, Greenwald, & Banaji, in press) conditions as analogous to two items of a scale and consequently impose invalid psychometric assumptions by decomposing the performance conditions as separate indicators of the construct. BJGC mistook their poor model fits as showing problems with the IAT rather than as indicating problems with their assumptions.

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“…It is worth noting that Anderson (1977) found that for lengths of rods the bisection of 2-variable model failed. Yet, contrary to his finding, our Experiment 1 validated a 3-variable bisymmetry model.…”

Section: Instructionmentioning

confidence: 98%

“…Taking a random sample of subjects and allowing random discrepancies from the equality of bisymmetry, then e.g., by applying the t-test or Wilcoxon-test (depending on the distributional assumptions of the difference), it is possible to test whether bisymmetry holds in the population represented by the sample. It is worth noting that in the context of information integration, 2-variables bisection is tested by variants of monotone analysis of variance (see experiments in, e.g., Carterette & Anderson, 1979;Anderson, 1977;Weiss, 1975). Mokken, (1993, 2000) observed that the equation of 2-variables bisymmetry (2) can be written in a matrix design form (see Fig.…”

Section: Bisymmetry For N Stimulimentioning

confidence: 99%