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Assessing Individual Change Without Knowing the Test Properties: Item Bootstrapping
Juan Botella1, Desirée Blázquez1, Manuel Suero1
1Department of Social Psychology and Methodology, Universidad Autónoma de Madrid, Madrid, Spain.
Abstract:
Assessing significant change (or reliable change) in a person often involve comparing the responses of that person in two administrations of a test or scale. Several procedures have been proposed to determine if a difference between two observed scores is statistically significant or rather is within the range of mere random fluctuations due to measurement error. Application of those procedures involve some knowledge of the test properties. But sometimes those procedures cannot be employed because the properties are unknown or are not trustworthy. In this paper we propose the bootstrap of items procedure to create confidence intervals of the individual's scores without using any known psychometric properties of the test. Six databases containing the responses of several groups to one or more subscales have been analyzed using two methods: bootstrap of items and a classical procedure based on confidence intervals to estimate the true score. The rates of significant change obtained were very similar, suggesting that item bootstrapping is a promising solution when other methods cannot be applied.
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Work Done During Volume Change
Consider a gas confined to a cylinder fitted with a movable piston at one end. If the gas expands from volume V1 to volume V2, it exerts a force on the piston, such that the piston moves by a distance dr.
The work done by the gas on the piston can be expressed as

