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    Area of Science:

    • Data analysis
    • Psychometrics
    • Information science

    Background:

    • Sorting tasks are fundamental in data analysis and cognitive science.
    • Measuring dissimilarity between sets is crucial for various analytical methods.
    • Existing measures may not adequately account for variations in set sizes.

    Purpose of the Study:

    • To investigate and compare three distinct dissimilarity measures for unconstrained sorting tasks.
    • To analyze how these measures handle differences in cell sizes within sortings.
    • To evaluate the practical performance of these measures using real-world data.

    Main Methods:

    • The study employs multidimensional scaling (MDS), a statistical technique for visualizing similarity of data.
    • Three specific dissimilarity measures, all confirmed as metrics, are tested.
    • Empirical data from sorting tasks involving occupation names and behavior names are utilized.

    Main Results:

    • All three investigated dissimilarity measures are mathematically metric.
    • The measures exhibit variations in their compensation strategies for differing cell sizes.
    • Empirical tests provide insights into the performance of each measure with specific datasets.

    Conclusions:

    • The choice of dissimilarity measure can impact sorting task analysis, particularly concerning cell size.
    • Multidimensional scaling is a viable method for empirically testing these measures.
    • Further research may refine dissimilarity measures for improved accuracy in sorting tasks.