Please enable JavaScript.

Coggle requires JavaScript to display documents.

Visualizing Magnitude: Graphical Number Representations Help Users Detect…

- - - - i- Thimbleby and Williams (2013) studied nomograms to
        facilitate calculations on infusion pump parameters, such as
        medication volume and rate of infusion.
      - ii. Gould et al. (2013) developed a graphical representation
        to help people visualize the rate of infusion in an infusion
        pump programming task. In the graphical representation,
        shown in Figure 1b, the rate of infusion can be inferred from
        the gradient of the line (connecting duration of infusion and
        volume to be infused)
        
        . Results showed that people were faster and equally
        accurate in solving problems with the graphical representation.
      - iii. The results of Thimbleby and Williams (2013) and Gould
        et al. (2013) show that graphical representations can help
        people make sense of numbers. However, these studies
        focused on calculation tasks in which the graphical
        representation was used as an external support aid to perform
        a mental calculation. While calculation tasks are important, we
        are primarily interested here in number entry tasks.
      - iv. A recent study by Tu et al. (2014) evaluated the benefits
        of a graphical number representation to help people detect
        number entry errors.
        
        The representation consists of a circle, where digits (0-9) and the decimal point each have a specific position on the circle, and an arrowed line connecting the positions shows the order of characters for a number.
        
        Tu et al. found that participants made fewer errors when using
        this graphical representation, but at the expense of slower task completion times, suggesting a speed-accuracy trade-off.
        
        A further limitation of Tu et al.’s representation is that it does not have a direct mapping with the semantics of the number, so the meaning of the representation has to be learned by participants. - Given this concern, we were motivated to
        develop a visualization technique for representing the
        magnitude of a number that is easy to understand and use.
    - - i. In developing our representation for visualizing the
        magnitude of a number, we took inspiration from Norman’s
        (1994) Naturalness Principle. Norman argues that information
        representations should be designed to match the properties of
        what they are intending to represent.
      - ii. For instance, the physical
        properties of representation can be used to represent the size
        of the number
      - iii. An advantage of such
        a proportional representation is that it changes an abstract
        symbol like the Arabic notation into a perceptual one that is
        much easier to interpret and compare. This can make it far
        easier for the user to perceive large differences in magnitude,
        which would be harder to detect in a textual representation.
      - iv. our graphical representation consists of a block
        whose size is proportional to the number. The width of the
        block represents the order of magnitude, and the height of the
        block represents the overall value of the number. So, for
        instance, the blocks of values 90 and 900 are equally high, but
        differ in width. Similarly, 100 and 900 have an equal block
        width, but differ in height
      - v. Another reason why a block with two dimensions was used
        rather than a bar or line, which only has one dimension, was to
        make more efficient use of space, and to be able to show a wider range of numbers
    - - i. We consider whether our
        representation system helped participants detect number entry
        errors. We assume that the addition of the visualized number
        block changes the abstract task of comparing digits and
        interpreting their magnitude to a perceptual one of comparing
        block sizes.
      - ii. Small differences in size might be hard to detect
        but larger differences will be easier to perceive. The
        expectation is that this kind of representation will make it
        easier to detect large severe errors, such as out-by-ten errors
      - iii. A secondary aim of our study was to investigate how the
        cost of accessing the to-be-entered number affects the errors
        people make, and if this is different for textual and graphical
        representations.
      - iv. Previous studies showed that if it takes more
        effort to access the information needed for a task, people try to
        encode the information better in memory, and this deeper
        encoding leads to fewer errors being made on that task
      - v. when a
        prescription form showing the to-be-entered numbers was
        placed further away from the input device, participants
        memorized the numbers in chunks and as a result made fewer
        errors.
      - vi. Soboczenski et al. (2013) encouraged deeper encoding
        by presenting numbers in a transcription task in a less legible
        font color, and found this also resulted in fewer errors
      - vii. We speculate that it might be
        easier for participants to adopt a more memory-intensive
        strategy with a graphical number representation because this
        representation would allow a number’s magnitude to be
        directly perceived