Week 3-2: Information Theory and Perceptual Judgments

1. Week 3-2: Information Theory and Perceptual Judgments

2. Week 3 Topics • Lecture 3-1 • Modeling the Human Operator as a Communications Channel • Information Theory • Lecture 3-2 • Perceptual Judgments • Unidimensional • Multidimensional

3. Perceptual Judgment • Perceptual Judgment: Judgments of stimulus magnitudes above threshold • Contrast with detection: stimulus at threshold • Operator must make a judgment about the magnitude of a stimulus that is well above threshold, thus detection is not an issue, e.g., • Will my car fit in that parking space? • Do I need to mow the lawn? • Is it so cold that I need a jacket?

4. Perceptual Judgment • Unidimensional judgments • stimuli vary along one dimension only • observer places stimuli into 2 or more categories • Multidimensional judgments • stimuli vary along more than one dimensions • observer places stimuli into 2 or more categories spread across multiple dimensions • information theory assesses the consistency of match between the stimulus and its categorization

5. Unidimensional Judgment • Channel capacity • With 5 or more categories errors begin to occur much more frequently • HT < HS Maximum capacity 4 categories = 2 bits, 8 categories = 3 bits

6. Unidimensional Judgment • Channel capacity (cont.) • Cause of limited capacity? • Not sensory • discrimination performance is typically very good for a number of stimulus domains • difference threshold or just noticeable difference (JND) is typically less than 10% • Memory: categories must be remembered • Miller (1956): working memory capacity is generally 7 +/- 2 items ~ 2-3 bits of information

7. Multidimensional Judgment • Used when stimuli vary along more than one dimension • Most real-world stimuli are multidimensional • Independent vs. dependent dimensions • Independent (orthogonal): change along one dimension does not affect the other dimension • Dependent(correlated): change along one dimension is accompanied by change along the other dimension

8. 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 ? 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 ? not 0 1 2 3 4 5 6 7 8 9 Multidimensional Judgment • Human performance • higher channel capacity withmultidimensional information • Egeth & Pachella (1969) • unidimensional capacity: 3.4 bits (10 levels) • multidimensional capacity: 5.8 bits (57 levels) • dimensions do not sum perfectly, some information is lost

9. 10 8 6 4 2 Bits/dimension Multidimensional Judgment • Additional independent dimensions increase HTbut with a cost (diminishing returns in bits per dimension)

10. 10 8 6 4 2 Bits/dimension Multidimensional Judgment • Correlated dimensions • max HSand HTis less due to redundancy, but • cost (bits/dim.) for extra dimensions is less (Note: slope representing perfect performance is less than that for independent dimensions)

11. Multi-dimensional Judgment and Displays • Separable vs. integral dimensions • Separable: each dimension can be physically specified independent of the other dimension(s) • Example: color and fill texture of an object, perpendicular vectors • Integral: one dimension must be present for the other dimension to be defined • dimensions are dependent • Examples: color and brightness of an object, rectangle height & width

12. Multi-dimensional Judgment and Displays • What happens if a display has multiple dimensions, but the operator must make a unidimensionaljudgment? • Real World Examples? • Laboratory Example: Garner’s sorting task • Observers sort two-dimensional (or multi-dimensional) stimuli into discrete categories of a single dimension • Three conditions • control • orthogonal • redundant

13. Garner’s Sorting Task Conditions • control: sort along each dimension while ignoring the other dimension, which is constant • dimensions uncorrelated • e.g., judging height of rectangles of constant width and width of rectangles of constant height • orthogonal: sort along each dimension while ignoring the other dimension, which varies • dimensions uncorrelated • e.g., judging height of rectangles while width varies and width of rectangles while height varies • redundant:sort along either of two dimensions • dimensions perfectly correlated • e.g., judging the width or height of rectangles of constant aspect ratio (r = 1.0) or area (r = -1.0)

14. Multi-dimensional Judgment and Displays • Human Performance for Garner’s sorting task • Typical performance • best: redundant sort: redundancy gain • middle: control • worst: orthogonal sort: orthogonal cost • Effect of separable or integral dimensions • integral dimensions (e.g., rectangles): increases redundancy gain and orthogonal cost • separable dimensions (e.g., vectors): minimizes redundancy gain and orthogonal cost, BUT... • gain/cost increased if judged dimension has low saliency

15. Multi-dimensional Judgment and Displays • More on integral dimensions • integral dimensions can produce emergent properties: a unidimensional stimulus property that results from combining 2 or more dimensions • redundancy gain or orthogonal cost can depend on sign of correlation • referred to as configuraldimensions • gain/cost depends on saliency of emergent feature • e.g., rectangles: height and width correlation, rHW rHW = -1.0, emergent feature: shape rHW = 1.0, emergent feature: area

16. Multi-dimensional Judgment and Displays: Summary • Stimuli can vary along multiple dimensions • When operator classifies along all dimensions • more information can be transmitted • bits per dimension is less (loss increased) • greater loss for correlated (dependent) dimensions compared to independent dimensions • When operator classifies along one dimension • integral displays produce a redundancy gain, depending on the emergent properties of their configuration • separable displays can produce a redundancy gain if stimuli are difficult to detect (dual coding)

17. Dimensionality and Displays: Design Implications • Industrial Sorting Tasks: sorting of products • often little control over stimulus (the product) • minimize uncorrelated (irrelevant) dimensions • Symbolic sorting: sorting of information from displays • total control over stimulus (part of the design!) • correlated dimensions represented by integral displays can produce emergent features, aiding categorization, e.g, temp. & pressure in a boiler • unidimensional judgment impaired by integral displays of uncorrelated dimensions

18. Next time… • If you have not already done so • Read W3 and N2 • Homework 2 is due 9-25