Measures of Dispersion and Variability: Range, QD, AD and SD
DETECTION THEORY CHAPTER 6
1. Detection and Discrimination of Compound Stimuli: Tools for Multidimensional Detection Theory CHAPTER 6, Detection Theory: A User’s Guide
2. One dimensional Multidimensional- “compound” stimuli Whether theses “cues” are combined by the observer Detection / discrimination Visual appearance / quality of sound
3. One dimensional review Φ(z)-area from the left tail of the distribution to the criterion Correct rejections- Φ(c)= Φ(1)=0.84 (p.376) 1- Φ(z)=Φ(-z)
4. Two ways to draw joint distributions The highest point- greatest likelihood, means of both variables point (μx,μy)
7. Projection Joint distributions Marginal distribution Distribution of x (ignoring y) The joint distribution is said to be projected onto the x-axis Vertical criterion line As if the eyes were closed
8. The probability is the same when only the tone is presented as when both the tone and light are presented, but the light was ignored
9. Equal standard deviations Joint distribution: circular Unequal standard deviations Joint distribution: elliptical
10. Add the values of loudness and brightness and use the sum as the basis for a decision Φ(1.41)=0.92 92% > 84%
11. Perceptual independence and dependence of distributions Lack of correlations Statistically independent variables, perceptually independence Perceptually dependence X and y axes are nonorthogonal Distribution is elliptical
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13. Decision Boundaries: The product rule Placing a separate criterion on each of them Divided into four regions
14. Maximum Maximum: above both the criterion in order to say yes Shaded area: .84*.84 = .71 Unshaded area:”no” response (miss rate) 1-.71=.29
15. Minimum Minimum: either above the y criterion or to the right of the x criterion ‘yes’ rate of an incautious observer Miss rate: .16*.16=.026 Hit rate:1-.026= .974
17. Decision rules Inattention, criterion fluctuation produce low performance; does not affect sensitivity, d’ Bias-free measure: d’ (6.2)
18. Decisional separability A condition that the decision boundary is a straight line parallel to one of the axes Ignores one of the components Ex. Consider only the loudness dimension Effective sensitivity: d’x p(c)= if d’x = 1 , p(c)max=.69
19. Maximum Sets criteria at both axes Exceeds both criteria kx=ky=0.5 Hx=Hy=0.69 H2=0.692=0.48 F2=0.312=0.10 p(c)=0.5(0.48+0.90)=0.69
20. Minimum Sets criteria at both axes Exceeds either criteria H2=0.9, F2=0.52 p(c)=0.69
21. Maximize p(c) adopt a symmetric criterion Strong response bias for “yes” rate [(H+F)/2] Maximum: 0.29 Minimum: 0.71
22. SDT solution Apply product rule twice Both stimulus and no-stimulus distribution Maximum (6.5) Minimum (6.6)
23. ROC curve Decision separable rule= maximum rule= minimum rule= 0.69 Differ in bias
24. The optimal rule Both component contribute to the decision If the sum is above the sum value”yes” Effective d’ = 1.41 ; p(c)max= 0.76
25. Deduce predictions Inductive problems Two dimensions, two observables Two values of sensitivity One or two values of criterion Assumptions about independence Form of decision bound The nature of the decision rule
26. Two ways to attack this problem… Simplifying assumptions No sensitivity or bias parameters H2&F2 (Hx, Hy, Fx, Fy four values)assume that both components are equally detectable Hx =Hy = 1 ; Fx = Fy =1 “both” -“either”
