1. 10 / 31 Outline Perception workshop groups Signal detection theory Scheduling meetings

2. Detection experiment Question –How sensitive is an observer to a sensory stimulus; for example, light?

3. Detection experiment Question –How sensitive is an observer to (for example) light? Classic experiment –Yes/No task

4. Detection experiment Question –How sensitive is an observer to (for example) light? Classic experiment –Yes/No task –Measure threshold intensity needed to have 50% hits

14. Threshold

18. Jane Nancy

19. Summary of results Thresholds –Jane = 20 –Nancy = 25

20. Summary of results Thresholds –Jane = 20 –Nancy = 25 False alarm rates –Jane = 51% –Nancy = 18.7%

21. Look at one intensity level I = 25

24. Jane’s Hit Rate P(H) =.84

25. Nancy’s Hit Rate P(H) =.5

26. Look at one intensity level I = 25 –Jane Hit rate: P(H) =.84

27. Look at one intensity level I = 25 –Jane Hit rate: P(H) =.84 False alarm rate: P(FA) =.51

28. Look at one intensity level I = 25 –Jane Hit rate: P(H) =.84 False alarm rate: P(FA) =.51 –Nancy Hit rate: P(H) =.5

29. Look at one intensity level I = 25 –Jane Hit rate: P(H) =.84 False alarm rate: P(FA) =.51 –Nancy Hit rate: P(H) =.5 False alarm rate: P(FA) =.187

30. Signal detection theory terms Hits - p(H) –Proportion of “yes” responses when signal is present

31. Signal detection theory terms Hits - p(H) –Proportion of “yes” responses when signal is present Misses - p(M) –Proportion of “no” responses when signal is present

32. Signal detection theory terms Hits - p(H) –Proportion of “yes” responses when signal is present Misses - p(M) –Proportion of “no” responses when signal is present False alarms - p(FA) –Proportion of “yes” responses when signal is not present

33. Signal detection theory terms Hits - p(H) –Proportion of “yes” responses when signal is present Misses - p(M) –Proportion of “no” responses when signal is present False alarms - p(FA) –Proportion of “yes” responses when signal is not present Correct rejections - p(CR) –Proportion of “no” responses when signal is not present

34. Relationships between terms P(H) + P(M) = 1

35. Relationships between terms P(H) + P(M) = 1 P(FA) + P(CR) = 1

36. Relationships between terms P(H) + P(M) = 1 P(FA) + P(CR) = 1 Only need to specify P(H) and P(FA)

37. Extreme detection strategies Most liberal (always say yes)

38. Extreme detection strategies Most liberal (always say yes) –P(H) = 1, P(FA) = 1

39. Extreme detection strategies Most liberal (always say yes) –P(H) = 1, P(FA) = 1 Most conservative (always say no)

40. Extreme detection strategies Most liberal (always say yes) –P(H) = 1, P(FA) = 1 Most conservative (always say no) –P(H) = 0, P(FA) = 0

41. Signal Detection Theory

42. Assume an internal measure of signal strength.

43. Signal Detection Theory Assume an internal measure of signal strength (X). –E.g. firing rate of ganglion cell

44. Signal Detection Theory Assume an internal measure of signal strength (X). –E.g. firing rate of ganglion cell X is corrupted by noise

45. Signal Detection Theory Assume an internal measure of signal strength (X). –E.g. firing rate of ganglion cell X is corrupted by noise –E.g. random variations in firing rate

46. Signal Detection Theory Assume an internal measure of signal strength (X). –E.g. firing rate of ganglion cell X is corrupted by noise –E.g. random variations in firing rate When signal is not present, X = X 0 + N

48. Signal Detection Theory Assume an internal measure of signal strength (X). –E.g. firing rate of ganglion cell X is corrupted by noise –E.g. random variations in firing rate When signal is not present, X = X 0 + N When signal is present, X = X S + N

50. o Firing rate when signal is present o Firing rate when signal is not present

51. Criterion Set a criterion level, C

52. Criterion Set a criterion level, C If X > C –Report a signal

53. Criterion Set a criterion level, C If X > C –Report a signal If X < C –Report no signal

54. o Firing rate when signal is present o Firing rate when signal is not present C=20, Liberal criterion

55. Liberal criterion = High hit rate

56. Liberal criterion = High false alarm rate

57. o Firing rate when signal is present o Firing rate when signal is not present C=30, Conservative criterion

58. Conservative criterion = Low hit rate

59. Conservative criterion = Low false alarm rate

60. Probability distribution on X (no signal)

61. Probability distribution on X (signal)

62. Liberal criterion

63. Conservative criterion

64. ROC curve

70. A B C No signal Signal

71. A B C

72. A B C

73. A B C No signal Signal

74. A B C

75. A B C

76. Determinants of performance No signal Signal

77. Determinants of performance XNXN XSXS No signal Signal

78. Determinants of performance XNXN XSXS ∆X No signal Signal

79. Determinants of performance XNXN XSXS 1. Difference in average strength of Signal measure ∆X = X S - X N ∆X No signal Signal

80. Determinants of performance 1. Difference in average strength of Signal measure ∆X = X S - X N 2. Amount of noise  ∆X  No signal Signal

81. Determinants of performance 1. Difference in average strength of Signal measure ∆X = X S - X N 2. Amount of noise  3. Sensitivity d’ = ∆X /  ∆X  No signal Signal

82. D’ determines which ROC curve your data will fall on

83. d’ =.83 d’ = 1.2 d’ = 2.5 D’ determines which ROC curve your data will fall on

84. Criterion determines where your data will sit on an ROC curve

85. Conservative criterion Liberal criterion Criterion determines where your data will sit on an ROC curve

87. Measuring sensitivity

88. Pick a stimulus level for a yes / no task

89. Measuring sensitivity Pick a stimulus level for a yes / no task Measure hit rate and false alarm rate

90. Measuring sensitivity Pick a stimulus level for a yes / no task Measure hit rate and false alarm rate Use p(H) and p(FA) to calculate d’

91. Measuring sensitivity Pick a stimulus level for a yes / no task Measure hit rate and false alarm rate Use p(H) and p(FA) to calculate d’ d’ = absolute measure of sensitivity

92. Blood test example Get a blood test for level of protein A.

93. Blood test example Get a blood test for level of protein A. Doctor says that test is positive for liver cancer.

94. Blood test example Get a blood test for level of protein A. Doctor says that test is positive for liver cancer. Doctor recommends surgery to collect tissue sample for biopsy.

95. Blood test example Get a blood test for level of protein A. Doctor says that test is positive for liver cancer. Doctor recommends surgery to collect tissue sample for biopsy. What should you ask the doctor about the blood test?

96. No cancer Cancer

97. Liberal criterion No cancer Cancer

98. Conservative criterion No cancer Cancer