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Signal Detection Theory I. Challenges in Measuring Perception II. Introduction to Signal Detection Theory III. Applications of Signal Detection Theory
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Part 1 Challenges in Measuring Perception
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Psychophysics Psychophysics is the science of establishing quantitative relations between physical stimulation and perceptual events.
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The Method of Limits Experimenter adjusts intensity until the stimulus is detected.
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The Method of Limits Advantage: Measurements are made quickly. Disadvantage: It is not clear exactly what’s being measured (no control for bias).
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“Catch Trials” The subject is asked to make a response when no stimulus has been presented (also called “noise only” trials).
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Not All Errors Are Equal 1. Reporting stimulus is present when it’s absent (“false alarm”). Versus 2.Reporting stimulus is absent when it’s present (“miss”).
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Correct Responses Differ, Too 1. Reporting stimulus is present when it’s present (“hit”). Versus 2.Reporting stimulus is absent when it’s absent (“correct rejection”).
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Stimulus-Response Matrix Response Stimulus “No”“Yes” Present Absent Miss Correct Rejection Hit False Alarm
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Part II Introduction to Signal Detection Theory S.D.T. In Words
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Signal Detection Theory S.D.T. is a procedure for measuring sensitivity to stimulation, independent of the subject’s response bias.
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Signal Detection Theory S.D.T. reduces the stimulus-response matrix to two meaningful quantities. 1. Detectability (d’) - a subject’s sensitivity to stimulation. 2. Criterion ( ) - a subject’s inclination to favor a particular response; bias.
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Part II Introduction to Signal Detection Theory S.D.T. In Pictures
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Distributions of Sensory Responses
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Spontaneous Activity is Constant
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Distributions of Sensory Responses Spontaneous Activity is Normally Distributed The “Noise” Distribution
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Distributions of Sensory Responses The “Noise” Distribution The “Signal + Noise” Distribution A Mild Stimulus is Presented (d’=1)
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Distributions of Sensory Responses The “Noise” Distribution The “Signal + Noise” Distribution A Moderate Stimulus is Presented (d’=2)
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Distributions of Sensory Responses The “Noise” Distribution The “Signal + Noise” Distribution An Intense Stimulus is Presented (d’=3)
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Distributions of Sensory Responses Sub-Threshold Stimulus is Presented (d’=0) The “Noise” Distribution The “Signal + Noise” Distribution
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Criterion The “Noise” Distribution The “Signal + Noise” Distribution
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Neutral Criterion The “Noise” Distribution The “Signal + Noise” Distribution.5
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Liberal (low) Criterion The “Noise” Distribution The “Signal + Noise” Distribution.2.6
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Conservative (high) Criterion The “Noise” Distribution The “Signal + Noise” Distribution.6.2
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Receiver Operating Space
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Receiver Operating Characteristics d’=0
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R.O.C. Curves d’=1 d’=0
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R.O.C. Curves d’=1 d’=0
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R.O.C. Curves d’=1 d’=2 d’=0
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R.O.C. Curves d’=1 d’=2 d’=3 d’=0
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R.O.C. Curves
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d’ = -1 d’ = -2 d’ = -3
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Part II Introduction to Signal Detection Theory S.D.T. In Numbers
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Normal Distributions S.D.T. is based on normal distributions. Each normal distribution is described by a mean and a standard deviation.
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Normal Distributions A given point on a normal distribution can be described be described 3 ways. 1. Percentile (also proportion) 2. Z-score (# of standard deviations) 3. Probability Density (likelihood)
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Computing Detectability d’ = zHits - zFalse Alarms In excel, the “normsinv” function is used: Input = proportion Output = z-Score Conceptually, detectability (d’) increases with the area under the R.O.C. curve.
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Computing Criterion = Hit Density / False Alarm Density In excel, the “normsdist” function is used: Input = z-Score Output = density Conceptually, is equal to the slope of the R.O.C. curve at single point.
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Part III Applications of Signal Detection Theory
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S.D.T. Applications S.D.T. can be used in perceptual discrimination experiments.
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S.D.T. And Discrimination The “slow” distribution The “fast” distribution
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S.D.T. Applications S.D.T. can be used in non-perceptual research, including memory experiments.
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S.D.T. And Memory The “new items” distribution The “old items” distribution
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