12 Explain why the following statement is true, or provide a counter-example: A receiver- operator characteristic curve, which plots the Type I error of a test against the Type II error from that same test, always slopes downward. See Figure 12.8(b) for an example of this kind of curve. a) Five possible thresholds FUR- & T3 TA B Type II error bad drugs (b) Receiver-operator characteristic (ROC) curve good drugs Ts T₁ T₂ T3 T₁ T Figure 12.8. Adjusting the rejection threshold creates a tradeoff between Type I error and Type II error. (a) Five possible thresholds. (b) Receiver-operator characteristic (ROC) curve.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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12 Explain why the following statement is true, or provide a counter-example: A receiver-
operator characteristic curve, which plots the Type I error of a test against the Type II
error from that same test, always slopes downward. See Figure 12.8(b) for an example
of this kind of curve.
(a) Five possible thresholds
Density
bad drugs
WIK
good drugs
B
(b) Receiver-operator characteristic
(ROC) curve
Type I error
T3
Type II error
T₁
T₂
T3
TA
T
Figure 12.8. Adjusting the rejection threshold creates a tradeoff between Type I error and Type II error. (a) Five possible
thresholds. (b) Receiver-operator characteristic (ROC) curve.
Transcribed Image Text:12 Explain why the following statement is true, or provide a counter-example: A receiver- operator characteristic curve, which plots the Type I error of a test against the Type II error from that same test, always slopes downward. See Figure 12.8(b) for an example of this kind of curve. (a) Five possible thresholds Density bad drugs WIK good drugs B (b) Receiver-operator characteristic (ROC) curve Type I error T3 Type II error T₁ T₂ T3 TA T Figure 12.8. Adjusting the rejection threshold creates a tradeoff between Type I error and Type II error. (a) Five possible thresholds. (b) Receiver-operator characteristic (ROC) curve.
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