So im not sure how to even start this question. How do we calculate the sensitity and specificity only given the sample Mean and sigma. Suppose a diagnostic test for disease D gives results that are continuous and normally distributed. For people without disease D, the distribution is normal with a mean of 80 and a standard deviation of 15; and for those with disease D, it is normal with a mean of 120 and a standard deviation of 20. You decide that levels ≥ 100 will be classified as positive, and levels < 100 as negative. Find the sensitivity and specificity of this test. Change the cut point from 100 to 90, recalculate the sensitivity and specificity. Pick several more cut points and plot the ROC curve.

Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case you require the unanswered parts also, kindly re-post that parts separately. From the given information, The people without disease D, the distribution if normal with mean 80 and standard deviation is 15. For people with disease D, it is normal with mean 120 and standard deviation 20. The levels>100 will be classified as positive. The levels <100 will be classified as negative. Sensitivity: Sensitivity=Ppositive|with disease D =PX>100| X~N120, 20 =PX-μσ>100-μσ =PZ>100-12020 =1-PZ≤-1 =0.8413, obtained from the excel function, =1-NORM.DIST(-1,0,1,TRUE) Specificity: Sensitivity=PNegative|without disease D =PX<100| X~N80, 15 =PX-μσ<100-μσ =PZ<100-8015 =PZ<1.3333 =0.9088, obtained from the excel function, =NORM.DIST(1.3333,0,1,TRUE) Cut points are changed from 100 to 90. The levels>90 will be classified as positive. The levels <90 will be classified as negative. Sensitivity: Sensitivity=Ppositive|with disease D =PX>90| X~N120, 20 =PX-μσ>90-μσ =PZ>90-12020 =1-PZ≤-1.5 =0.9332, obtained from the excel function, =1-NORM.DIST(-1.5,0,1,TRUE)

Answered: Suppose a diagnostic test for disease D…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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So im not sure how to even start this question. How do we calculate the sensitity and specificity only given the sample Mean and sigma.

Suppose a diagnostic test for disease D gives results that are continuous and normally distributed. For people without disease D, the distribution is normal with a mean of 80 and a standard deviation of 15; and for those with disease D, it is normal with a mean of 120 and a standard deviation of 20. You decide that levels ≥ 100 will be classified as positive, and levels < 100 as negative. Find the sensitivity and specificity of this test. Change the cut point from 100 to 90, recalculate the sensitivity and specificity. Pick several more cut points and plot the ROC curve.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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