ROC SONAR, originally an acronym for Sound Navigation And Ranging, is a process

Question

ROC SONAR, originally an acronym for Sound Navigation And Ranging, is a process where sound in water is categorized. Active sonar is where a sound is emitted and the reflected sound is assessed. For our example, we will have two possibilities, either the object that reflects is a submarine, or, it is a whale. Suppose the following results from 100 sound waves:

2. What are the: ppv, npv, specificity, sensitivity, type 1 error, type 2 error, alpha, beta, power. Provide the formula for each using the letters assigned in Q1.

a.) PPV
= A / (A + B)
90 / (90 + 4) = 95.7%

b.) NPV
= D / (C + D)
2 / (4 + 2) = 33.3%

c.) Specificity
= D / (B + D)
2 / (4 + 2) = 33.3%

d.) Sensitivity
= A / (A + C)
90 / (90 + 4) = 95.7%

I understood how to work this problem up until this point. I'm not sure I understand how to do 2.e-i

e.) type 1 error

f.) type 2 error

g.) alpha

h.) beta

i.) power

If it's not too much trouble please show your steps in solving this problem. Thank you so much for your help!

Explanation / Answer

Assuming we have formed H0, as follows:

H0: it is whale

Ha: it is not whale but submarine

e) Type-1 error:

it is the probability of rejecting H0 (null hypothesis) when it is true.

type-I error probability= B/(A+B) = 4.25%

f) Type 2-error:

it is the probability of not rejecting H0 (null hypothesis) when it is false.

type-II error probability= C/(C+D) = 66.67%

G) Alpha: is observed significant level

It is probability of observing type-I error.

ans is 4.25%

h) Beta is probability of type-II error.

ans is = C/(C+D) = 66.67%

I) Power of test : rejecting H0 when it is false = 1- beta= 1-.6667 = 0.333 = 33.33%

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