Bayes Theorem Calculators Blank v2(Fall 2023)

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Virginia Commonwealth University *

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Nov 24, 2024

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Table of Contents Bayes Theorem and Calculator Contingency Table Step by Step Template Contigency Tables Solution (Acme) Probability Tree Template Solution (NLP Prevalenc Solution (NLP Prevalenc Calculator for NPV and PPV Solution (COVID Prevalen Solution (COVID Prevalen Calculator for Sensitivity and Spe Solution (Sensitivity and Specificit Solution (Sensitivity and Specificit
) ce 30%) ce 50%) nce 60%) nce 20%) ecificity ty COVID Prevalence 60%) ty COVID Prevalence 20%)
TreePlan Student License, For Education Only TreePlan.com Event A BAYES THEOREM Bayes Theorem Calculator Bayes Theorem Calculator (Using Sensitivity/Specificity/Prevalence Language) A not A Total Enter Enter Event B B P(A and B) P(not A and B) P(B) P(A) Given Prevalence of Disease Given not B P(A and not B) P(not A and not B) P(not B) P(B|A) Given Sensitivity (P(T+|D+)) Given Total P(A) P(not A) 1 P(not B|not A) Given Specificity (P(T-|D-)) Given Remember our friend, the multiplication rule… Probability Formula Probability Formula Conditional ProbabilityNumerator Denominator P(A|B) 0.000% =P4*P3/(P4*P3+(1-P3)*(1-P5)) PPV= P(D+|T+) 0.000% =U4*U3/(U4*U3+(1-U3)*(1-U5)) P(A|B) P(A and B) P(B) P(not A|B) 100.000% =1-P7 False Positive Rate= P(D-|T+) 100.000% =1-U7 P(not A|B) P(not A and B) P(B) P(A|not B) #DIV/0! =1-P10 False negative Rate= P(D+|T-) #DIV/0! =1-U10 P(A|not B) P(A and not B) P(not B) P(not A|not B) #DIV/0! =P5*(1-P3)/(P5*(1-P3)+(1-P4)*P3) NPV= P(D-|T-)) #DIV/0! =U5*(1-U3)/(U5*(1-U3)+(1-U4)*U3) P(not A|not B) P(not A and not B) P(not B) P(B) 100.000% =P4*P3+(1-P5)*(1-P3) P(T+) 100.000% =U4*U3+(1-U5)*(1-U3) P(B|A) P(A and B) P(A) From the contingency table, it is easy to see that P(not B) 0.000% =1-P11 P(T-) 0.000% =1-U11 P(not B|A) P(A and not B) P(A) P(B|not A) P(not A and B) P(not A) P(not B|not A) P(not A and not B) P(not A) The multiplication rule also states that Each bracket above denotes a complement pair meaning that the two conditional probabilities must sum to 1 Understanding which Probabilities are Complement of each Other PPV= (Sensitivity * Prevalence) / ((Sensitivity*Prevalence)+(1-Specificity)*(1-Prevalence)) PV= (Specificity *(1-Prevalence)) / (Specificity *(1-Prevalence)+(1-Sensitivity)*(Prevalence P(A|B)= P(B|A)*P(A) / [P(B|A)*P(A) + P(B|not A)*P(not A)] As you can see, the expanded Bayes equation is equivalent to… BAYES THEOREM allows us to calculate P(A|B) from P(B|A) P(A and B) = P(A|B) * P(B ) We can solve for P(A|B ) as follows: P (A|B ) = P(A and B) / P(B ) We need P(A and B) and P(B). Let's tackle P(B) first. P(B) = P(A and B) + P(not A and B) P(A|B) = P(B|A)*P(A) / [ P(B|A)*P(A) + P(B|not A)*P(not A) ] P(A and B) =P(B|A) * P(A) P(not A and B) = P(B|not A) * P(not A) This allows us to substitute those formulas to obtain the following for P(B) : P(B) = P(B|A) * P(A) + P(B|not A) * P(not A) Recalling our previous equation P(A|B) = P(A and B) / P(B) from above… We can now substitute for both P(A and B) and P(B) Leaving us with Bayes Theorem P(A|B) = P(A and B) / P(B) Many students find this equation confusing. If you understand contingency tables, I promise you that you can solve any problem. LEARN CONTINGENCY TABLES ? P(A and B) P(not A and B) P(A and B) P(A and B) P(not A and B) P(B) Red boxes denote the complement pairs P(A) P(not A) P(B|A) P(not B|A) P(B|not A) P(not B|not A) P(A and B) P(not A and B) P(not A and not B) P(A and not B) P(B) P(not B) P(A|B) P(not A|B) P(A|not B) P(not A|not B) P(A and B) P(A and not B) P(not A and not B) P(not A and B) P(A and B) P(A and B) P(not A and B) P(B)
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A not A B P(A and B) P(not A and B) not B P(A and not B) P(not A and not B) P(A) P(not A) Disease No Disease Test+ 0 1 Test - 0 0 0 1 Given P(T+|D+) True Positive Rate=Se P(T-|D-) True Negative Rate=S P(D+) Prevalence Need Numerator Denominator P(D+|T+) 0 1 P(D-|T+) 1 1 P(D+|T-) 0 0 P(D-|T-) 0 0 P(T+) P(T-) Posterior probabilities meaning AFTER the test is done and more information is known. To use this calculator, enter the necessary information in the gray boxes. Auto Calculator
P(B) P(not B) 1 1 0 1 ensitivity Specificity Probability 0.000% PPV 100.000% #DIV/0! #DIV/0! NPV 100.000% TPR 0.000% TNR Suppose you have a disease with pre has a sensitivity (True positive rate) o negative rate) of 95%. A person tests their chances are of actually having t To solve the problem, you can simply set u multiplication rule, you have all the tools y completing a contingency table on your o relationships between joint and conditiona boxes to the right 1-9 so that you can follo Step 1: Box 9 is easy to fill out as this is t equal 1. Step 2: The probability of A is also given, This allows us to compute Box 8 as '1- Box Step 3: We are also given the P(B|A). This of the test (0.85). Recalling that P(A and B and B) by multiplying 0.85 by 0.0002 . This Now, we can also compute Box 4 by subt value is 0.00003 . Step 4: We are also given the specificity B|not A). This is 0.95. Given the multiplica A) =P(not B|not A)* P(not A) . We thus multi (0.94981) goes in Box 5 . We can now calculate Box 2 as 0.9998 - 0.9 Step 5: The last step to complete your co rows B and not B. Box 3 is 0.00017 + 0.04 + 0.94981 or 0.04984.
Now that you have your completed contin compute any conditional probability. Returning to the problem at hand, we nee is positive. This is simply Box 1/Box 3 or 0 means that there is only a 0.34% probabil positive test. Alternatively, 99.66% of pati have the disease (i.e. false positive test). Practice makes perfect so please practice On the left is a calculator that will autocom prevalence of event A (i.e. P(A)), Sensitivit A-)). It will also compute for you the poste trees involving screening (i.e. receiving ne you receive new information, you have to new probabilties are called "posterior" pro "conditional" probabilities since they depe
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Event A= Dis Event B= Tes B not B Step 1 B not B Step 2 B not B B not B Step 3 B not B B evalence 0.0002 (P(A)) and the test of 85% and specificity (True s positive and wants to know what the disease. up a contingency table. Along with the you need. Please work through own so that you understand the al probabilities. I have numbered the ow along step by step.. the Grand Total box which must always , so we can place this value in box 7 . x 7 'or ' 1-0.0002 '. Box 8 is P(not A) . s is the sensitivity or true positive rate B )= P(B|A)* P(A) , we can compute P(A s value (0.00017) goes into Box 1 . tracting 0.00017 from 0.0002 . This (true positive rate) which is the P(not ation rule, we know that P(not B and not iple 0.95 by 0.9998 . This value 94981 . This value is 0.04999 . ontingency box is to sum up the two 499 or 0.05016. Box 6 equals 0.00003
not B Step 4 B not B B not B Step 5 YOU B not B B not B ngency table, you should be able to ed the probability of disease if the test 0.00017/0.05016. This calculation lity of having the disease even with a ients with a positive screen will NOT e completing contingency tables. mplete a contingency table if given ty (i.e. P(B|A)) and Specificity (i.e. P(B-| erior probabilities to use for decision ew information). Remember that when adjust your "prior" probabilities. The obabilties because they are end on the information received.
sease status (A= disease, Not A= no disease) st status (B= positive test, Not B= negative test) A not A 1 2 3 4 5 6 7 8 9 A not A 1 2 3 4 5 6 7 8 1 A not A 1 2 3 4 5 6 0.0002 8 1 A not A 1 2 3 4 5 6 0.0002 0.9998 1 A not A 0.00017 2 3 4 5 6 0.0002 8 1 A not A 0.00017 2 3 CONTINGENCY TABLES STEP by STEP
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3E-05 5 6 0.0002 0.9998 1 A not A 0.00017 2 3 3E-05 0.94981 6 0.0002 0.9998 1 A not A 0.00017 0.04999 3 3E-05 0.94981 6 0.0002 0.9998 1 MADE IT! A not A 0.00017 0.04999 0.05016 3E-05 0.94981 6 0.0002 0.9998 1 A not A 0.00017 0.04999 0.05016 3E-05 0.94981 0.94984 0.0002 0.9998 1
B Not B B Not B Solut P(B | A) P(Not B | Not A) P(A) P(A | B) P(Not A | B) P(A | Not B) P(Not A | Not B) P(B) P(Not B) Posterior probabilities meaning AFTER the test is done and more information is known.
Event Outcom A not A Scree B not B A P(A and B P(A and Not B P(A) A 0 0 0 tion Need Numerator 0 1 0 0
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me to Predict A Not A ening Test B Not B Not A P(Not A and B) P(B) P(Not A and Not B) P(Not B) P(Not A) 1 Not A 1 1 0 0 1 1 Denominator Probability 1 0% 1 100% 0 #DIV/0! 0 #DIV/0! 100% 0% To use this Calculat Step 1: Change the labels for to be predicted (Event A) in Step 2: Change the labels for test (Event B) in cells D Step 3: Enter the required probabilities in the blue/gray boxes (C21:C23). The contingency table above and probabilities below will autopopulate.
Can we imp tor the outcome cells D3:D4. the screening D6:D7.
Try this example from ACME. prove our ability to predict an outcome using a research firm?
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Test Predicts Good Test Predicts Bad Test Predicts Good Test Predicts Bad Give P(Test Predicts Good | Market Good) P(Test Predicts Bad | Market Not Good) P(Market Good) P(Market Good | Test Predicts Good) P(Market Not Good | Test Predicts Good) P(Market Good | Test Predicts Bad) P(Market Not Good | Test Predicts Bad) P(Test Predicts Good) P(Test Predicts Bad) Posterior probabilities meaning AFTER the test is done and more information is known.
Event Outcom A not A Scree B not B Market Good P(Market Good and Test Predicts Good P(Market Good and Test Predicts Bad P(Market Good) Market Good 0.32 0.08 0.4 en 0.8 0.7 0.4 Need Numerator 0.32 0.18 0.08 0.42
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me to Predict Market Good Market Not Good ening Test Test Predicts Good Test Predicts Bad Market Not Good P(Market Not Good and Test Predicts Good) P(Test Predicts Good) P(Market Not Good and Test Predicts Bad) P(Test Predicts Bad) P(Market Not Good) 1 Market Not Good 0.18 0.5 0.42 0.5 0.6 1 Denominator Probability 0.5 64% 0.5 36% 0.5 16% 0.5 84% 50% 50% To use this Calcu Step 1: Change the labels f to be predicted (Event A) Step 2: Change the labels fo test (Event B) in cell Step 3: Enter the required probabilities in the blue/gray boxes (C21:C23). The contingency table above and probabilities below will autopopulate.
Can we imp ulator for the outcome in cells D3:D4. or the screening ls D6:D7.
Try this example from ACME. prove our ability to predict an outcome using a research firm?
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TreePlan Student License, For Education Only TreePlan.com Event Outcome to Predict A not A Screening Test B not B G P(B | A) P(Not B | not A) P(A) P(A | B) P(not A | B) P(A | Not B) P(not A | Not B) P(B) P(Not B) PRI Enter data into the gray boxes. The contingenc
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TreePlan Student License, For Education Only TreePlan.com A not A PO B Not B M
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TreePlan Student License, For Education Only TreePlan.com P(B) = P(A and B
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TreePlan Student License, For Education Only TreePlan.com A not A B Not B Given (enter as proportions) True Positive Rate=Sensitivity True Negative Rate=Specificity Prevalence Solutions Probability 0.000% Positive Predictive Value (PPV) 100.000% #DIV/0! #DIV/0! Negative Predictive Value (NPV) 100.00% Test Positive Rate #DIV/0! Test Negative Rate IOR PROBABILITIES AFTER THE NEW INFORMATION IS OB B P(A) cy table, probability tree and conditional probabilities will autopopul PROBABILITY TREES Step 3: Enter the required pro cells.The contingency table, Pr Solutions table will au To use this Calculator Step 1: Change the labels for the o predicted (Event A) in the gra Step 2: Change the labels for the s (Event B) in the gray cel
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TreePlan Student License, For Education Only TreePlan.com 0 Not B B P(not A) 1 Not B OSTERIOR PROBABILITIES AFTER THE NEW INFORMATION IS OBTA A P(B) 1 not A A P(Not B) 0 not A MULTIPLICATION RULE: P(B|A) * P(A) = P(A and B) = P(A|B)* P(B) P(B) = P(A and B) + P(Not A and B)
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TreePlan Student License, For Education Only TreePlan.com MULTIPLICATION RULE: P(A and B) = P(A|B)*P(B) P(A|B)= P(A and B) ÷ P(B) We have P(A and B), need P(B) B) + P(Not A and B) from calculations above so we can solve for P(A|
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TreePlan Student License, For Education Only TreePlan.com BTAINED (GIVEN IN THIS CASE) Prior Conditional Probabilities 0 P(B | A) late. obabilities in the gray robability Trees, and utopopulate. r outcome to be ay cells. screening test lls.
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TreePlan Student License, For Education Only TreePlan.com 1 P(Not B | A) 1 P(B | not A) 0 P(Not B | not A) AINED (CALCULATED IN THIS CASE) Posterior Conditional Probabilities P(A | B) 0.0000 P(not A | B) 1.0000 P(A | Not B) #DIV/0! P(not A | Not B) #DIV/0!
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TreePlan Student License, For Education Only TreePlan.com |B)
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TreePlan Student License, For Education Only TreePlan.com Event B B Not B TOTALS B Not B TOTALS Joint Probabilities P(A and B) 0 Event B: Test Result Try this example: Using the Word "Offer" to screen for Spam
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TreePlan Student License, For Education Only TreePlan.com P(A and Not B) 0 P(not A and B) 1 P(not A and Not B) 0 Joint Probabilities P(A and B) 0 P(not A and B) 1 P(A and Not B) #DIV/0! P(not A and Not B) #DIV/0!
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TreePlan Student License, For Education Only TreePlan.com Ev A P(A and B) P(A and Not B) P(A) Event A: Co A 0 0 0 CONTINGENCY TAB Natural Learning Process mails in inboxes. Assume 10% of spam and desired received emails are cons probability that a new m is spam? With the ever increasing happen to the probabilit appears in the email if th 30%)? ver increasing preval probability of it being a spam the prevalence (i.e. P(D+) is 5 Solution: If the word offer appears in an e email and a 23% probability that contain the word "offer", there is 91% probability that it is not a S If the prevalence is 50% instead "offer" appears increases to 88.9 change .
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TreePlan Student License, For Education Only TreePlan.com vent A not A TOTALS P(not A and B) P(B) P(not A and Not B) P(Not B) P(not A) 1 ondition Status not A TOTALS 1 1 0 0 1 1 BLE sing (NLP) can be used to detect spam e- e that the word "offer" occurs in 80% and d emails respectively. If 30% of the sidered spam emails. What is the message that arrives with the word "offer" g prevalence of spam emails, what would ty an email being spam if the word "offer" he prevalence (i.e. P(D+) is 50% instead of lence of spam emails, what would happen to the m email if the word "offer" appears in the email if 50% instead of 30%). email, there is a 77% probability that it is a SPAM t it is not a SPAM email. If the email does not s only a 9% probability of being a SPAM email and a SPAM email. d of 30%, the probability of being spam if the word 9% even if the accuracy of the NLP software doesn't
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TreePlan Student License, For Education Only TreePlan.com ID 0 1 2 3 4 5 6
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TreePlan Student License, For Education Only TreePlan.com Name Value Prob Pred Kind NS TreePlan 0 0 0 E 2 0 E 2 0 E 2 1 T 0 1 T 0 2 T 0 2 T 0
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TreePlan Student License, For Education Only TreePlan.com S1 S2 S3 S4 S5 Row 1 2 0 0 0 9 3 4 0 0 0 4 5 6 0 0 0 14 0 0 0 0 0 2 0 0 0 0 0 7 0 0 0 0 0 12 0 0 0 0 0 17
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TreePlan Student License, For Education Only TreePlan.com Col Mark 1 1 5 1 5 1 9 1 9 1 9 1 9 1
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TreePlan Student License, For Education Only TreePlan.com Event Outcome to Predict A Spam not A Not Spam Screening Test B Word "Offer" not B Word "Offer" P(Word "Offer" Appears | Spam) 0.8 P(Word "Offer" does not Appear | Not Spam) 0.9 P(Spam) 0.3 Probability P(Spam | Word "Offer" Appears) 77.419% P(Not Spam | Word "Offer" Appears) 22.581% P(Spam | Word "Offer" does not Appear) 8.696% P(Not Spam | Word "Offer" does not Appear) 91.304% P(Word "Offer" Appears) 31.00% P(Word "Offer" does not Appear) 69.00% Enter data into the gray boxes. The conting
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TreePlan Student License, For Education Only TreePlan.com Spam Not Spam Word "Offer" Appears Word "Offer" does not Appear MULTIPLICATION P(
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TreePlan Student License, For Education Only TreePlan.com MULTIPLICA We P(B) = P(A and B) + P(Not A an
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TreePlan Student License, For Education Only TreePlan.com " Appears " does not Appear Given (enter as proportions) True Positive Rate=Sensitivity True Negative Rate=Specificity Prevalence Solutions Positive Predictive Value (PPV) Negative Predictive Value (NPV) Test Positive Rate Test Negative Rate PRIOR PROBABILITIES AFTER THE NEW P(Spam) gency table, probability tree and conditional probab PRO Step 3: Enter the required p cells.The contingency table Solutions table will
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TreePlan Student License, For Education Only TreePlan.com 0.3 P(Not Spam) 0.7 POSTERIOR PROBABILITIES AFTER THE NEW P(Word "Offer" Appears) 0.31 P(Word "Offer" does not Appear) 0.69 N RULE: P(B|A) * P(A) = P(A and B) = P(A|B)* P(B) (B) = P(A and B) + P(Not A and B)
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TreePlan Student License, For Education Only TreePlan.com ATION RULE: P(A and B) = P(A|B)*P(B) P(A|B)= P(A and B) ÷ P(B) e have P(A and B), need P(B) nd B) from calculations above so we can solve for P
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TreePlan Student License, For Education Only TreePlan.com W INFORMATION IS OBTAINED (GI Word "Offer" Appears bilities will autopopulate. OBABILITY TREES probabilities in the gray e, Probability Trees, and l autopopulate. To use this Calculator Step 1: Change the labels for the outcome to be predicted (Event A) in the gray cells. Step 2: Change the labels for the screening test (Event B) in the gray cells.
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TreePlan Student License, For Education Only TreePlan.com Word "Offer" does not Appear Word "Offer" Appears Word "Offer" does not Appear W INFORMATION IS OBTAINED (CALCUL Spam Not Spam Spam Not Spam
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TreePlan Student License, For Education Only TreePlan.com P(A|B)
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TreePlan Student License, For Education Only TreePlan.com IVEN IN THIS CASE) Prior Conditional Probabilities 0.8 P(Word "Offer" Appears | Spam)
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TreePlan Student License, For Education Only TreePlan.com 0.2 P(Word "Offer" does not Appear | Spam) 0.1 P(Word "Offer" Appears | Not Spam) 0.9 P(Word "Offer" does not Appear | Not Spam) P( LATED IN THIS CASE) Posterior Conditional Probabilities P(Spam | Word "Offer" Appears) 0.7742 P(Not Spam | Word "Offer" Appears) 0.2258 P(Spam | Word "Offer" does not Appear) 0.08696 P(Not Spam | Word "Offer" does not Appear) P( 0.91304
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TreePlan Student License, For Education Only TreePlan.com Event B Word "Offer" Appears Offer" does not Appear TOTALS Word "Offer" Appears Offer" does not Appear TOTALS Joint Probabilities P(Spam and Word "Offer" Appears) 0.24 Event B: Test Result Try this example: Using the Word "Offer" to screen for Spam
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TreePlan Student License, For Education Only TreePlan.com P(Spam and Word "Offer" does not Appear) 0.06 P(Not Spam and Word "Offer" Appears) 0.07 (Not Spam and Word "Offer" does not Appear) 0.63 Joint Probabilities P(Spam and Word "Offer" Appears) 0.24 P(Not Spam and Word "Offer" Appears) 0.07 P(Spam and Word "Offer" does not Appear) 0.06 (Not Spam and Word "Offer" does not Appear) 0.63
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TreePlan Student License, For Education Only TreePlan.com Ev Spam P(Spam and Word "Offer" Appears) P(Spam and Word "Offer" does not Appear) P(Spam) Event A: Co Spam 0.24 0.06 0.3 CONTINGENCY TAB Natural Learning Process mails in inboxes. Assume 10% of spam and desired received emails are cons probability that a new m is spam? With the ever increasing happen to the probabilit appears in the email if th 30%)? ver increasing preval probability of it being a spam the prevalence (i.e. P(D+) is 5 Solution: If the word offer appears in an e email and a 23% probability that contain the word "offer", there is 91% probability that it is not a S If the prevalence is 50% instead "offer" appears increases to 88.9 change .
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TreePlan Student License, For Education Only TreePlan.com vent A Not Spam TOTALS P(Not Spam and Word "Offer" Appears) P(Word "Offer" Appears P(Not Spam and Word "Offer" does not Appear) P(Word "Offer" does no P(Not Spam) 1 ondition Status Not Spam TOTALS 0.07 0.31 0.63 0.69 0.7 1 BLE sing (NLP) can be used to detect spam e- e that the word "offer" occurs in 80% and d emails respectively. If 30% of the sidered spam emails. What is the message that arrives with the word "offer" g prevalence of spam emails, what would ty an email being spam if the word "offer" he prevalence (i.e. P(D+) is 50% instead of lence of spam emails, what would happen to the m email if the word "offer" appears in the email if 50% instead of 30%). email, there is a 77% probability that it is a SPAM t it is not a SPAM email. If the email does not s only a 9% probability of being a SPAM email and a SPAM email. d of 30%, the probability of being spam if the word 9% even if the accuracy of the NLP software doesn't
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TreePlan Student License, For Education Only TreePlan.com s) ot Appear)
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TreePlan Student License, For Education Only TreePlan.com ID 0 1 2 3 4 5 6
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TreePlan Student License, For Education Only TreePlan.com Name Value Prob Pred Kind NS TreePlan 0 0 0 E 2 0 E 2 0 E 2 1 T 0 1 T 0 2 T 0 2 T 0
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TreePlan Student License, For Education Only TreePlan.com S1 S2 S3 S4 S5 Row 1 2 0 0 0 9 3 4 0 0 0 4 5 6 0 0 0 14 0 0 0 0 0 2 0 0 0 0 0 7 0 0 0 0 0 12 0 0 0 0 0 17
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TreePlan Student License, For Education Only TreePlan.com Col Mark 1 1 5 1 5 1 9 1 9 1 9 1 9 1
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TreePlan Student License, For Education Only TreePlan.com Event Outcome to Predict A Spam not A Not Spam Screening Test B Word "Offer" not B Word "Offer" P(Word "Offer" Appears | Spam) 0.8 P(Word "Offer" does not Appear | Not Spam) 0.9 P(Spam) 0.5 Probability P(Spam | Word "Offer" Appears) 88.889% P(Not Spam | Word "Offer" Appears) 11.111% P(Spam | Word "Offer" does not Appear) 18.182% P(Not Spam | Word "Offer" does not Appear) 81.818% P(Word "Offer" Appears) 45.00% P(Word "Offer" does not Appear) 55.00% Enter data into the gray boxes. The conting
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TreePlan Student License, For Education Only TreePlan.com Spam Not Spam Word "Offer" Appears Word "Offer" does not Appear MULTIPLICATION P(B
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TreePlan Student License, For Education Only TreePlan.com MULTIPLICA We P(B) = P(A and B) + P(Not A an
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TreePlan Student License, For Education Only TreePlan.com " Appears " does not Appear Given (enter as proportions) True Positive Rate=Sensitivity True Negative Rate=Specificity Prevalence Solutions Positive Predictive Value (PPV) Negative Predictive Value (NPV) Test Positive Rate Test Negative Rate PRIOR PROBABILITIES AFTER THE NEW P(Spam) gency table, probability tree and conditional probab PRO Step 3: Enter the required prob cells.The contingency table, Pro Solutions table will auto
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TreePlan Student License, For Education Only TreePlan.com 0.5 P(Not Spam) 0.5 POSTERIOR PROBABILITIES AFTER THE NEW P(Word "Offer" Appears) 0.45 P(Word "Offer" does not Appear) 0.55 N RULE: P(B|A) * P(A) = P(A and B) = P(A|B)* P(B) B) = P(A and B) + P(Not A and B)
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TreePlan Student License, For Education Only TreePlan.com ATION RULE: P(A and B) = P(A|B)*P(B) P(A|B)= P(A and B) ÷ P(B) e have P(A and B), need P(B) nd B) from calculations above so we can solve for P
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TreePlan Student License, For Education Only TreePlan.com W INFORMATION IS OBTAINED (GI Word "Offer" Appears bilities will autopopulate. OBABILITY TREES babilities in the gray obability Trees, and opopulate. To use this Calculator Step 1: Change the labels for the outcome to be predicted (Event A) in the gray cells. Step 2: Change the labels for the screening test (Event B) in the gray cells.
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TreePlan Student License, For Education Only TreePlan.com Word "Offer" does not Appear Word "Offer" Appears Word "Offer" does not Appear W INFORMATION IS OBTAINED (CALCUL Spam Not Spam Spam Not Spam
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TreePlan Student License, For Education Only TreePlan.com P(A|B)
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TreePlan Student License, For Education Only TreePlan.com IVEN IN THIS CASE) Prior Conditional Probabilities 0.8 P(Word "Offer" Appears | Spam)
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TreePlan Student License, For Education Only TreePlan.com 0.2 P(Word "Offer" does not Appear | Spam) 0.1 P(Word "Offer" Appears | Not Spam) 0.9 P(Word "Offer" does not Appear | Not Spam) P( LATED IN THIS CASE) Posterior Conditional Probabilities P(Spam | Word "Offer" Appears) 0.8889 P(Not Spam | Word "Offer" Appears) 0.1111 P(Spam | Word "Offer" does not Appear) 0.18182 P(Not Spam | Word "Offer" does not Appear) P( 0.81818
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TreePlan Student License, For Education Only TreePlan.com Event B Word "Offer" Appears Offer" does not Appear TOTALS Word "Offer" Appears Offer" does not Appear TOTALS Joint Probabilities P(Spam and Word "Offer" Appears) 0.4 Event B: Test Result Try this example: Using the Word "Offer" to screen for Spam
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TreePlan Student License, For Education Only TreePlan.com P(Spam and Word "Offer" does not Appear) 0.1 P(Not Spam and Word "Offer" Appears) 0.05 (Not Spam and Word "Offer" does not Appear) 0.45 Joint Probabilities P(Spam and Word "Offer" Appears) 0.4 P(Not Spam and Word "Offer" Appears) 0.05 P(Spam and Word "Offer" does not Appear) 0.1 (Not Spam and Word "Offer" does not Appear) 0.45
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TreePlan Student License, For Education Only TreePlan.com Ev Spam P(Spam and Word "Offer" Appears) P(Spam and Word "Offer" does not Appear) P(Spam) Event A: Co Spam 0.4 0.1 0.5 CONTINGENCY TAB Natural Learning Proces mails in inboxes. Assume 10% of spam and desired received emails are cons probability that a new m is spam? With the ever increasing happen to the probabilit appears in the email if th 30%)? ver increasing preva probability of it being a spam the prevalence (i.e. P(D+) is 5 Solution: If the word offer appears in an e email and a 23% probability that contain the word "offer", there i 91% probability that it is not a S If the prevalence is 50% instead "offer" appears increases to 88.9 change .
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TreePlan Student License, For Education Only TreePlan.com vent A Not Spam TOTALS P(Not Spam and Word "Offer" Appears) P(Word "Offer" Appears P(Not Spam and Word "Offer" does not Appear) P(Word "Offer" does no P(Not Spam) 1 ondition Status Not Spam TOTALS 0.05 0.45 0.45 0.55 0.5 1 BLE ssing (NLP) can be used to detect spam e- e that the word "offer" occurs in 80% and d emails respectively. If 30% of the sidered spam emails. What is the message that arrives with the word "offer" g prevalence of spam emails, what would ty an email being spam if the word "offer" he prevalence (i.e. P(D+) is 50% instead of alence of spam emails, what would happen to the m email if the word "offer" appears in the email if 50% instead of 30%). email, there is a 77% probability that it is a SPAM t it is not a SPAM email. If the email does not is only a 9% probability of being a SPAM email and a SPAM email. d of 30%, the probability of being spam if the word 9% even if the accuracy of the NLP software doesn't
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TreePlan Student License, For Education Only TreePlan.com s) ot Appear)
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TreePlan Student License, For Education Only TreePlan.com ID 0 1 2 3 4 5 6
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TreePlan Student License, For Education Only TreePlan.com Name Value Prob Pred Kind NS TreePlan 0 0 0 E 2 0 E 2 0 E 2 1 T 0 1 T 0 2 T 0 2 T 0
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TreePlan Student License, For Education Only TreePlan.com S1 S2 S3 S4 S5 Row 1 2 0 0 0 9 3 4 0 0 0 4 5 6 0 0 0 14 0 0 0 0 0 2 0 0 0 0 0 7 0 0 0 0 0 12 0 0 0 0 0 17
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TreePlan Student License, For Education Only TreePlan.com Col Mark 1 1 5 1 5 1 9 1 9 1 9 1 9 1
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TreePlan Student License, For Education Only TreePlan.com Event Disease Disease (A) Disease No Disease (not A) No Disease Screening Test Test positive (B) Test positive Test negative (not B) Test negative Given (enter as pr P(Test positive | Disease) P(Test negative | No Disease) P(Disease) Solution Probability P(Disease | Test positive) 0.000% P(No Disease | Test positive) 100.000% P(Disease | Test negative) #DIV/0! P(No Disease | Test negative) #DIV/0! P(Test positive) 100.00% P(Test negative) #DIV/0! PRIOR PROBABIL Enter data into the gray boxes. The contingency table, probab
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TreePlan Student License, For Education Only TreePlan.com Disease No Disease POSTERIOR PROB Test positive Test negative MULTIPLICATION RULE: P(T P(T+) = P
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TreePlan Student License, For Education Only TreePlan.com MULTIPLICATION We ha P(D+|
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TreePlan Student License, For Education Only TreePlan.com roportions) True Positive Rate=Sensitivity True Negative Rate=Specificity Prevalence ns Positive Predictive Value (PPV) Negative Predictive Value (NPV) Test Positive Rate Test Negative Rate LITIES AFTER THE NEW INFORMATION IS O Test positive P(Disease) bility tree and conditional probabilities will autopop PROBABILITY TREES To use this Calculator Step 1: Change the labels for the to be predicted (Event A) in the g Step 3: Enter the required gray cells. The contingency and Solutions table w Step 2: Change the labels for the test (Event B) in the gray ce
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TreePlan Student License, For Education Only TreePlan.com 0 Test negative Test positive P(No Disease) 1 Test negative BABILITIES AFTER THE NEW INFORMATION IS OBT Disease P(Test positive) 1 No Disease Disease P(Test negative) 0 No Disease T+|D+) * P(D+) = P(D+ and T+) = P(D+|T+)* P(T+) P(D+ and T+) + P(D- and T+)
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TreePlan Student License, For Education Only TreePlan.com N RULE: P(D+ and T+) = P(D+|T+)* P(T+) ave P(D+ and T+) and P(T+) Solve for P(D+|T+) |T+)= P(D+ and T+) ÷ P(T+)
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TreePlan Student License, For Education Only TreePlan.com OBTAINED (GIVEN IN THIS CASE) Prior Conditional Probabilities 0 P(Test positive | Disease) pulate. e outcome gray cells. d probabilities in the the table, Probability Trees, will autopopulate. screening ells.
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TreePlan Student License, For Education Only TreePlan.com 1 P(Test negative | Disease) 1 P(Test positive | No Disease) 0 P(Test negative | No Disease) TAINED (CALCULATED IN THIS CASE) Posterior Conditional Probabilities P(Disease | Test positive) 0.0000 P(No Disease | Test positive) 1.0000 P(Disease | Test negative) #DIV/0! P(No Disease | Test negative) #DIV/0!
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TreePlan Student License, For Education Only TreePlan.com
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TreePlan Student License, For Education Only TreePlan.com Event B Test positive Test negative TOTALS Test positive Test negative TOTALS Joint Probabilities P(Disease and Test positive) 0 Event B: Test Result
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TreePlan Student License, For Education Only TreePlan.com P(Disease and Test negative) 0 P(No Disease and Test positive) 1 P(No Disease and Test negative) 0 Joint Probabilities P(Disease and Test positive) 0 P(No Disease and Test positive) 1 P(Disease and Test negative) #DIV/0! P(No Disease and Test negative) #DIV/0!
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TreePlan Student License, For Education Only TreePlan.com Ev Disease P(Disease and Test positive) P(Disease and Test negative) P(Disease) Event A: Co Disease 0 0 0 CONTINGENCY TAB Example: Let’s assume; a diagnostic test has 9 have Covid-19. If a patient tests posi actually have the disease? What if the prevalence of COVID is re the probability of COVID with a posit (i.e. Solution: if a person has a positi have COVID. If the test is negati COVID.
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TreePlan Student License, For Education Only TreePlan.com When the prevalence (i.e. P(D+) accuracy has a P(COVID|Test +)
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TreePlan Student License, For Education Only TreePlan.com vent A No Disease TOTALS P(No Disease and Test positive) P(Test positive) P(No Disease and Test negative) P(Test negative) P(No Disease) 1 ondition Status No Disease TOTALS 1 1 0 0 1 1 BLE 99% accuracy and 60% of all people itive, what is the probability that they educed to 20%. How does this change tive test. ears in the email if the prevalence ive COVID test, there is a 99.3% probability that they ive, there is 98.5% probability that they don't have Diag abse typically the test which is
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TreePlan Student License, For Education Only TreePlan.com ) goes down to 20%, the same test with the same of 96.1%.
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TreePlan Student License, For Education Only TreePlan.com gnostic Testing: When we discuss diagnostic testing in medicine, our events are ence/presence of disease and positive or negative test result. Each company will y publish a sensitivity and specificity which are characteristics of the test and once is performed, patients are generally counseled based on the PPV and NPV of a test s based on the prevalence of the disease. The calculations are still the same as any other screening test, we have discussed thus far. Try the example below.
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TreePlan Student License, For Education Only TreePlan.com ID 0 1 2 3 4 5 6
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TreePlan Student License, For Education Only TreePlan.com Name Value Prob Pred Kind NS TreePlan 0 0 0 E 2 0 E 2 0 E 2 1 T 0 1 T 0 2 T 0 2 T 0
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TreePlan Student License, For Education Only TreePlan.com S1 S2 S3 S4 S5 Row 1 2 0 0 0 9 3 4 0 0 0 4 5 6 0 0 0 14 0 0 0 0 0 2 0 0 0 0 0 7 0 0 0 0 0 12 0 0 0 0 0 17
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TreePlan Student License, For Education Only TreePlan.com Col Mark 1 1 5 1 5 1 9 1 9 1 9 1 9 1
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TreePlan Student License, For Education Only TreePlan.com Event Disease Disease (A) COVID No Disease (not A) No COVID Screening Test Test positive (B) Test predic Test negative (not B) Test predic Given (enter as P(Test predicts COVID | COVID) 0.99 P(Test predicts No COVID | No COVID) 0.99 P(COVID) 0.6 Solutio Probability P(COVID | Test predicts COVID) 99.331% P(No COVID | Test predicts COVID) 0.669% P(COVID | Test predicts No COVID) 1.493% P(No COVID | Test predicts No COVID) 98.507% P(Test predicts COVID) 59.80% P(Test predicts No COVID) 40.20% PRIOR PROBAB Enter data into the gray boxes. The contingency table, proba
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TreePlan Student License, For Education Only TreePlan.com COVID No COVID POSTERIOR PRO Test predicts COVID Test predicts No COVID MULTIPLICATION RULE: P(T+
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TreePlan Student License, For Education Only TreePlan.com MULTIPLICAT W P
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TreePlan Student License, For Education Only TreePlan.com cts COVID cts No COVID proportions) True Positive Rate=Sensitivity True Negative Rate=Specificity Prevalence ons Positive Predictive Value (PPV) Negative Predictive Value (NPV) Test Positive Rate Test Negative Rate BILITIES AFTER THE NEW INFORMATION IS Test predicts COVID P(COVID) ability tree and conditional probabilities will autopo PROBABILITY TREES To use this Calcul Step 1: Change the labels for t predicted (Event A) in th Step 3: Enter the required cells. The contingency tab Solutions table w Step 2: Change the labels for t (Event B) in the gra
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TreePlan Student License, For Education Only TreePlan.com 0.6 Test predicts No COVID Test predicts COVID P(No COVID) 0.4 Test predicts No COVID OBABILITIES AFTER THE NEW INFORMATION IS OB COVID P(Test predicts COVID) 0.598 No COVID COVID P(Test predicts No COVID) 0.402 No COVID : P(T+|D+) * P(D+) = P(D+ and T+) = P(D+|T+)* P(T+) +) = P(D+ and T+) + P(D- and T+)
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TreePlan Student License, For Education Only TreePlan.com TION RULE: P(D+ and T+) = P(D+|T+)* P(T+) We have P(D+ and T+) and P(T+) Solve for P(D+|T+) P(D+|T+)= P(D+ and T+) ÷ P(T+)
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TreePlan Student License, For Education Only TreePlan.com S OBTAINED (GIVEN IN THIS CASE) Prior Conditional Probabilities 0.99 P(Test predicts COVID | COVID) opulate. lator the outcome to be he gray cells. d probabilities in the gray ble, Probability Trees, and will autopopulate. the screening test ay cells.
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TreePlan Student License, For Education Only TreePlan.com 0.01 P(Test predicts No COVID | COVID) 0.01 P(Test predicts COVID | No COVID) 0.99 P(Test predicts No COVID | No COVID) BTAINED (CALCULATED IN THIS CASE) Posterior Conditional Probabilities P(COVID | Test predicts COVID) 0.9933 P(No COVID | Test predicts COVID) 0.0067 P(COVID | Test predicts No COVID) 0.01493 P(No COVID | Test predicts No COVID) 0.98507 )
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TreePlan Student License, For Education Only TreePlan.com
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TreePlan Student License, For Education Only TreePlan.com Event B Test predicts COVID Test predicts No COVID TOTALS Test predicts COVID Test predicts No COVID TOTALS Joint Probabilities P(COVID and Test predicts COVID) 0.594 Event B: Test Result
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TreePlan Student License, For Education Only TreePlan.com P(COVID and Test predicts No COVID) 0.006 P(No COVID and Test predicts COVID) 0.004 P(No COVID and Test predicts No COVID) 0.396 Joint Probabilities P(COVID and Test predicts COVID) 0.594 P(No COVID and Test predicts COVID) 0.004 P(COVID and Test predicts No COVID) 0.006 P(No COVID and Test predicts No COVID) 0.396
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TreePlan Student License, For Education Only TreePlan.com Ev COVID P(COVID and Test predicts COVID) P(COVID and Test predicts No COVID) P(COVID) Event A: Co COVID 0.594 0.006 0.6 CONTINGENCY TAB Example: Let’s assume; a diagnostic test has 9 have Covid-19. 1. If a patient tests positive, what is the disease? 2. If a patient tests negative, what is disease? Suppose the prevalence of COVID is 3. How does this change the probabi 4. How does this change the probabi
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TreePlan Student License, For Education Only TreePlan.com 4. How does this change the probabi test? ears in the email if the prevalence Solution: 1. If a person has a positive COV COVID. 2. If the test is negative, there is When the prevalence (i.e. P(D+ accuracy has a ... [see next tab 3. P(COVID|Test +) of 96.1%. Th 4. P(No COVID|Test-) of 99.7%. T
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TreePlan Student License, For Education Only TreePlan.com vent A No COVID TOTALS P(No COVID and Test predicts COVID) P(Test predicts COVID) P(No COVID and Test predicts No COVID) P(Test predicts No COV P(No COVID) 1 ondition Status No COVID TOTALS 0.004 0.598 0.396 0.402 0.4 1 BLE 99% accuracy and 60% of all people the probability that they actually have s the probability that they don't have the reduced to 20%. ility of COVID with a positive test? ility of not having COVID with a negative Diag abse typically the test which is
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TreePlan Student License, For Education Only TreePlan.com ility of not having COVID with a negative e (i.e. VID test, there is a 99.3% probability that they have s 98.5% probability that they don't have COVID. +) goes down to 20%, the same test with the same for details] his PPV is decreased from 99.3%. This NPV is increased from 98.5%.
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TreePlan Student License, For Education Only TreePlan.com VID) gnostic Testing: When we discuss diagnostic testing in medicine, our events are ence/presence of disease and positive or negative test result. Each company will y publish a sensitivity and specificity which are characteristics of the test and once is performed, patients are generally counseled based on the PPV and NPV of a test s based on the prevalence of the disease. The calculations are still the same as any other screening test, we have discussed thus far. Try the example below.
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TreePlan Student License, For Education Only TreePlan.com ID 0 1 2 3 4 5 6
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TreePlan Student License, For Education Only TreePlan.com Name Value Prob Pred Kind NS TreePlan 0 0 0 E 2 0 E 2 0 E 2 1 T 0 1 T 0 2 T 0 2 T 0
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TreePlan Student License, For Education Only TreePlan.com S1 S2 S3 S4 S5 Row 1 2 0 0 0 9 3 4 0 0 0 4 5 6 0 0 0 14 0 0 0 0 0 2 0 0 0 0 0 7 0 0 0 0 0 12 0 0 0 0 0 17
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TreePlan Student License, For Education Only TreePlan.com Col Mark 1 1 5 1 5 1 9 1 9 1 9 1 9 1
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TreePlan Student License, For Education Only TreePlan.com Event Disease Disease (A) COVID No Disease (not A) No COVID Screening Test Test positive (B) Test predic Test negative (not B) Test predic Given (ent P(Test predicts COVID | COVID) 0.99 P(Test predicts No COVID | No COVID) 0.99 P(COVID) 0.2 S Probability P(COVID | Test predicts COVID) 96.117% P(No COVID | Test predicts COVID) 3.883% P(COVID | Test predicts No COVID) 0.252% P(No COVID | Test predicts No COVID) 99.748% P(Test predicts COVID) 20.60% P(Test predicts No COVID) 79.40% PRIOR PRO Enter data into the gray boxes. The contingency table, p
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TreePlan Student License, For Education Only TreePlan.com COVID No COVID POSTERIOR Test predicts COVID Test predicts No COVID MULTIPLICATION RULE: P(T+
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TreePlan Student License, For Education Only TreePlan.com MULTIPLICAT W P
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TreePlan Student License, For Education Only TreePlan.com cts COVID cts No COVID ter as proportions) True Positive Rate=Sensitivity True Negative Rate=Specificity Prevalence Solutions Positive Predictive Value (PPV) Negative Predictive Value (NPV) Test Positive Rate Test Negative Rate OBABILITIES AFTER THE NEW INFORMATION IS OBT Test predicts COVID P(COVID) probability tree and conditional probabilities will autopopula PROBABILITY TREES Step 3: Enter the required probabilities boxes. The contingency table, Probabi and Solutions table will autopopu To use this Calculator Step 1: Change the labels for the outcome to b predicted (Event A) in the gray cells. Step 2: Change the labels for the screening tes (Event B) in the gray cells.
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TreePlan Student License, For Education Only TreePlan.com 0.2 Test predicts No COVID Test predicts COVID P(No COVID) 0.8 Test predicts No COVID R PROBABILITIES AFTER THE NEW INFORMATION IS OBTAIN COVID P(Test predicts COVID) 0.206 No COVID COVID P(Test predicts No COVID) 0.794 No COVID : P(T+|D+) * P(D+) = P(D+ and T+) = P(D+|T+)* P(T+) +) = P(D+ and T+) + P(D- and T+)
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TreePlan Student License, For Education Only TreePlan.com TION RULE: P(D+ and T+) = P(D+|T+)* P(T+) We have P(D+ and T+) and P(T+) Solve for P(D+|T+) P(D+|T+)= P(D+ and T+) ÷ P(T+)
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TreePlan Student License, For Education Only TreePlan.com TAINED (GIVEN IN THIS CASE) Prior Conditional Probabilities 0.99 P(Test predicts COVID | COVID) ate. in the gray ility Trees, ulate. be st
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TreePlan Student License, For Education Only TreePlan.com 0.01 P(Test predicts No COVID | COVID) 0.01 P(Test predicts COVID | No COVID) 0.99 P(Test predicts No COVID | No COVID) NED (CALCULATED IN THIS CASE) Posterior Conditional Probabilities P(COVID | Test predicts COVID) 0.9612 P(No COVID | Test predicts COVID) 0.0388 P(COVID | Test predicts No COVID) 0.00252 P(No COVID | Test predicts No COVID) 0.99748
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TreePlan Student License, For Education Only TreePlan.com
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TreePlan Student License, For Education Only TreePlan.com Event B Test predicts COVID Test predicts No COVID TOTALS Test predicts COVID Test predicts No COVID TOTALS Joint Probabilities P(COVID and Test predicts COVID) 0.198 Event B: Test Result
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TreePlan Student License, For Education Only TreePlan.com P(COVID and Test predicts No COVID) 0.002 P(No COVID and Test predicts COVID) 0.008 P(No COVID and Test predicts No COVID) 0.792 Joint Probabilities P(COVID and Test predicts COVID) 0.198 P(No COVID and Test predicts COVID) 0.008 P(COVID and Test predicts No COVID) 0.002 P(No COVID and Test predicts No COVID) 0.792
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TreePlan Student License, For Education Only TreePlan.com Ev COVID P(COVID and Test predicts COVID) P(COVID and Test predicts No COVID) P(COVID) Event A: Co COVID 0.198 0.002 0.2 CONTINGENCY TAB Example: Let’s assume; a diagnostic test has 9 have COVID. 1. If a patient tests positive, what is the disease? 2. If a patient tests negative, what is disease? Suppose the prevalence of COVID is 3. How does this change the probabi 4. How does this change the probabi
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TreePlan Student License, For Education Only TreePlan.com 4. How does this change the probabi test? ears in the email if the prevalence Solution: 1. If a person has a positive COV COVID. 2. If the test is negative, there is When the prevalence (i.e. P(D+ accuracy has a 3. P(COVID|Test +) of 96.1%. Th 4. P(No COVID|Test-) of 99.7%. T
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TreePlan Student License, For Education Only TreePlan.com vent A No COVID TOTALS P(No COVID and Test predicts COVID) P(Test predicts COVID) P(No COVID and Test predicts No COVID) P(Test predicts No COV P(No COVID) 1 ondition Status No COVID TOTALS 0.008 0.206 0.792 0.794 0.8 1 BLE 99% accuracy and 60% of all people the probability that they actually have s the probability that they don't have the reduced to 20%. ility of COVID with a positive test? ility of not having COVID with a negative Diag abse typically the test which is
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TreePlan Student License, For Education Only TreePlan.com ility of not having COVID with a negative e (i.e. VID test, there is a 99.3% probability that they have s 98.5% probability that they don't have COVID. +) goes down to 20%, the same test with the same his PPV is decreased from 99.3%. This NPV is increased from 98.5%.
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TreePlan Student License, For Education Only TreePlan.com VID) gnostic Testing: When we discuss diagnostic testing in medicine, our events are ence/presence of disease and positive or negative test result. Each company will y publish a sensitivity and specificity which are characteristics of the test and once is performed, patients are generally counseled based on the PPV and NPV of a test s based on the prevalence of the disease. The calculations are still the same as any other screening test, we have discussed thus far. Try the example below.
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TreePlan Student License, For Education Only TreePlan.com ID 0 1 2 3 4 5 6
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TreePlan Student License, For Education Only TreePlan.com Name Value Prob Pred Kind NS TreePlan 0 0 0 E 2 0 E 2 0 E 2 1 T 0 1 T 0 2 T 0 2 T 0
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TreePlan Student License, For Education Only TreePlan.com S1 S2 S3 S4 S5 Row 1 2 0 0 0 9 3 4 0 0 0 4 5 6 0 0 0 14 0 0 0 0 0 2 0 0 0 0 0 7 0 0 0 0 0 12 0 0 0 0 0 17
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TreePlan Student License, For Education Only TreePlan.com Col Mark 1 1 5 1 5 1 9 1 9 1 9 1 9 1
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TreePlan Student License, For Education Only TreePlan.com Disease Disease (A) No Disease (not A) Test Test positive (B) Test negative (not B) Given (enter as proportions) P(Not A | Not B) NPV P(A | B) PPV P(B) Test Positive Rate Need Probability P(B | A) 0% Sensitivity P(Not B | A) 100% P(B | Not A) #DIV/0! Enter data into the gray boxes. The contingency table, prob probabilities will autopopulate. Given the NPV, PPV, and test positivity rate, we can also calculate the sensitivity and s previous COVID example, to calculate the Sensitivty and Specificity. Perform the calculatio prevalence was 60% as well as where the prevalence was 20%. What do you noti
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TreePlan Student License, For Education Only TreePlan.com P(Not B | Not A) #DIV/0! Specificity P(A) 100% Prevalence P(Not A) 0% 1-Prevalence PRIOR PROBABILITIES AFTER THE NEW IN P(A) A 1.00 Not A P(Not A) 0.00 POSTERIOR PROBABILITIES AFTER THE N P(B) P MULTIPLICATION RULE: P(B|A) * P(A) = P(A P(B) = P(A and B) + P(Not A
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TreePlan Student License, For Education Only TreePlan.com B 0 Not B P(Not B) 1 MULTIPLICATION RULE: P(A and B) P(A|B)= P(A and B) ÷ P( We have P(A and B), need P(B) = P(A and B) + P(Not A
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TreePlan Student License, For Education Only TreePlan.com A Not A B Not B e bability tree and conditional Step 3: Enter the required probabilities in cells. The contingency table, Probability Tr Solutions table will autopopulate. pecifity of a test. Use the data below from the ons using your results from the example where the tice about the sensitvity and specificity?
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TreePlan Student License, For Education Only TreePlan.com NFORMATION IS OBTAINED (CALCULATED IN Prior Conditional Probabilities P(B | A) T+ 0.0000 T- P(Not B | A) 1.0000 P(B | Not A) T+ #DIV/0! T- P(Not B | Not A) #DIV/0! NEW INFORMATION IS OBTAINED (GIVEN IN Posterior Conditional Probabilities P(A | B) A 0.0000 PROBABILITY TREES and B) = P(A|B)* P(B) and B)
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TreePlan Student License, For Education Only TreePlan.com Not A P(Not A | B) 1.0000 P(A | Not B) A 1.00000 Not A P(Not A | Not B) 0.00000 ) = P(A|B)*P(B) (B) d P(B) A and B)
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TreePlan Student License, For Education Only TreePlan.com CALCULATOR Ev A Event B B P(A and B) not B P(A and Not B) TOTALS P(A) Event A: D Disease Test+ 0 Test - 1 Event B: Test Result CONTINGENCY TABLE the gray rees, and . To use this Calculator Step 1: Change the labels for the outcome to be predicted (Event A) in the gray cells. Step 2: Change the labels for the screening test (Event B) in the gray cells.
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TreePlan Student License, For Education Only TreePlan.com TOTALS 1 N THIS CASE) Joint Probabilities P(A and B) 0 P(A and Not B) 1 P(Not A and B) 0 P(Not A and Not B) 0 THIS CASE) Joint Probabilities P(A and B) 0
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TreePlan Student License, For Education Only TreePlan.com P(Not A and B) 0 P(A and Not B) 1 P(Not A and Not B) 0
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TreePlan Student License, For Education Only TreePlan.com vent A not A TOTALS P(Not A and B) P(B) P(Not A and Not B) P(Not B) P(Not A) 1 Disease Status No Disease TOTALS 0 0 0 1
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TreePlan Student License, For Education Only TreePlan.com 0 1
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TreePlan Student License, For Education Only TreePlan.com ID Name 0 TreePlan 1 2 3 4 5 6
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TreePlan Student License, For Education Only TreePlan.com Value Prob Pred Kind NS S1 0 0 0 E 2 1 0 E 2 3 0 E 2 5 1 T 0 0 1 T 0 0 2 T 0 0 2 T 0 0
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TreePlan Student License, For Education Only TreePlan.com S2 S3 S4 S5 Row Col 2 0 0 0 9 1 4 0 0 0 4 5 6 0 0 0 14 5 0 0 0 0 2 9 0 0 0 0 7 9 0 0 0 0 12 9 0 0 0 0 17 9
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TreePlan Student License, For Education Only TreePlan.com Mark 1 1 1 1 1 1 1
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TreePlan Student License, For Education Only TreePlan.com Disease Disease (A) No Disease (not A) Test Test positive (B) Test negative (not B) Given (enter as proportions) P(Not A | Not B) 0.98507 NPV P(A | B) 0.99331 PPV P(B) 0.598 Test Positive Rate Need Probability P(B | A) 99% Sensitivity Enter data into the gray boxes. The contingency table, prob probabilities will autopopulate. Given the NPV, PPV, and test positivity rate, we can also calculate the sensitivity an previous COVID example, to calculate the Sensitivty and Specificity. Perform the calc the prevalence was 60% as well as where the prevalence was 20%. What do yo
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TreePlan Student License, For Education Only TreePlan.com P(Not B | A) 1% P(B | Not A) 1% P(Not B | Not A) 99% Specificity P(A) 60% Prevalence P(Not A) 40% 1-Prevalence PRIOR PROBABILITIES AFTER THE NEW IN P(A) A 0.60 Not A P(Not A) 0.40 POSTERIOR PROBABILITIES AFTER THE N P MULTIPLICATION RULE: P(B|A) * P(A) = P(A P(B) = P(A and B) + P(Not A
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TreePlan Student License, For Education Only TreePlan.com P(B) B 0.598 Not B P(Not B) 0.402 MULTIPLICATION RULE: P(A and B) P(A|B)= P(A and B) ÷ P( We have P(A and B), need P(B) = P(A and B) + P(Not A
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TreePlan Student License, For Education Only TreePlan.com A Not A B Not B e bability tree and conditional Step 3: Enter the required probabilities in the gray cells. The contingency table, Probability Trees, and Solutions table will autopopulate. nd specifity of a test. Use the data below from the culations using your results from the example where ou notice about the sensitivity and specificity?
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TreePlan Student License, For Education Only TreePlan.com NFORMATION IS OBTAINED (CALCULATED IN Prior Conditional Probabilities P(B | A) T+ 0.9900 T- P(Not B | A) 0.0100 P(B | Not A) T+ 0.0100 T- P(Not B | Not A) 0.9900 NEW INFORMATION IS OBTAINED (GIVEN IN Posterior Conditional Probabilities P(A | B) A PROBABILITY TREES and B) = P(A|B)* P(B) and B)
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TreePlan Student License, For Education Only TreePlan.com 0.9933 Not A P(Not A | B) 0.0067 P(A | Not B) A 0.01493 Not A P(Not A | Not B) 0.98507 ) = P(A|B)*P(B) (B) d P(B) A and B)
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TreePlan Student License, For Education Only TreePlan.com CALCULATOR Ev A Event B B P(A and B) not B P(A and Not B) TOTALS P(A) Event A: D Disease CONTINGENCY TABLE Solution: Both the sensitivity and specificity for the test are 99%. To use this Calculator Step 1: Change the labels for the outcome to be predicted (Event A) in the gray cells. Step 2: Change the labels for the screening test (Event B) in the gray cells.
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TreePlan Student License, For Education Only TreePlan.com Test+ 0.59399938 Test - 0.00600186 TOTALS 0.60000124 N THIS CASE) Joint Probabilities P(A and B) 0.59399938 P(A and Not B) 0.00600186 P(Not A and B) 0.00400062 P(Not A and Not B) 0.39599814 THIS CASE) Joint Probabilities P(A and B) 0.59399938 Event B: Test Result
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TreePlan Student License, For Education Only TreePlan.com P(Not A and B) 0.00400062 P(A and Not B) 0.00600186 P(Not A and Not B) 0.39599814
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TreePlan Student License, For Education Only TreePlan.com vent A not A TOTALS P(Not A and B) P(B) P(Not A and Not B) P(Not B) P(Not A) 1 Disease Status No Disease TOTALS
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TreePlan Student License, For Education Only TreePlan.com 0.00400062 0.598 0.39599814 0.402 0.39999876 1
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TreePlan Student License, For Education Only TreePlan.com ID Name 0 TreePlan 1 2 3 4 5 6
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TreePlan Student License, For Education Only TreePlan.com Value Prob Pred Kind NS S1 0 0 0 E 2 1 0 E 2 3 0 E 2 5 1 T 0 0 1 T 0 0 2 T 0 0 2 T 0 0
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TreePlan Student License, For Education Only TreePlan.com S2 S3 S4 S5 Row Col 2 0 0 0 9 1 4 0 0 0 4 5 6 0 0 0 14 5 0 0 0 0 2 9 0 0 0 0 7 9 0 0 0 0 12 9 0 0 0 0 17 9
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TreePlan Student License, For Education Only TreePlan.com Mark 1 1 1 1 1 1 1
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TreePlan Student License, For Education Only TreePlan.com Disease Disease (A) No Disease (not A) Test Test positive (B) Test negative (not B) Given (enter as proportions) P(No COVID | Test - COVID) 0.99748 NPV P(COVID | Test + COVID) 0.96117 PPV P(Test + COVID) 0.206 Test Positive Rate Need Probability P(Test + COVID | COVID) 99% Sensitivity P(Test - COVID | COVID) 1% P(Test + COVID | No COVID) 1% Enter data into the gray boxes. The contingency table, prob probabilities will autopopulate. Given the NPV, PPV, and test positivity rate, we can also calculate the sensitivity and spe COVID example, to calculate the Sensitivty and Specificity. Perform the calculations using y 60% as well as where the prevalence was 20%. What do you notice ab
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TreePlan Student License, For Education Only TreePlan.com P(Test - COVID | No COVID) 99% Specificity P(COVID) 20% Prevalence P(No COVID) 80% 1-Prevalence PRIOR PROBABILITIES AFTER THE NEW IN P(COVID) COVID 0.20 No COVID P(No COVID) 0.80 POSTERIOR PROBABILITIES AFTER THE N P(Test + COVID) P MULTIPLICATION RULE: P(B|A) * P(A) = P(A P(B) = P(A and B) + P(Not A
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TreePlan Student License, For Education Only TreePlan.com Test + COVID 0.206 Test - COVID P(Test - COVID) 0.794 MULTIPLICATION RULE: P(A and B) P(A|B)= P(A and B) ÷ P( We have P(A and B), need P(B) = P(A and B) + P(Not A
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TreePlan Student License, For Education Only TreePlan.com COVID No COVID Test + COVID Test - COVID e bability tree and conditional Step 3: Enter the required probabilities in the gray cells. The contingency table, Probability Trees, and Solutions table will autopopulate. ecifity of a test. Use the data below from the previous your results from the example where the prevalence was bout the sensitivity and specificity?
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TreePlan Student License, For Education Only TreePlan.com NFORMATION IS OBTAINED (CALCULATED IN Prior Conditional Probabilities P(Test + COVID | COVID) T+ 0.9900 T- P(Test - COVID | COVID) 0.0100 P(Test + COVID | No COVID) T+ 0.0100 T- P(Test - COVID | No COVID) 0.9900 NEW INFORMATION IS OBTAINED (GIVEN IN Posterior Conditional Probabilities P(COVID | Test + COVID) COVID ) 0.9612 PROBABILITY TREES and B) = P(A|B)* P(B) and B)
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TreePlan Student License, For Education Only TreePlan.com No COVID P(No COVID | Test + COVID) 0.0388 P(COVID | Test - COVID) COVID 0.00252 No COVID P(No COVID | Test - COVID) 0.99748 ) = P(A|B)*P(B) (B) d P(B) A and B)
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TreePlan Student License, For Education Only TreePlan.com CALCULATOR Ev A Event B B P(COVID and Test + COVID) not B P(COVID and Test - COVID) TOTALS P(COVID) Event A: D Disease Test+ 0.19800102 Test - 0.00200088 Event B: Test Result CONTINGENCY TABLE Solution: Both the sensitivity and specificity for the test are 99%. It does not matter whether we use the NPV, PPV, and test positivity from the example with prevalence 60% vs 20%, the sensitivity and specificity are still the same. This is because the sensitivity and specificity of the test are NOT affected by the prevalence of the disease. To use this Calculator Step 1: Change the labels for the outcome to be predicted (Event A) in the gray cells. Step 2: Change the labels for the screening test (Event B) in the gray cells.
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TreePlan Student License, For Education Only TreePlan.com TOTALS 0.2000019 N THIS CASE) Joint Probabilities P(COVID and Test + COVID) 0.19800102 P(COVID and Test - COVID) 0.00200088 P(No COVID and Test + COVID) 0.00799898 P(No COVID and Test - COVID) 0.79199912 THIS CASE) Joint Probabilities P(COVID and Test + COVID) 0.19800102
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TreePlan Student License, For Education Only TreePlan.com P(No COVID and Test + COVID) 0.00799898 P(COVID and Test - COVID) 0.00200088 P(No COVID and Test - COVID) 0.79199912
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TreePlan Student License, For Education Only TreePlan.com vent A not A TOTALS P(No COVID and Test + COVID) P(Test + COVID) P(No COVID and Test - COVID) P(Test - COVID) P(No COVID) 1 Disease Status No Disease TOTALS 0.00799898 0.206 0.79199912 0.794
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TreePlan Student License, For Education Only TreePlan.com 0.7999981 1
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TreePlan Student License, For Education Only TreePlan.com ID Name 0 TreePlan 1 2 3 4 5 6
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TreePlan Student License, For Education Only TreePlan.com Value Prob Pred Kind NS S1 0 0 0 E 2 1 0 E 2 3 0 E 2 5 1 T 0 0 1 T 0 0 2 T 0 0 2 T 0 0
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TreePlan Student License, For Education Only TreePlan.com S2 S3 S4 S5 Row Col 2 0 0 0 9 1 4 0 0 0 4 5 6 0 0 0 14 5 0 0 0 0 2 9 0 0 0 0 7 9 0 0 0 0 12 9 0 0 0 0 17 9
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TreePlan Student License, For Education Only TreePlan.com Mark 1 1 1 1 1 1 1
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