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Signal Detection and Conditional Probability in Consumer Behavior Analysis

This document explores signal detection theory, conditional probability, and Bayes' theorem, particularly in the context of consumer behavior related to McDonald's Big Mac and Diet Coke purchases. It provides a framework for calculating hit and false alarm rates based on the given data. Definitions of hits and false alarms are presented, along with various probabilities such as P(resp=yes|stim=yes) and P(resp=yes|stim=no). The analysis aims to derive insights into consumer purchasing habits, demonstrating the application of these statistical methods in real-world scenarios.

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Signal Detection and Conditional Probability in Consumer Behavior Analysis

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  1. Signal detection, conditional probability and Bayes’ theorem Takashi Yamauchi TAMU

  2. Given the data above, calculate d’, hit and false alarm. d’ = Hit= False alarm =

  3. d’ = Z(Hit) – Z(False alarm) Hit= False alarm =

  4. Definitions of hit and false alarm • Hit = P(resp = yes | stim = yes) • False alarm = P(resp = yes | stim = no)

  5. P(X | Y) = P(X, Y) / P(Y)

  6. Big Mac McDonald’s Diet Coke 100 Among all customers, how many of them bought Big Mac? Among all customers, how many of them bought Diet Coke? Among all customers, how many bought both Big Mac And Diet Coke? Among those bought Diet Coke, how many also bought Big Mac? 10 40 20 30

  7. Big Mac McDonald’s Diet Coke 100 • Among all customers, how many of them bought Big Mac? • P(Big Mac)=? • Among all customers, how many of them bought Diet Coke? • P(Diet Coke) =? • Among all customers, how many bought both Big Mac And Diet Coke? • P(Big Mac & Diet Coke) = ? • Among those bought Diet Coke, how many also bought Big Mac? • P(Big Mac | Diet Coke) =? 10 40 20 30

  8. P(Big Mac | Diet Coke) = P(Big Mac, Diet Coke) / P(Diet Coke) P(X | Y) = P(X, Y) / P(Y)

  9. McDonald’s 100 Big Mac 10 40 20 Diet Coke 30

  10. McDonald’s 100 Big Mac 10 40 20 Diet Coke 30

  11. McDonald’s 100 X 10 40 20 Y P(Y=yes)=? P(X=yes)=? P(Y=yes, X=yes)=? P(X=yes | Y=yes)=? 30

  12. 100 X Y 10 40 20 Hit =? P(resp=yes | stim = yes) False Alarm =? P(resp=yes | stim = no) 30

  13. Conditional probability P(X | Y) = P(X, Y) / P(Y) P(X| Y) P(Y) = P(X, Y) P(Y | X) = P(X, Y) / P(X) P(Y | X) P(X) = P(X, Y) Bayes’ theorem P(X | Y) P(Y) = P(Y | X) P(X) P(X | Y) = P(Y | X) P(X) / P(Y)

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