(because and both equal 1). The value of is a particular confidence criterion ci σF0 σF1 on the memory strength (R axis, and the value of is the decision criterion for + F) r Remember judgments on the recollection (R) axis. The proportion of Remember judgments for a confidence rating of or greater, P(F > and corresponds to i + R ci R > r), the mass in the top right quadrant, and the proportion of Know judgments for a confidence rating of or greater corresponds to the mass in the top left quadrant. For a i target item, the probability that aggregate memory strength (F exceeds the decision + R) criterion (ci) is: P(F > ci) = . + R To find the proportion of items for which > ci and (and so receive Remember F + R R > r judgments), the above quantity is multiplied by the relative likelihood of observing a particular value of and the entire expression is integrated with respect to over the R, R range of to infinity. For Remember judgments to targets, the expression would be: r P (F > ci and |Target) = , + R R > r where is normal probability density function. For Remember judgments to lures, the ϕ corresponding expression would be: P (F > and |Lure) = . + R ci R > r Note that and represent decision criteria, and all are free parameters. r, c2, c3, c4, c5, c6 In addition, and are free parameters, whereas and are both set to µF1, µR1, µF0 µR0 σR1, 0, and , and are all set to 1 the subscripts 0 and 1 refer to lures and σR0 σF0 σF1 targets, respectively). Thus, these equations simplify to: P (F > ci and |Target) = , + R R > r P (F > ci and |Lure) = . + R R > r
(because σF0 and σF1 both equal 1). The value of ci is a particular confidence criterion on the memory strength (R + F) axis, and the value of r is the decision criterion for Remember judgments on the recollection (R) axis. The proportion of Remember judgments for a confidence rating of i or greater, P(F + R > ci and R > r), corresponds to the mass in the top right quadrant, and the proportion of Know judgments for a confidence rating of i or greater corresponds to the mass in the top left quadrant. For a target item, the probability that aggregate memory strength (F + R) exceeds the decision criterion (ci) is: P(F + R > ci) = . To find the proportion of items for which F + R > ci and R > r (and so receive Remember judgments), the above quantity is multiplied by the relative likelihood of observing a particular value of R, and the entire expression is integrated with respect to R over the range of r to infinity. For Remember judgments to targets, the expression would be: P (F + R > ci and R > r |Target) = , where ϕ is normal probability density function. For Remember judgments to lures, the corresponding expression would be: P (F + R > ci and R > r |Lure) = . Note that r, c2, c3, c4, c5, and c6 represent decision criteria, and all are free parameters. In addition, µF1, µR1, and σR1, are free parameters, whereas µF0 and µR0 are both set to 0, and σR0 , σF0 and σF1 are all set to 1 the subscripts 0 and 1 refer to lures and targets, respectively). Thus, these equations simplify to: P (F + R > ci and R > r |Target) = , P (F + R > ci and R > r |Lure) = .
CDP%20Model%20(final).docx