This article examines a two process model, Recall to Reject.  Recall to Reject assumes that there are two processes operating in recognition memory decisions:

Familiarity: A quick and dirty process based on global similarity between test item and items stored in memory.  Poor at making fine discriminations between items.
Recall: A slower process that retrieves entire item and can be used to make finer discriminations between items.

Prior Evidence in favor of Recall to Reject:

Jones and Heit (1993): Frequency judgments of related distractors were not influenced by presentations of targets even when targets were presented many times.

Hintzman, Curran & Oppy (1992): Frequency estimates of related distractors distributed bi-modally, with some subjects saying that they had never been presented (presumably because of recall to reject) and some subjects saying they had been presented as often as the targets had actually been presented (presumably because of familiarity).

Hintzman & Curran (1994): Used response signal technique.  In a response signal technique Ss are given a signal to respond to an item and must respond immediately (or close to it) even if they need to guess.  The basic idea behind response signal techniques is that they allow you to know how much and what kind of processing has gone on up to that point (e.g. 500 msec). When Ss were signaled to respond at short deadlines false alarms to related distractors were as common as hits.  But at long deadlines, presumably after the recall to reject process kicked in, false alarms to related distractors declined.

Some Mathematical Background

To measure overall sensitivity and to control for response bias they use d_L , a measure of sensitivity (like d', A', etc.) that's based on a logistic distribution rather than a normal distribution.  The formula for  d_L  is given by the following equation.

(1)  d_L  > 0 when the hit rate is greater than the false alarm rate.
(2)  d_L  = 0  when HR=FA 
(3)  d_L  < 0 when the false alarm rate is greater than the hit rate. 
(4) Larger values of  d_L indicate greater differences between the hit rate and false alarm rate.

Data collected in these experiments were fit to two different functions.

The Monotonic Function:

The Monotonic Function predicts that as the response deadline is increased  d_L for related distractors will increase monotonically approaching some asymptote.  This is the function you would expect based on a simple single process model in which there is no Recall to Reject mechanism:



Making sense of this function:
 

(1) l₁  is the asymptote that d_L is approaching.  Notice why...As lag increases u/(lag-d) approaches 0.  This means that the function as a whole approaches d_L(lag) = l₁ / 1 = l₁

(2) u  is the rate at which d_L is approaching the aymptote.  Inspection of the equation suggests that when u is large the rate of approach is slow.  Again, notice why...assume u is very small, say at the limit u = 0.  In that case, the function would jump immediately to the aymptote.  Now assume that u is large.  In this case the funciton will not immediately jump to the asymptote. When u is larger it will take longer to reach the asymptote because you will be dividing l₁ by a larger number.

(3) d  is the lag at which d_L is greater than chance. Notice here that the function as a whole is undefined when performance is less than or equal to chance. Mathematically this is because (lag - d ) would be a negative number if performance were less than chance resulting in the square root of a negative number and would be 0 if performance were equal to chance resulting in a 0 denominator.
 

The Non-Monotonic Function: This function assumes that  d_L increases until a particular point in processing (i.e. when the recall to reject mechanism kicks in) and then decreases approaching some lower asymptote.  This is the function you would expect if the Recall to Reject mechanism existed.
 
According to this function, d_L conforms to the first function until the recall to reject mechanism kicks in.

From that point forward it conforms to a second function:

 
Making Sense of This Equation:  Notice that this equation adds two new parameters.
 
lag* is the lag at which the recollect to reject process kicks in.

l₂ is the lower asymptote
 

Notice first that the denominator of this equation is exactly the same as the denominator of the monotonic function.  This means that all the work will be done by the numerator.

Also notice that when the recollect to reject process first kicks in, that is when lag = lag*, the numerator becomes:

l₂ + [(l₁ - l₂)(lag* - d)/(lag* - d)] l₂ + [(l₁ - l₂] l₁ This, of course, is just exactly where the monotonic function left off.  This is nice because even though there are, in a sense, two different functions, the one begins where the other one left off.

Finally, notice that as  lag becomes increasingly greater than lag* the entire expression  [(l₁ - l₂)(lag* - d)/(lag - d)] approaches 0.  This means that the numerator of the function as a whole,  [ l₂  + (l₁ - l₂)(lag* - d)/(lag - d)], approaches  l₂ (the lower asymptote) as lag increases. At the same time (as before) the denominator of the function as a whole is approaching 1.  So as lag increases the entire function approaches l₂ / 1 =  l₂

Enough Math, Time for Some Data

First they reanalyze the data from Hintzman and Curran's Experiments 2 & 3. As lag increases uncorrected recognition of related lures first increases and then decreases.

However, to control for response bias, they calculated d_L for each item type at each response threshold.  For neither Experiment did they find evidence of the inverted U pattern predicted by the Recall to Reject account.

They also fit Hintzman and Curran's data to the monotonic model and the non-monotonic model described above.  The non-monotonic model did not fit the data significantly better than the monotonic model.  Remember, the non-monotonic model is the one you're rooting for if you're a fan of the Recall to Reject account.

Some Experiments of Their Own:

Expeirment 1: Presented subjects with Pseudowords at acquisition 0, 1 or 3 times.  Lures at test were either highly similar (differ by a single vowel) or moderately similar (differ by a vowel and the final consonant).

Results Experiment 1:  When d_Lwas used to correct for response bias, there was no evidence for the inverted U function.  Moreover, the monotonic function fit the data as well as did the non-monotonic function.

Experiment 2: Same basic design, only for half of the pseudowords participants studies both the pseudoword and a related word.  This was done to prevent participants from being able to adopt some idiosyncratic strategy ("I know if PROMBAR was presented then nothing similar to PROMBAR was presented").

Results Experiment 2:  No effect of whether or not items had seen a related item at acquisition.  Again when d_Lwas used to correct for response bias, there was no evidence for the inverted U function.  In the model fitting the monotonic function fit the data as well as did the non-monotonic function.

General Discussion

That's not what was found in any of the analyses they conducted.  There didn't even seem to be an inkling of anything like that.

The authors argue that other paradigms may produce evidence for a recall to reject mechanisms and in particular that associative recognition may demonstrate such a pattern (Rotello & Heit, 2000).

They also point out that one could adopt a dual process account in which familiarity judgments continue to increase even as the recollection process kicks in.  These processes might tend to balance each other out and lead to a flattening of the curve.

They also discuss an exhaustive search model in which an detailed search of memory is performed and if the item can't be located its rejected.  This is rather like what happens when our subjects tell us, "If that word had been on the list I would have remembered it."

Overall, this article provided a test of one prediction one might derive from a Recall to Reject account and failed to find evidence in support of it.