A fundamental question in the study of cognition is whether memory strength varies continuously or whether memories sometimes fall below a threshold and fail completely. Previous studies examining this question have relied exclusively on 1 methodreceiver operating characteristics-so in the current study, we addressed this issue by using a completely different approach. We tested memory for single items and for arbitrary associations (e.g., memory for random word pairs) by using a 4-alternative forcedchoice test in which subjects either made a single choice or a first and a second choice. In item recognition, single-and second-choice scores were directly related, as expected if a continuous strength signal supported performance. In contrast, in associative recognition, single-and second-choice scores were found to be unrelated, as predicted by high-threshold theories. However, when the word pairs were encoded as single compound words rather than arbitrary associations, associative recognition appeared to rely more on a continuous strength process. The results support memory models that include both a continuous familiarity process and a threshold recollection process.recollection ͉ signal detection model ͉ threshold model ͉ dual process model ͉ associative recognition D oes memory sometimes fail, such that the strength of a memory trace falls below one's memory threshold? If so, then our attempts to discriminate between studied items and new items would be effectively reduced to random guesses. However, another possibility, consistent with signal detection theory (1, 2), is that memory never truly fails, but instead varies in a continuous manner such that the things we have encountered previously are simply more familiar on average than things that are new. In this way, memories never fall below a threshold, and thus even the very weakest of memory signals should be useful in discriminating between old and new items.Memory theorists have debated the existence of a memory threshold for more than half a century (2, 3), and recent neurocomputational models have postulated that the hippocampus supports a threshold recollection process whereby qualitative information is retrieved with some probability, whereas the surrounding cortex supports a continuous memory strength process that underlies familiarity-based discriminations (4-6). However, the empirical evidence relevant to this debate has come almost exclusively from the analysis of receiver operating characteristics (ROCs), functions that relate correct and incorrect recognition memory responses as response bias varies. These functions are important because threshold theories predict linear ROCs, whereas signal detection theories predict curved ROCs (7). ROC results from humans and rats have provided evidence for a memory threshold when subjects are required to retrieve arbitrary associations from memory (8-11), but other studies have reported evidence more in favor of signal detection theory, particularly in tests of item recognition where subjects must discrimin...