Sometimes I find a paper that is so perfectly useful for whatever I’m doing, that tells me what I need to know when I didn’t know for sure the information I wanted even existed that I’m really grateful to the authors for writing it. In the moment, I want to tell them so, but I rarely act on this impulse. This seems like a shame. There’s nothing but awkwardness preventing me expressing my appreciation, but who doesn’t welcome knowing that someone else appreciates their work? So let me highlight a few papers that I found useful and inspiring for a project I recently finished.

My colleagues and I published a new paper (it’s open-access) in Annals of the New York Academy of Sciences examining whether holding information in mind affects the speed with which children make simple decisions. (I’ll be speaking about this paper at the International Meeting of the Psychonomic Society in Amsterdam on Friday.) In complex working memory span tasks (also called storage-plus-processing tasks), participants do two things at once: they remember a list of items (e.g., storage), and they make simple decisions (e.g., processing). These tasks are nice for testing hypotheses about working memory resources, e.g., should we believe there are separate mental resources for storing versus processing? One way to examine this is to see whether the simple decisions people must make during the task become slower as the number of memoranda increase. We are not the first to investigate this in adults or children. But our study’s design, planned because we were pilot-testing for an adaptive training study, afforded a few unique features. Whether any individual shows interference between storage and processing could vary depending on how much information they need to store. Usually, researchers would set the list to a particular length for convenience, a length that would be easy for some individuals, but difficult for others. Our procedure was adaptive depending on accuracy. The list length increased or remained constant when participants recalled correctly, but decreased when they recalled incorrectly. For each individual, that gives us a lot of data from trials where they correctly recalled a manageable but not too easy list.

If holding information in mind slows processing, then as each new item is added to the list, processing judgments should steadily become slower. If holding and processing information do not require the same resource, then processing speed should be constant regardless of how many items are remembered. Previous studies looking at similar tasks have shown both patterns by comparing the speed of the last processing item with speed of the first. Because we had a lot of data with different list lengths per child, I first plotted our data for the entire list. When I saw the results, I wondered whether something could be wrong, because the patterns were definitely not linear: the first responses were very slow, but after the first responses, it looked like processing response times increased. After ruling out mundane explanations, I started to wonder whether non-linear patterns like we observed were present in other published data. Most researchers unfortunately did not report enough information about their data to tell. But the thorough, detailed reports of a few papers suggested that the non-linearity we observed might not be a fluke. Here are some really useful papers to study if you want to dive deeply into the dynamics of storage-plus-processing tasks. These are by no means the only great papers on this topic, but each is substantial, rich, and gave me something I needed to decide what I thought our data might mean.

Engle, Cantor, and Carullo (1992): Engle et al. recorded the amount of time participants viewed each component of reading span and operation span tasks. They presented viewing times for the first part of the sentence or arithmetic operation, the average of the remaining components of the sentence or operation, and the time spent viewing the to-be-remembered item in Figures 2 and 4. Though these dependent variables were not the same as ours, they made clear that the time used to perform various operations sometimes changed non-linearly with memory load. This seemed particularly true for the memory item’s viewing times, which was important for interpreting our data because in our task, the processing judgment was performed on the memory item itself.

Friedman and Miyake (2004; $orry for the paywall): Friedman and Miyake presented a detailed report of reading times per sentence as a function of memory list length and order within the list for a reading span task (Table 4). They found that the reading times usually increased linearly within a list, but not for the longest lists, and not when participants controlled the pace of the trial.

Jarrold, Tam, Baddeley, and Harvey (2011; $orry again): Jarrold et al. present processing task times as a function of list length and position within a list during complex span tasks in Figures 3 and 5 (episodes 1-7 in the upper row of each figure were most comparable to our analysis). Though usually these times do not usually look like they deviate much from linearity, there are some instances where the response in position 1 is slower than the next response, like we found.