Replication and Analysis of Ebbinghaus’ Forgetting Curve

This paper describes a replication of one of the most important early experiments in psychology, namely Ebbinghaus' classic experiment on forgetting from 1880 and 1885. We replicated the experiment that yielded the famous forgetting curve describing forgetting over intervals ranging from 20 minutes to 31 days. Ebbinghaus' goal was to find the lawful relation between retention and time-since-learning. This is why he fitted the data to two different functions (a power function, 1880, and a logarithmic function, 1885), as have many theorists since. This papers also includes an analysis—including one with a new model—of the shape of the Ebbinghaus' forgetting curve and its replications. Do the replicated forgetting curves have the same shape, or must we conclude that Ebbinghaus' forgetting curve was idiosyncratic and that quite different shapes may occur?

There is currently an increasing interest in replication studies in psychology, motivated by a growing uneasiness in the community about unreliable findings in psychology. It seems particularly important to try to replicate classic studies that are included in every textbook on cognitive psychology and may also be known by the general public. A good example of this is the classic study by Bartlett, which until 1999 had only had unsuccessful replication attempts, until finally Bergman and Roediger succeeded in replicating the basic findings. One of the reasons earlier replications may have failed is because not all details were well-documented in the original study from 1932. The exact instructions, for example, were not included. This may explain why Wynn and Logie had found the forgetting gradient in their experiment to be quite different from the one in Bartlett's experiment. Bergman and Roediger also argue that this may have been caused by certain differences in the study design. Replication of classic experiments, thus, serves the dual purpose of verifying the reliability of the original results and uncovering more precisely how the original experiment was conducted.

It is hard to overestimate the importance of Hermann Ebbinghaus' contribution to experimental psychology. Influenced by the work of the German philosopher Herbart, he was the first to carry out a series of rigorous experiments on the shape of forgetting, which he completed in 1880. The experiment itself was preceded by a period in which he tried out a variety of materials and methods. After having tested himself with tones, numbers, and poem stanzas, he decided that none of these served his purposes. Tones were too cumbersome to handle and too difficult to reproduce for him, he did not find digits zero to nine suitable as basic units for the long-running experiments he envisioned, and the poem fragments he tried to learn (from Byron’s Don Juan) were deemed too variable in the meanings they evoked and therefore likely to cause measurement error (p. 14–17). He, therefore, introduced nonsense syllables, which had more uniform characteristics than existing words or other verbal material. In his later experiments on learning, however, he did verify his results with the Don Juan verses, confirming both his main results on learning and his intuition that the latter stimuli did indeed yield much more variance in the data. Since his introduction of nonsense syllables, a large number of experiments in experimental psychology has been based on highly controlled, artificial stimuli.

In all experiments reported by Ebbinghaus, he used only himself as a subject. Single-subject designs are not unusual in memory psychology. Especially in the study of autobiographical memory we find several diary studies based on one person’s personal memories. They have the advantage that there is no inter-subject variability, although they still require hundreds of trials to reduce the variance due to differences in stimuli and other factors. This places a great burden on the subject. Indeed, Ebbinghaus’ forgetting curve is based on seven months of experimenting, often up to three sessions per day. Wagenaar meticulously recorded one daily memory during six years and spent several months recalling these.

A disadvantage of a single-subject design is that it remains unclear what the shape of forgetting would be with other subjects. Are the results universal or did the subject happen to have a memory that was exceptional in some way. The generality of the results can be assessed with a faithful replication. There have been a number of—mostly early—replications of Ebbinghaus’s forgetting curve, notably by Radossawljewitsch and Finkenbinder, but these authors used a much slower presentation rate of the stimuli of 2 s per stimulus, where Ebbinghaus learned at 0.4 s per stimulus. This was partially the result of the development of devices for mechanical presentation by Müller and colleagues, who presented materials at a rate one stimulus per second. Slowing down the presentation this much alters the nature of the processing with more time to generate meaningful associations to otherwise meaningless syllables. Though the resulting forgetting curves are clearly of interest to the field, we feel that the slow method of presentation form a large departure from Ebbinghaus’ original study. Also, Finkenbinder’s longest retention interval is 3 days, instead of 31 days and though in the experiment by Radossawljewitsch the retention interval range extends up to 120 days, his design suffers from an uneven distribution of intervals throughout time and time-of-day. Stimuli were learned in order: in the first few days of the study all 5 min intervals were learned, then the 20 min intervals, and so on. Because he did not use a pre-experimental practice phase, the early intervals took longer to learn while the subjects were still getting used to the materials and the procedure; it is likely that this has affected the shape of the forgetting curve reported by him. There are other differences between these two studies and Ebbinghaus’, for example, the degree to which was learned and whether the subjects were allowed to pause between lists.

There are several unanswered questions about Ebbinghaus’ results that formed part of the motivation for us to undertake this replication. His basic stimulus was a ‘row’ of thirteen nonsense syllables, which he studied until he could correctly recall it in the correct order twice in succession. A question that seems pertinent is how stimuli at different serial positions were learned and how these were forgotten over time. Another question is how his measure of choice, namely savings (see below) is related to the nowadays more common measure of percentage correct. Finally, we were interested in the role of interference or fatigue in the course of the experiment.

To help answer these questions, we consulted not only the widely published text of 1885, which was translated into English in 1913, but also an earlier report of 1880. This is a handwritten manuscript that he submitted for his Habilitation, which in Germany is a requirement to be considered for a full professorship. This text (the so called Urmanuscript or original manuscript) has been typeset and republished in German in 1983. Even with this additional source, however, we still could not answer the questions above.

For these reasons, we decided to replicate Ebbinghaus’ forgetting experiment. If our replication yielded similar results, this would support the generality of Ebbinghaus’ curve and through a more detailed analysis of our data, we would be able to address the issues above. In the course of preparing for our study, we found that there has been at least one other replication study, namely by Heller, Mack, and Seitz. This study has been published only in German, without an English abstract, and is not easily accessible; at the time of writing, it is not available in electronic format (i.e., it is not available online) and it has never been cited in international journals in English. It is, however, a thorough study and an excellent replication attempt. Where the Ebbinghaus texts are unclear about certain details, we have mostly followed Heller et al. as a guideline so that we can also compare our results with theirs. Because we feel this is an important study that has not received the readership it deserves, we will mention more of its details here than we would have had it been more accessible at this point in time.

In 1885, Ebbinghaus introduces the savings measure of learning and memory (it does not appear in this form in his earlier text from 1880). Savings is defined as the relative amount of time saved on the second learning trial as a result of having had the first. Suppose, one has to repeat a list for 25 times in order to reach twice perfect recollection and that after one day, one needs 20 repetitions to relearn it. This is 5 less than the original 25; we can say that on relearning we saved 20% with respect to the original 25 rehearsals (5/25 = 0.2 or 20%). If it takes just as long to relearn the list as it took to learn it originally, then savings is 0. If the list is still completely known at the second trial (i.e., no forgetting at all), then savings is 1 or 100%. Ebbinghaus prefers to express savings in terms of time spent learning and relearning but the principle remains the same. After Ebbinghaus’ publication in 1885, the savings measure remained popular for several decades. Eventually, researchers found the savings method too unreliable compared with other methods of measuring memory and in the following decades it was used much less with some exceptions. Later, an important improvement was suggested, where learning is not to the 100% criterion but to a much lower one, such as 50% correct. These improved versions of the method are used nowadays, for example, when studying forgetting of foreign languages.

In the following, we will first report our replication experiment. Then, in the Discussion section we will revisit the shape of forgetting, analyze the effects of serial position on forgetting, and investigate what mathematical equations present a good fit to the Ebbinghaus forgetting curve and its replications. Finally, we will study whether there is evidence for a jump at 24 hours in these curves, which some authors have attributed to the effect of sleep.