Replication and Analysis of Ebbinghaus’ Forgetting Curve

The current study was set up to replicate the findings by Ebbinghaus. Despite a quite detailed account of his experiment, we found some information to be lacking and we had to estimate or guess these details, as outlined below. Also, we did not have the seven months available that Ebbinghaus invested in the experiment, but we had to accommodate our design to a 75 day period. We nonetheless believe that our experiment is close enough to his to be still called a replication.

There were a few differences between Ebbinghaus’ study, Heller et al.’s replication, and ours. (i) Because we were limited in time, like Heller et al., we ran only 10 replications per time interval, instead of the 12 to 45 by Ebbinghaus. This means the variance in our data is larger than in Ebbinghaus’ especially at the longest time intervals; apart from that no systematic differences were introduced. (ii) We were not able to experiment at a fixed time of day. Ebbinghaus (1880), who started experimenting in the morning at (A) 10:00, and then sometimes also at (B) 12:00 and usually at (C) 19:00 to 20:00, noticed that there was a difference between these times of the day in his ability to acquire a list. He subtracted 5% for B and 13% for C from the learning times at these hours to normalize the data with respect to time A. Heller et al. were also able to conduct experimental sessions at specific times throughout the day, but they did not find such a time-of-day effect and hence did not implement a correction. (iii) Our stimulus material conformed to the phonotactics of the Dutch language and thus differs from both Ebbinghaus and Heller et al. Also, in contrast to both Ebbinghaus and Heller et al. we removed syllables that had too much meaning in order to further balance the level of difficulty of the stimuli. (iv) Our subject, J. Dros, was younger than H. Ebbinghaus, who was 29 during his experiments in 1879–1880. The ages of the two subjects in Heller et al. are not given. (v) Ebbinghaus gives exact testing dates for each of the short time-intervals but not for the longer ones (24 hours and up). Hence, we do not know exactly when he learned and relearned the lists for the longer intervals. This makes it impossible to calculate the number of interfering lists between learning and relearning. It also makes it nearly certain that our schedule differed from his (and from that of Heller et al. who also do not supply such a schedule).

Subject

The second author, J. Dros, (22 years, male) was the only subject in the experiment. This experiment was reviewed and approved by the Review Board of the Psychology Department of the University of Amsterdam (see www.lab.uva.nl). The project is filed with case number 2014-BC-3879 (contact is Dr. R.H. Phaf). Consent was implicit as the second author of the paper was also the only subject on which we report. This was also approved by the Review Board. The subject's native language is Dutch, making this the first non-German replication of Ebbinghaus’ forgetting experiment.

Materials

The learning material consisted of 70 lists. Each list consisted of 104 nonsense syllables, which in turn consisted of 8 ‘rows’ of 13 syllables.

Nonsense syllables

Each syllable consisted of 3 or 4 lower-case letters. The structure of a syllable was a lower-case consonant-vowel-consonant (CVC) structure. The consonant of the syllable was always one of b, d, f, g, h, j, k, l, m, n, p, r, s, t, or w. The vowel could be one of e, i, o, u, aa, uu, ee, ei, eu, oe, ie, oo or ui. The double-letters stand for standard Dutch vowels. The last consonant of the syllable was one of f, g, k, l, m, n, p, r, s, or t.

The number of different possible consonant-vowel-consonant combinations on the basis of these letter combinations is 2100 (15 × 14 × 10). Not every possible consonant-vowel-consonant combination was included in the learning material; we removed words that had too much meaning in Dutch, in order to further balance the difficulty of the stimuli. Syllables with meanings in other languages spoken by the subject, such as English and German, were not excluded.

Row and list construction

Using the pseudo-random generator of Excel 2010, rows of 13 syllables were constructed. Within a row we did not allow two syllables with the same vowel in direct succession. We also did not allow two identical syllables within one row, but we did allow them in different rows within a single list. When syllables needed to be adjusted we first tried changing only the first or second letter of a syllable until the criteria were met. If this did not suffice, additional letters were changed. The adjustment process was not purely random but was carried out by hand during stimulus preparation by the authors.

Procedure

The only independent variable in this experiment was the time-interval, which started at the end of learning a list for the first time. The time-interval ended at the beginning of learning a list for the second time. The time-intervals between learning and relearning were the same as Ebbinghaus: 20 minutes, 1 hour, 9 hours, 1 day, 2 days, 6 days and 31 days. For each time interval, 10 lists were learned and relearned (for the 9 hour interval only 9 lists were learned due to unforeseen circumstances).

We need to elaborate on the choice of these time intervals as there is some confusion about the exact length of the shorter retention intervals used by Ebbinghaus. He mentions both 15 min (in 1880) and 19 min (in 1885) for the shortest interval, and 63 min and 8.75 hours (525 min) for the longer intervals. He also states that relearning took place “after about one third of an hour, after 1 hour, after 9 hours, one day, two days, six days, or 31 days.” (p. 66). Heller et al. followed the latter intervals, using 20 min, 60 min and 9 hours, etc. We have also used these, given that this seems to have been the intended lengths of Ebbinghaus’ retention intervals. The deviations these values by Ebbinghaus are based on corrections after the experiment.

Ebbinghaus’ shortest interval (‘20 minutes’) is based on almost immediately relearning a list of eight rows and hence the interval depends on how long it took to learn the eight lists. When relearning the lists so soon it takes much less time to relearning them, than the original learning, so that the intervals between learning and relearning of lists is not constant, with List 8 being relearned earliest (e.g., 20 min) and List 1 latest (e.g., 10 min). Ebbinghaus (p. 50) states that the average time is about 15 min and argues that that whereas he does not know exactly how to correct for these variable learning times, the error will be small. We recalculated the average of the times stated on page 51 of the 1880 text and find it to be 1010 s or 16.8 min. Ebbinghaus keeps using the value of 15 min throughout his text from 1880, including for fitting his ‘power function’ equation (see below). The learning and relearning times given in his 1885/1913 volume are the same as in 1880, but to each interval he has now added 88 s for reasons that are not made clear. The average of these learning intervals then becomes 18.3 min. Given that he also remarks that for the shortest interval “relearning of the first series of a test followed almost immediately or after an interval of one or two minutes upon the learning of the last series of the same test” (p. 66) may explain rounding 18.3 min to 19 min, the value used throughout the text from 1885. In general, it seems he made more or less intuitive corrections for the variable learning times and changed his mind from 1880 to 1885 about the most appropriate method to approach this. We have used 19 min, 63 min, and 8.75 hours in the graphs and tables (and fits), for Ebbinghaus’ data. For the other data sets, we use 20 min, 1 hour, and 9 hours.

Measurement of repetitions and time

The main measurement was the number of repetitions needed to correctly reproduce the syllables in a row in the correct order.

For the forgetting curve experiment, Ebbinghaus learned until twice correct, but in later experiments switched to once correct, because he found there to be no essential difference in the outcomes. We chose to also learn to once correct. Heller et al. (p. 8) seem to be using the once-correct criterion as well but this is not made entirely clear.

Ebbinghaus uses elapsed time to calculate the number of repetitions, because he finds keeping count too distracting. Heller et al. use a chain with wooden, colored beads, much like a rosary to keep count. We found that word processing software (Microsoft Word) was handy to keep track of the number of repetitions. During learning, each single repetition of a row was counted by pressing the button ‘1’ on the keyboard at the beginning of every single repetition of a row. At the end of learning a list, the total number of 1’s for each row was counted and entered into the database.

We also measured the time in seconds needed to learn a list. A clock was shown on the computer screen during the task and we recorded the begin times and end times of learning a list. Subtracted from the time were the pauses of 15 s between two rows (cf., p. 19). When relearning a list, the extra time (15 s) introduced by the voice recording of the first retrieval attempt was subtracted from the total relearning time.

The practice phase and experimental phase

Following Ebbinghaus, we preceded the experimental phase of the experiment with a practice phase to prevent as much as possible general learning effects due to growing experience with the task and materials. The practice phase took place between 08-11-2011 and 29-11-2011. A total of 14 lists was learned and relearned after 20 minutes (Heller et al. relearned lists after one hour). After these, a further 19 lists were learned only (i.e., not relearned later) for additional familiarization with the task.

In the experimental phase, which took place between 01-12-2011 and 13-02-2012, a total of 69 lists was learned and relearned (9 for the 9 hour interval). The total time spent on data collection in the experimental phase amounted to about 70 hours. We distributed the ten lists for each time interval as much as possible over the whole experimental period. Due to the limited time available to run the whole experiment, we were not able to achieve this for the 31 days time interval condition, so that we decided to learn these lists near the beginning of this experimental period.

List learning phase

All lists were printed on paper (black ink, font ‘Calibri’, 11 points) (eight rows per page; a row was actually printed in a column format for easier studying). The non-studied rows were covered by sheets of paper. The subject was seated behind a desk in a quiet room. The main goal was to learn a list as quickly as possible, to learn each row until it could be reproduced correctly once.

Following Ebbinghaus (p.18), the syllables were softly spoken from the first syllable to the 13th syllable at a constant speed of 150 beats per minute. The repetition of a row took 5.2 s on average. Our subject preferred to speak the syllables in a jambus-like manner, where syllables were paired so that the emphasis always was on the second syllable (i.e. wes-hóm, niem-hág, etc…). The last syllable (13th syllable) was not paired to another syllable and was not spoken with an emphasis. Here, we use an approach similar to Heller et al. and not to Ebbinghaus, who prefers a ¾ rhythm, stressing the first syllable in each group of three (this is in fact the reason he gives for his preference for rows of length 10, 13, or 16 syllables, see Ebbinghaus, p. 19).

During the learning phase, the subject had a continuous choice to either read or reproduce the syllables. Towards the end of the learning process, occasional attempts were made to produce an entire row by heart. When there was a moment of hesitation during such ‘blind’ reproduction, the rest of the list was read (i.e., not blind) to the end. Blind reproduction always started with the first syllable of a row. Rows were not learned in parts. Each time the 13th syllable had been reached and the row still contained errors, it was read again from the beginning. After having learned one row and before starting the next one, there was an interval of 15 sec. The interval served as a moment of rest and pause. All of this was aimed at following Ebbinghaus as closely as possible. Each row was thus learned to a 100% correct criterion before moving to learning the next row.

During the pre-pretraining phase, a metronome was used at first to achieve a recitation rate of 150 beats, but this was found to be too intrusive and distracting. Eventually, the rhythm was internalized and the metronome was only used for occasional rate checks. During the experimental phase, it was not used. After each rehearsal of a row, there was a little transition-pause of about 3 beats to take a breath before the next repetition of the row.

Learning of a list was considered complete, if all rows had thus been learned in order. The retention interval was started at the time a list had been learned. On most days two or three lists were learned or relearned with a maximum of four. The full learning schedule is given in Fig 1.

Relearning phase

We added one additional measurement to Ebbinghaus’ procedure: the number of correct syllables at first reproduction of a row at relearning, not necessarily at the right location. We recorded the recall of the first time a row was relearned with an Olympus WS-450s voice-recorder. After the last relearning session of the experimental phase, the sound files were transcribed and scored.

Rows were relearned in the same order as during original learning. During relearning, the subject was seated at a desk with a computer. A word processing program was opened on the computer and a clock was visible on the screen. A sheet of paper with a list printed on it was laid in front of the subject with only the syllables from the row to be learned visible. The other rows were covered by a piece of paper. During learning, the subject used the ‘1’ button on the keyboard to count the number of repetitions. Following Ebbinghaus (p. 19), after successful relearning there was a 15 second pause. Then, the row learned last was covered, a next row uncovered and the procedure was repeated.

Relearning of a row started with turning on the voice recorder. Then the row was read once as described above. Twenty seconds after turning the voice recorder on, the subject stopped recall attempts and turned the voice recorder off. After that, relearning continued in the usual fashion. This procedure was repeated for every row in the list. After a list had been relearned, the audio file of the recording was saved on a computer.