Replication and Analysis of Ebbinghaus’ Forgetting Curve

The forgetting curve

The main objective was to replicate Ebbinghaus’ famous forgetting curve. The average number of repetitions is given in Table 1 and the number of seconds spent on learning and relearning each list, with the calculated savings scores, is given in Table 2. The raw data of this experiment are freely available online at the website of the Open Science Foundation (URL: https://osf.io/6kfrp/). To see whether there were differences between the time-intervals in the average number of repetitions at first learning, a one-way independent ANOVA with the average number of repetitions per list as the dependent variable and the time-interval as the independent variable. There was no significant effect for the time-interval, F(6, 69) = 0.691, p = 0.658. This means that the average number of repetitions per list did not differ significantly per time interval, indicating there were no randomization confounds.

Savings scores (based on time in s) are compared with those of Ebbinghaus, and Mack and Seitz in Table 3 and plotted with error bars in Fig 2 using loglog coordinates and in Fig 3 using log coordinates only for the time axis. Despite the fact that the original experiment dates from 1880 and replications were done over a century later, and despite the fact that our replication was carried out in a Dutch language context, the four forgetting curves share many characteristics. To facilitate a direct comparison we have overlaid the four curves in Fig 4 where we have normalized the savings scores such that the first data point (at 20 min) was always equal to 1.0. Given expected individual differences, we find the resemblance of the four graphs remarkable. The greatest deviation is by Dros at 31 days; his savings score is much lower that any of the other three. We can only speculate at the reason for this. It may be that this subject simply has more long-term forgetting. Another explanation bears on the fact that the lists for the 31 day interval were all learned early in the experiment (see Fig 1) and learning times were shorter at the beginning, due to greater initial enthusiasm, less pro-active interference, or yet another reason. It is also possible that the low savings score on the 31 day point is an effect of the relatively short time period in which initial learning took place for the 31-day data point (i.e., massed learning); learning for other intervals was more widely spaced. We were forced to place the learning sessions at the beginning because of the limited time available by the subject for data collection. Ebbinghaus could spread his sessions of a seven-month interval, though we do not know the exact schedule for the intervals past 9 hours, nor do we know anything about the schedule followed by Mack and Seitz. Finally, we considered where the number of intervening lists had influenced retention at the 31-day-point. For this time point, the number of intervening lists varied from 23 to 33. Our analysis, however, revealed virtually no relationship with savings score as a function of intervening lists (R ² was about 8.4%). Our data did not allow us to further disentangle the effect of number of intervening lists versus time because list number and time were too strongly confounded in our design.

We found a gradual increase in learning time throughout the course of the experiment as can be seen in Fig 5, where averaged learning time in s has been plotted for consecutive ten-day periods (‘bins’). In the course of the 75 days of the experimental phase there was an average increase in learning time of 2.67 s per day for a list (this linear regression explained 56.18% of the variance). If we correct for this steady increase, which mostly affects the 31 day interval, the corrected savings measure would be 0.137 for the 31 day interval instead of 0.0410. This, however, is still well below the values for the three others, which are in the 0.20 range. This steady increase in learning time may be due to pro-active interference or fatigue. Ebbinghaus and Heller et al. do not report or analyze this.

We also analyzed the false alarms and correct answers measured on first relearning. We did a one-way independent ANOVA with the number of false alarms per row as the dependent variable and the retention interval as the independent variable. There was no significant effect for the time interval, F(6, 512) = 0.753, p > 0.608, indicating that the number of false alarms was not significantly different for the time-intervals. A one-way independent ANOVA with the number of hits per row as the dependent variable and retention interval as the independent variable, however, yielded a significant effect for the time-interval, F(6, 512) = 3.85, p < 0.01, which we will analyze further in the next section.

Serial position effects

In Fig 6, we have plotted the average serial position curves for each retention interval and for the grand average. Even if a correct syllable was not mentioned at the correct position, it was still scored as correct for its intended position (this was rare and had only a small effect on the data). Fig 6 shows clear serial position curves for all retention intervals.

In Fig 6, it also seems that there is more forgetting with time in the middle positions. In Fig 7A, overall forgetting is shown, where the average of all positions is shown for each retention interval. Though there is forgetting, these curves are much shallower than the savings curves, which are shown as well for comparison. In Fig 7B, forgetting is shown for four groups of serial positions, indicating that indeed there is virtually no forgetting in the final positions 11 to 13. A regression line is nearly horizontal for positions 11–13 (slope -0.000183) and 1–2 (slope is -0.000112) with the largest decrease over time found in positions 3–8 (slope is -0.0114) and 9–10 (slope is -0.0119). The averaged curve has a slope of -0.00930, with all slopes calculated over the untransformed scores (i.e., not on a logarithmic scale).