The gain of using the MCM function lies primarily in the fact that its parameters can be interpreted more clearly, that it is associated with a type of consolidation mechanism, and that also explains other types of data than the savings function [ 41 — 43 ].
The MCM function assumes a neural system consolidation mechanism [ 44 , 45 ] that has been dubbed the 'Standard Consolidation Theory' [ 46 , 47 ], where the latter authors propose a different theory, the so called Multiple Trace Theory of consolidation.
It is here not our goal to evaluate the merits of these theories; we have reviewed these and other theories of consolidation elsewhere [ 48 ]. We merely want to apply the MCM equation to these four savings curves and evaluate the goodness-of-fit, viewing it as a conceptual improvement of the summed exponential. If we compare the MCM equation or summed exponential function to the other functions, this only makes sense if we rely on the AIC , which takes into account the varying number of parameters.
The average AIC is 0. Summarizing, Ebbinghaus' data fit his own equations and the power function best. The AIC indicates that on average the MCM equation or summed exponential function is on average better than all equations considered thus far, where the difference with the power function is 1. The difference with Ebbinghaus' own equations is only 0. It is likely, however, that Ebbinghaus actively searched for an equation that achieves such an exceptional fit, which in his eyes was no more than a 'summary' of the forgetting curve see citation above.
This also explains why he has no problems substituting a 'logarithmic' equations for the earlier 'power' equation: it shows a slightly better fit. Fitting data is always done with a purpose. Ebbinghaus achieved a concise summary of his forgetting data, the power function is a parsimonious description of the forgetting function that shows a good or at least adequate fit in many types of forgetting experiments, and the MCM equation attempts to capture the shape of a hypothetical consolidation process in the brain albeit at the expense of additional parameters.
Taking into account these extra parameters, however, does not give a worse fit on the AIC and approaches a meaningful improvement over the power function. When looking at the shapes of the four curves in Fig 2 , savings after 1 day or 2 days seems higher than expected. Ebbinghaus [ 8 ] notices this as well but merely writes it off as a discrepancy from his fitted curve see above that still falls within the error bars [ 8 ], p.
He clearly did not trust this data point because in his text from [ 9 ] he reports that he later had replicated this 24 hour data point. The replicated data for this point gave a very similar score, so we must consider it a valid measurement.
Jenkins and Dallenbach [ 50 ], however, interpreted the discrepancy as an effect of sleep, which motivated them to investigate this closer in an experiment on the effect of sleep on forgetting.
They also refer to the forgetting curve by Radossawljewitsch [ 16 ], who also found higher savings after both 1 and 2 days 0. To them, this is suggestive of a very strong effect of sleep, but Finkenbinder [ 17 ] points out that Radossawljewitsch's 8-hour data point may not be reliable, because these lists were all relearned during the afternoon, when there was less rapid learning resulting in fewer savings.
He, therefore, suggests using a corrected savings score at 8 hours of 0. Even if savings would be 0. Using free recall and retention up to 8 hours, the seminal study by Jenkins and Dallenbach [ 50 ] yielded a positive effect of sleep on recall. This effect has since been replicated many times, for example in recent studies on the effects of different sleep stages on both procedural and declarative memory e. Whereas the older studies from the s and before typically confound the sleep manipulation with time-of-day effects or fatigue, this is no longer the case in the recent studies, so that there is now very strong evidence that sleep does indeed have an effect on memory independent of the effects of, say, rest or lack of interference.
In some of the sleep-memory experiments cited above, we even see a temporary increase in the forgetting curve, where subjects score better than after learning in the days following sleep, but not if they skipped the night of sleep after learning e. This result—and other studies—suggests that the first night of sleep after learning has a particularly important effect on memory that may continue to evolve for several days afterwards.
Such an effect may also be observed in savings curve by Mack and to some extent in the Seitz curve, both show a tendency to increase in savings score for two days following learning. Given that we can trace the history of research on the effects of sleep on memory to the 24 hour point of Ebbinghaus' forgetting curve, we think it is interesting to evaluate this data point more formally.
If we can establish the jump in the curve more formally, it will make a stronger case that the 'true shape' of the long-term forgetting curve has a jump in at 24 hours or perhaps right after the subject has slept , although we may not conclude from this that the local increase is due to sleep per se, which would require more research is necessary for that. If we first informally inspect the data points shown in Fig 2 and compare them with the fitted power function, we see relatively less forgetting at either day 1, day 2, or both.
In all four panels, at least one of these points is above the fitted power function curve at a distance of at least one standard error. We also see this effect for the Memory Chain Model curve in Fig 3 , though somewhat less pronounced in the Seitz panel, the fitted curve crosses the error bars at 1 and 2 days. The reason for this is that the Memory Chain Model already incorporates the effects of a hypothetical consolidation process.
The current body of research on sleep and memory would predict such a boost after one or two nights and attribute it to sleep, though for this particular type of experiments this has to established more firmly in further experiments.
Whatever its cause, we can better quantify the visually observed boost by including it in the equations fitted. We, therefore, made a variant of the power function that differs only in the addition of a constant boost factor to the savings of the retention intervals of 1 day and higher. This power function with boost is also plotted in Fig 2. The results are mixed, though on average they suggest a trend towards improvement with a boost parameter.
A difference in average AIC of 1. The boost parameter in Table 5 shows the size of the upward jump after 24 hours. We see that for Ebbinghaus, this jump is small 0.
The Dros data show no evidence for a boost but these fits are probably influenced strongly by the very low 31 day data point. The result was a high-quality forgetting curve that has rightfully remained a classic in the field.
Replications, including ours, testify to the soundness of his results. His method can also be seen as a precursor to implicit memory tests in that certain inaccessible representations, seemingly forgotten, can still be relearned faster compared with others that do not show such an advantage.
This is evidence of implicit memory because the subjects may not be consciously aware they still possess traces of the memory representations, which cannot be recalled or recognized but that do show savings. The savings method is still used today as a sensitive method to study the decline of foreign languages in order to assess the true extent of linguistic knowledge retained over a long time [ 57 ].
Ebbinghaus [ 8 ] also emphasizes the importance of sleep for memory, but these remarks are limited to how low-quality or insufficient sleep may have inflated his own learning times at certain dates [ 8 ], p. In other words, he acknowledges the effects of previous sleep on current learning, but he does not admit to the role of sleep in slowing down long-term forgetting.
The formal analysis above suggests that the classic forgetting curve is not completely smooth but does show a jump at the 1 day retention interval. Current research on the effects of sleep on memory would predict such a jump, but for this particular type of experiment this remains to be established.
We would like to thank Annette de Groot and Jeroen Raaijmakers for helpful suggestions when writing this. The authors received no specific funding for this work. National Center for Biotechnology Information , U.
PLoS One. Published online Jul 6. Jaap M. Dante R. Chialvo, Editor. Author information Article notes Copyright and License information Disclaimer. University of Amsterdam, Amsterdam, The Netherlands,. Competing Interests: The authors have declared that no competing interests exist. Received Nov 22; Accepted Jan This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
This article has been cited by other articles in PMC. Introduction This paper describes a replication of one of the most important early experiments in psychology, namely Ebbinghaus' classic experiment on forgetting from and The Replication Experiment The current study was set up to replicate the findings by Ebbinghaus [ 8 , 9 ].
Subject The second author, J. Materials The learning material consisted of 70 lists. Nonsense syllables Each syllable consisted of 3 or 4 lower-case letters. Row and list construction Using the pseudo-random generator of Excel , rows of 13 syllables were constructed. 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.
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. 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.
Open in a separate window. Fig 1. Learning schedule during — for all lists, where labels in bold indicate when each of the lists 1 to 10 was first learned for each retention interval. Table 1 Average number of repetitions until once correct. Table 2 Time spent learning session S1 and relearning session S2 for each list with savings Q by Dros. Fig 2. Four loglog graphs with savings as a function of retention interval with fitted power function curves and curves with best fitting power functions with boost at 1 day see text for an explanation.
Fig 3. Four log graphs with savings as a function of retention interval with best-fitting Memory Chain Model retention functions see text for an explanation.
Fig 4. Normalized savings scores as a function of retention interval on a logarithmic scale, rescaled so the first data point is 1. Table 3 Savings for Ebbinghaus [ 8 ], p. Ebbinghaus Mack Seitz Dros 20 min 0. Fig 5. Learning time per list as a function of day of experiment with a fitted straight line.
Serial position effects In Fig 6 , we have plotted the average serial position curves for each retention interval and for the grand average.
Fig 6. Serial position for correct relearning scores for each retention interval and for the average of all retention intervals see text for an explanation. Fig 7. Proportion correct as a function of retention interval on a logarithmic scale. Effects of serial position on forgetting Ebbinghaus does not say anything about serial position curves or indeed about the order in which he acquired the syllables. Curve fitting Hermann Ebbinghaus [ 8 ] was the first to try to find a mathematical equation that describes the shape of forgetting.
Table 4 Fits of two equations proposed by Ebbinghaus in and to data from his own study and from three replication studies. Table 5 Fits of a number of equations to data from Ebbinghaus and replication studies. The hour point in Ebbinghaus' forgetting curve When looking at the shapes of the four curves in Fig 2 , savings after 1 day or 2 days seems higher than expected. Acknowledgments We would like to thank Annette de Groot and Jeroen Raaijmakers for helpful suggestions when writing this. References 1.
Psychological Science 2 : — When a student crams for a test they do not recall the information for the final at the end of the semester. If a student skims all of the previous chapters of the text and re reads notes then when the final exam comes they will be more likely be more prepared than those who have had to cram right before class. I think the biggest strength is that Ebbinghaus was able to teach students, professors, and well anyone who will ever learn that there is a better way to learn large amounts of information.
By discovering the spacing effect he has affected the way we learn and retain information. I know that he did not have access to the resources that others of his time did but I am surprised that he could not find anyone else to participate in the study of serial learning.
I have no doubts that his findings were true and accurate but if there was going to be anything that might have been skewed it could have been the fact that he may not have wanted to report how often he failed at being able to recall the list the first time.
I do not think that this would be ethical today. Hermann Ebbinghaus was a man ahead of his times when it came to psychological experiments. Ebbinghaus wrote several papers including in Fundamentals of psychology, and The Outline of Psychology. Schultz, D. A history of modern psychology 10th ed. The life and contributions of hermann ebbinghaus.
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Early and late items may not have to compete as much for rehearsal resources as the middle items. Middle items have more of a likelihood of being interfered with from earlier and later items, while the initial and terminal items do not have to face as much interference. Some have argued that the serial position effect is due to the working of different memory systems. Paired Associate PA learning involves having 2 items a Stimulus and Response item paired as stimuli e.
When the items pairs are committed to memory, the presentation of the first word the stimulus word should evoke the second word the response word. If the items used as Stimulus words in a PA task are too similar, discrimination ability decreases, leading to errors in recall. Learning of Response items--Meaningful responses are learned easier than non-meaningful responses. The connections between individual stimulus and response items is also mediated by certain factors.
Preexisting associations between the stimulus and response items can either help or hinder the association process. Inspirational Exam Quotes. Finding The Perfect Study Routine. Motivation To Study : 29 Strategies. Pomodoro Method : 9-Step Guide. Best Books About Studying. Higher grades, less sweat. Are You A…? Parent Student Educator. Your privacy protected.
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