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# Replication and Analysis of Ebbinghaus’ Forgetting Curve

Date: May 28 2020

Summary: This is a replication study on the discovery of the forgetting curve as reported by Hermann Ebbinghaus in 1880.

Keywords: ##bibliography #archive

# Bibliography

J. M. J. Murre and J. Dros, "Replication and Analysis of Ebbinghaus’ Forgetting Curve," PLoS ONE, vol. 10, no. 7, p. e0120644, Jul. 2015, doi: 10.1371/journal.pone.0120644.

### Study Set-up

1. Due to time constraints, 10 replications per time interval was used, 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.

2. Were not able to experiment at fixed times during the day.

3. Our stimulus material conformed to the phonotactics of the Dutch language

4. Our subject was younger than H. Ebbinghaus

5. We do not know exactly when he learned and relearned the lists for the longer intervals. Makes it impossible to calculate the number of interfering lists between learning and relearning. nearly certain that our schedule differed from his

A practice phase was used to prevent general learning effects due to growing experience with the task and materials.

The number of correct syllables at first reproduction of a row at relearning. Did not have to be the correct location where the word was learned.

The main value monitored was amount of repetitions required to correctly reproduce syllables in a row sequence.

Learning material consisted of 70 lists. Each list consisted of 104 nonsense syllables, which in turn consisted of 8 'rows' of 13 syllables.

Lists were printed on paper in black ink with font "Calibri" at size 11. There were eight rows per page. Each row was arranged into a column format for ease of study. Rows not being studied were covered by sheets of paper.

Syllables consisted of 3 or 4 lower-case letters. Its structure was a lower-case consonant-vowel-consonant.

Syllables with meanings in other languages spoken by the subject, such as English and German, were not excluded.

These are the key points that differentiate their study from Ebbinghaus's original study. Furthermore, listed is how the study was conducted.

### Useful Concepts

Savings is time minimized on an upcoming learning trial after having had prior exposure to that learning material. Hermann Ebbinghaus came up with this idea! An example of this concept is: imagine one repeated a list 25 times to prefectly memorize the list. After a day of rest, instead of 25 repititions to relearn the list, one only needs 20. In this sense, a saving of 20% took place.

Single-subject studies are normal in memory psychology. Especially common concerning autobiographical memory based on one's own memories [1]–[3]. A benefit is that no intersubject variability exists. However, these studies need hundreds of trials to decrease variance based on confounding stimuli.

Ebbinghaus used nonsense syllables as material to learn for his experiments. He did this because he thought that legitimate material could be complicated by his pre-existing memories leading to a higher variance in his experimental data. [4] Many scientists in experimental psychology now use this same approach.

Studies suggest that the first night's sleep post-learning has an important impact on memory that may continue to adapt several days after. A temporary increase in the forgetting curve where subjects score better than after learning in the days following sleep can be seen. However, it is not experienced if they skipped the night of sleep after learning [5]

How sleep can impact and benefit the learning of new material. The forgetting curve is not completely smooth and jumps at the 1 day retention interval. One possible explanation for this jump is based on the effects of sleep on memory. However, that explanation has not been proven for this study type.

Implicit memory: where an individual may not be consciously aware they still possess traces of memory representations but one cannot actively recall or recognize these representations. These old traces do show savings when relearning that corresponding material. RQ: This intuitively makes sense to me after much study and practice in languages and other domains. I wonder how long implicit memory lasts?

Memory Chain Model: posits memory passes through several neural processes - "stores" - as it transitions from short-term to long-term memory. [6] It can be used to model the forgetting curve and "savings". Store 1, the hippocampus, acts as a temporary storage which decreases exponentially in intensity. Store 2, the neocortex, is for long-term memory where it declines at a much slower rate. Store 1 gradually shifts its contents to Store 2. The decay rates in Store 1 and Store 2 are given by $\alpha_{1}$ and $\alpha_{2}$, respectively. The initial strength of the memory traces in Store 1 are given by $\mu_{1}$ and the rate of consolidating the contents of Store 1 to Store 2 is given by μ2. Lesioning Store 1, will produce a retrograde amnesia gradient that can be modeled by the Memory Chain Model simultaneously with the forgetting gradient of healthy controls. [7] The Memory Chain Model (MCM) equation for type of savings studied here is given by $Q(t) = \mu_{1}e^{a_{1}t} + \frac{\mu_{1}\mu_{2}(e^{-a_{2}t} - e^{-a_{1}t})}{a_{1} -a_{2}}$The MCM function has the same number of parameters but they are arranged differently. The proof that this equation is a mathematical formalization of the memory consolidation process can be found elsewhere. [7]

## How To Cite

Zelko, Jacob. Replication and Analysis of Ebbinghaus’ Forgetting Curve. https://jacobzelko.com/05282020172154-replication-ebbinghaus. May 28 2020.

## References

[1] W. A. Wagenaar, “My memory: A study of autobiographical memory over six years,” Cognit. Psychol., vol. 18, no. 2, pp. 225–252, 1986.

[2] M. Linton, “Memory for real-world events,” Explor. Cogn., pp. 376–404, 1975.

[3] J. R. Sehulster, “Content and temporal structure of autobiographical knowledge: Remembering twenty-five seasons at the Metropolitan Opera,” Mem. Cognit., vol. 17, no. 5, pp. 590–606, 1989.

[4] H. Ebbinghaus, “Ueber das gedächtnis,” 1885.

[5] R. Stickgold, L. James, and J. A. Hobson, “Visual discrimination learning requires sleep after training,” Nat. Neurosci., vol. 3, no. 12, pp. 1237–1238, 2000.

[6] J. M. Murre, M. Meeter, and A. G. Chessa, “Modeling amnesia: Connectionist and mathematical approaches,” Stat. Process Models Neurosci. Aging, pp. 119–162, 2007.

[7] J. M. Murre, A. G. Chessa, and M. Meeter, “A mathematical model of forgetting and amnesia,” Front. Psychol., vol. 4, p. 76, 2013.

## Discussion:

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