Spacing Effect

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What is Spacing Effect?

Spacing Effect is better learning on a later test when study episodes of the same item are separated by a gap of at least 1 second than when that item is studied in one uninterrupted bout of the same total time.

With any considerable number of repetitions a suitable distribution of them over a space of time is decidedly more advantageous than the massing of them at a single time.

That sentence is the 1913 translation of Ebbinghaus. He says the comparison in that chapter makes the assumption probable. He also says the numbers come from very few researches and from very limited conditions. The English name Spacing Effect is not in that sentence. Cepeda, Pashler, Vul, Wixted, and Rohrer (2006) use it for one contrast only. Spaced means a lag of 1 second or longer. Massed means the item stays present, or returns in under 1 second, for twice the time, with no other item in between. Saying a new colleague’s name ten times in the doorway is the shape of one bout. Saying it twice at the door and twice again after lunch is the shape of a gap. The ten and the twice are not a result from either paper. Spaced Repetition on this site is a review schedule that uses a gap on purpose. The schedule is not this definition, and it is not the optimal gap in the 2008 study below.

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Spacing Effect in 3 Depths

• Beginner: Two looks at least a second apart can beat one uninterrupted look of the same total time, on a later test. Ebbinghaus’s own comparison was coarser. He treated 38 repetitions spread over the three preceding days as matching 68 repetitions on the day before, for a 12-syllable series.
• Practitioner: Write the test date before you lengthen the gap. In the 2008 fact study, recall 7 days after the review was best, among the gaps they used, at a 1-day gap. Recall 70 days later was best at a 21-day gap. Both gains are against a gap of about 3 minutes, not against an uninterrupted double look.
• Advanced: The 2006 table’s overall means are 36.7 percent correct after massed study and 47.3 percent after spaced study, across 271 comparisons. Three middle bins, from 10 minutes through 7 days, do not reach a significant test. The 2008 curve rises and then falls. A 111 percent improvement there is not 111 percentage points, and it is not the 9 percent gap from 41.2 to 50.1.

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Origin

The pattern Ebbinghaus published in 1885 is distribution over days against massing on the day before. The narrow English definition, a lag of at least 1 second against an uninterrupted bout, is the 2006 review. Über das Gedächtnis appeared in Leipzig in 1885. This page uses Chapter VIII of Memory: A Contribution to Experimental Psychology, the Teachers College translation by Ruger and Bussenius (New York, 1913). Section 34 joins two of his own procedures. Six 12-syllable series, learned with an average of 410 repetitions, are the massed side. He treats that average as 68 repetitions for one series. Those 68 immediately successive repetitions left a series that could be recited without error the next day after 7 further repetitions. On the distributed side, nine 12-syllable series took 158, 109, and 75 repetitions on the first three days. The sum is 342, or 38 for one series. On the fourth day the nine series were learned with 56 repetitions, about 6 for one series. He calls 38 repetitions over the three preceding days just as favorable as 68 on the day just previous. The learner is himself. He warns that the count rests on very few researches. Cepeda and colleagues, in the 2006 review, place Jost (1897) and Thorndike (1912) beside that book as early demonstrations. Those two works were not re-read. No number from them is on this page. The 2006 paper then fixes the words. The spacing effect is enhanced learning for spaced episodes against massed episodes of a given item. The lag effect is a longer gap against a shorter gap when both gaps are already at least 1 second. Distributed practice is their name for both contrasts together. This page keeps the name Spacing Effect for the massed-against-spaced contrast. A longer gap is a second question. The review is Nicholas J. Cepeda, Harold Pashler, Edward Vul, John T. Wixted, and Doug Rohrer, “Distributed practice in verbal recall tasks: A review and quantitative synthesis,” Psychological Bulletin 132(3), May 2006, pages 354–380. The author PDF prints the DOI 10.1037/0033-2909.132.3.354. Cepeda was at the University of California, San Diego, and the University of Colorado at Boulder. Pashler, Vul, and Wixted were at San Diego. Rohrer was at the University of South Florida.

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Key Points

Four cuts keep a review schedule from inheriting a percent it did not measure. The bout, the bin, the test date, and the kind of percent each have their own number.

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Applications

Use the contrast when someone treats any second look, or any longer wait, as the percent in the table. Keep 41.2, 50.1, 36.7, and 47.3 inside the bins that produced them.

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Case Study

In 2008, Nicholas J. Cepeda, Edward Vul, Doug Rohrer, John T. Wixted, and Harold Pashler reported 1,354 people who finished three sessions on the laboratory’s Internet Memory Research panel. Cepeda’s affiliations on the paper are York University and the University of California, San Diego. Vul’s are San Diego and the Massachusetts Institute of Technology. Rohrer is at the University of South Florida. Wixted and Pashler are at San Diego. The journal text is Psychological Science 19(11), pages 1095–1102. The author PDF read here does not print a DOI. The journal record is 10.1111/j.1467-9280.2008.02209.x. The manuscript was received on 3 October 2007, and the revision was accepted on 28 March 2008. The question was how the gap between two study sessions changes a test given later, when the second session does not add trials just because the gap was long. Each person was randomly assigned to one of 26 gap-by-delay combinations. In the first session they learned 32 obscure but true facts. Every answer was one word of five or six letters. One item was the question of which European nation consumes the most spicy Mexican food. The answer was Norway. A fact answered correctly on the very first test was treated as already known and was dropped from later analyses for that person only. The others were practiced to one correct recall each. People answered between 61 and 96 questions before that criterion. When the nominal gap was zero, the second session began about 3 minutes later. In that session the full list ran twice, in a new order each time, and the correct answer was shown for 4 seconds whether the response was right or blank. The final session, after 7, 35, 70, or 350 days, gave a recall test and then a five-alternative recognition test, with no feedback. In a separate pilot, people who had never seen the facts chose each of the five alternatives about equally often. The recall comparison is the best gap they actually used against the about-3-minute gap. For a test at 7 days, that gap was 1 day: 60 people at about 3 minutes and 66 at 1 day, a 10 percent improvement, t(124) = 6.5, d = 1.3. For 35 days, the best gap was 11 days: 72 and 41 people, 59 percent, t(111) = 8.9, d = 0.6. For 70 days, the best gap was 21 days: 55 and 49 people, 111 percent, t(102) = 8.6, d = 1.7. For 350 days, the best gap was also 21 days: 45 and 25 people, 77 percent, t(68) = 3.9, d = 0.9. Each of those tests is printed with prep = .99. The paper does not print a p value beside them. The same four delays produced recognition improvements of 1, 10, 31, and 60 percent. A 59 percent improvement can sit next to a smaller d than a 10 percent improvement. The percent is not a ranking of the delays by itself. The paper also states a 64 percent increase in final recall, d = 1.1, and a 26 percent increase in final recognition, d = 1.5, for the optimal gap against the zero-day gap. Those two sentences are a summary beside the four rows. They are not a fifth sample. Cubic splines put the recall peaks near 3, 8, 12, and 27 days. Past those peaks, a still longer gap lowered the score. The 105-day gap was on that falling side for the delays they plotted. The lesson is a rise and then a fall in later recall of unknown trivia, among people who finished, when the second session was two passes. It is not a rate at which a class remembers a chapter, and it is not the 2006 gap from 41.2 to 50.1. The mean age of the people who finished was 34 years, the standard deviation was 11, the range was 18 to 72, and 72 percent were women. Noncompletion rose at the longer delays. The paper says initial knowledge did not differ reliably between people who finished and people who missed the final test, and it prints no test statistic for that check.

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Boundaries and Failure Modes

Spacing Effect is the wrong summary when a 3-minute gap is treated as the massed cell, when a non-significant bin is treated as a large guaranteed gain, or when a child’s month-later quiz is given an adult percent. The first boundary is the short end and the thin bins. Cepeda and colleagues say a massing benefit in Peterson, Hillner, and Saltzman (1962) appeared when the retention interval was 2 or 4 seconds, and not when it was 8 or 16 seconds. That paper was not re-read. No other cell from it is on this page. In Table 1, 12 of 271 massed-against-spaced comparisons showed no effect or a negative effect. The means still favor spacing in the middle bins, and the tests do not clear the bar. From 10 minutes up to 1 day, t(20) = 0.6, p = .535, on 11 comparisons. At 1 day, t(28) = 1.2, p = .249, on 15 comparisons. At 2 to 7 days, t(16) = 1.4, p = .190, on 9 comparisons. The 8-to-30-day bin is six studies, 32.8 percent against 62.2 percent, t(10) = 2.3, p below .05. One comparison at 31 days or more has no test on that row. The overall test is t(540) = 6.6, p below .001. A significant pooled row does not promote a non-significant bin into a significant one. The second boundary is the shape past the peak, and the 2008 discussion is not a measured doubling. For any delay they plotted, recall rose with the gap and then fell. The authors say the cost of a too-short gap is larger than the cost of a somewhat too-long gap, because the rise is steep and the later decline is gradual. That reading is Figure 3 of this trivia panel. Their discussion says that someone who wants to remember for several years would seem likely to gain from a review delayed by at least several months, potentially doubling what a less distributed schedule retains, with study time equated. “Potentially doubling” is that suggestion. It is not one of the four measured improvements, and the longest test they gave was 350 days. Deficient-processing accounts that rely on short-term memory fit poorly with gaps of days, on their argument. All-or-none accounts that always prefer a longer gap fit poorly with the downturn. Priming Effect is a faster correct decision that two letter strings are words when the words are common associates. A millisecond gap between word pairs is not a day between two study sessions. The third boundary is the export, and it is the common misuse. The 41.2, the 50.1, the 36.7, and the 47.3 belong to verbal recall comparisons in the 2006 set, with study time equated. The 10, 59, 111, and 77 percent belong to unknown trivia on a web panel, against a gap of about 3 minutes, among people who finished. Cepeda and colleagues point to a separate review for skills such as mirror tracing. No size from that review is on this page. Von Restorff Effect is better memory for the one item that differs in kind from similar neighbors. Remembering one odd fact is not a gap between two studies of the same fact. Frequency Illusion is the belief that a noticed thing happens a whole lot. One review that happened to work is not the 271 comparisons.

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Common Misconceptions

Three retellings turn a longer wait into a sure gain, treat two different percents as one kind of number, or read a fluent bout as the later score.

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Related Concepts

The later-recall gap sits next to a review schedule, a truth rating after repetition, a faster word decision, memory for one odd neighbor, and the belief that a noticed thing happens a whole lot.

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One-Line Takeaway