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But it doesn’t work well when the distribution’s skewed to one side. eg: I’ve run RCTs manipulating schedules. You might think shortened intervals would help struggling readers, but it has little effect on the population measure—just (likely) nudges some closer to the threshold.
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Lack of a good continuous measure makes it hard to characterize the dynamics of what’s going on, which makes it hard to make iterative improvements. I’ll need to find some good solution here. Unfortunately, response times are (AFAICT) not a strong enough predictor to use.
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Incidentally, this is part of why Ebbinghaus used nonsense syllables: he was memorizing sequences he’d *never* remember on the first try in subsequent tests. But it’d take less time to re-learn well-rehearsed sequences—time savings as a continuous proxy for depth of encoding.
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(Yes, I’m aware that some memory systems ask users to subjectively “grade” their memory 1-5, which would be slightly less discrete. I suspect it probably doesn’t add enough measurement resolution to be worth the user burden, but could be worth trying.)
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The thing I have to keep reminding myself about a statement like this is that it does *not* mean that the mechanic causes 20% increase in depth-of-encoding. It's more likely a fairly small increase for a large number of people right below the threshold.
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So it works pretty well initially, when the distribution’s spread out. e.g.: I’ve been running an RCT on retry mechanics. Of readers who forget an answer while reading an essay, about 20% more will succeed in their first review if the in-essay prompt gave them a chance to retry.
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What model are you using for the spacing effect? What are the parameters you’re fitting? Have you read into context based probabilistic models?
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Some parameters should be fitted for the content and some for learners and I have a hunch maybe that’ll help with your problem but depends on what model you’re using in the first place.
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(My knowledge of it is dated but I worked on models of spacing effect first couple of years of grad school and I developed a schedule optimizer circa 2008 alas my advisor didn’t support applied work.)
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I'm stubbornly (and probably foolishly) trying to see what I can understand without fitting to a probabilistic model. That's what sparked the interest in population measures. But, maybe unsurprisingly, I am not having much luck. :)
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One thing I did back then was computational/math analysis of whether we could approximate a function that looked like the spacing effect with linear combinations of power law or exponential functions and it cannot be done :-)
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