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Wanting to improve my own reading speed, I found the following as the first result of a Google search:

The PX Project, a single three-hour cognitive experiment, produced an average increase in reading speed of 386 percent.

It was tested with speakers of five languages, and even dyslexics were conditioned to read technical material at more than 3,000 words-per-minute (wpm), or 10 pages per minute. One page every six seconds.
How I Learned to Read 300 Percent Faster in 20 Minutes - Huffington Post

According to their own words, which I believe is accurate:

By comparison, the average reading speed in the U.S. is 200-300 wpm (one-half to one page per minute), with the top one percent of the population reading over 400 wpm.
ibid

I've known the average was 250 words per minute or so for quite some time, but people reading over 1000 wpm is extremely rare (I've only known one such person). So to increase the average reader at 250 by nearly four times, puts them in a bracket that doesn't exist. It would be a statistical anomaly. And they are not claiming to have done it just once or twice. They claim to do it consistently.

Does the PX Project increase reading speed by an average of 386%? Can an average reader's reading speed be increased in the first place, or does the science show it is a skill that quickly tops out? Are any methods proven to work at all?

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    I'm not sure, but I think that it's possible to have "an average [as in "mean"] increase in reading speed of 386 percent" without "an increase in the reading speed of an average reader by 386 percent". For example, what if it provided extreme increases in reading speed for very poor readers, that quickly taper off by the time you get to even moderately poor readers? Regardless, it does sound like a claim that needs some attention from a skeptic. – sumelic Jul 8 '17 at 19:20
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    @sumelic I suppose that's true, but the claim also includes training some people to read over three thousand words per minutes, which I find utterly unbelievable. Naturally, I take this with the assumption that comprehension doesn't suffer too much, as that seems the expected message. – fredsbend Jul 8 '17 at 20:32
  • 400% of 300 is much less than 3000. Perhaps something from the source provides an internal consistency. – user36688 Jul 9 '17 at 16:45
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    Anecdotal evidence (hence the comment not an answer): I tried the method for about two months. Yes, it increases reading speed, but from my experience, I didn't retain as much as when I read slower. Regardless, the method has allow me to vary my reading speed on parts of texts that don't seem as relevant, yet pick up on the essentials, on which I'll slow the pace. – ChrisR Jul 9 '17 at 20:47
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    @ChrisR that sounds similar to the "speed reading" programs that have been floating around for decades, if not centuries. They aren't really about increasing raw decoding skills (which, beyond a point, only improve asymptotically), but on skimming more efficiently. Being able to skim a novel in five minutes and successfully recall 75% of the characters' names, love interests, and political viewpoints is a fun parlor game, but isn't a good way to enjoy good literature. – Robert Columbia Apr 3 '18 at 14:23

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