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I'm reading through someone else's code for plotting the results of a psychology experiment, and (according to the code comments) they calculate the accuracy error of their behavioral paradigm as follows:

$\textit{accuracy error} = \sqrt{\frac{(\textit{accuracy}) (1-\textit{accuracy})}{\textit{total trials}}}$

It's output seems to be very similar to the original accuracy. What is this? Is this some sort of multiple comparison correction? Why would they do this?

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    $\begingroup$ This estimates the standard error of the "accuracy" as measured from "total trials" draws from a Bernoulli variable. $\endgroup$ – whuber Feb 18 '11 at 16:54
  • $\begingroup$ @whuber - Why not just use number correct / total trials like everywhere else? $\endgroup$ – eykanal Feb 18 '11 at 17:14
  • $\begingroup$ Because they're not actually estimating accuracy but the standard error. If they're actually estimating accuracy this way it's just WRONG. Check the values, are there any over 0.5? If there are then this isn't the accuracy estimate equation. $\endgroup$ – John Feb 18 '11 at 17:55
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    $\begingroup$ @whuber, @rolando2 Make answers, not comments (-; $\endgroup$ – user88 Feb 19 '11 at 11:36
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    $\begingroup$ @Karl There was some discussion of this a few months ago. For many reasons, it is indeed helpful to create full-fledged replies to questions whose answers may be buried in comments. Thank you for taking this on, and welcome to our site! $\endgroup$ – whuber Aug 23 '11 at 19:25
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Assuming that the estimated accuracy is number correct / total trials in some set of independent trials, the formula you give would be the standard error of the estimated accuracy. "Accuracy error" is not unreasonable, but I would just call it the standard error of the estimate.

[poking around in the unanswered questions]

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