An excel program runs a Monte Carlo coin experiment. 10,000 coins are tossed 1000 times, with the number of times N heads appearing recorded in a table. Call the number of times N heads appear during a run of the experiment Q. The average value of Q as well as its standard deviation is calculated at the experiment's end. My question is how do I calculate the error bars for such an experiment? I am not exactly sure how to do this, and I've been trying for the last few hours to find a solution, but all attempts have been fruitless. Any help would be greatly appreciated.
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1$\begingroup$ It depends on what the error bars are to represent; different things are possible. For example, it's quite common in this situation to use standard error bars to represent the standard deviation. So what, specifically, are your error bars intended to indicate? (In the previous incarnation of your question, now deleted -- I can't find it - it might have been possible to back the definition being used out. If you can point me to it, that might help.) $\endgroup$– Glen_bCommented Sep 29, 2013 at 3:49
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$\begingroup$ ... on the error bars you had on that question, what is the ratio of the error bar size to the standard deviation? $\endgroup$– Glen_bCommented Sep 29, 2013 at 6:18
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$\begingroup$ @Glen_b for the value N=0, we have Q=78. The error bar for that example was 9. I noticed that the error bar for each Q was about the square root of Q rounded to the nearest integer, but that doesn't make any sense.The ratio of error bar size to st. dev. was about 6 for the above Q. $\endgroup$– BronzeclocksofbeninCommented Sep 29, 2013 at 10:22
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$\begingroup$ How do they relate to the square root of the binomial variance $np(1-p)$? $\endgroup$– Glen_bCommented Sep 29, 2013 at 10:24
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$\begingroup$ @Glen_b If I take my probability in this case to be 78/1000, I find the square root of the variance to be 8.48. I checked this for all of the Q's in my example, and it's usually about one or two integer values off from the stated error bar. $\endgroup$– BronzeclocksofbeninCommented Sep 29, 2013 at 10:35
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