Hi. Music theorist here. I'm working on a paper analyzing a certain number of events in a piece of music statistically. I've found that my form of analysis has determined that another theorist's form of analysis identifies 423 out of 670 events in this piece of music being what I call "upper tier" events. This is as opposed to "lower tier" events.(adsbygoogle = window.adsbygoogle || []).push({});

I'm trying to figure out the statistical significance of this. So what I'm trying to figure out is, what are the chances that, out of 670 coin flips, 423-or-more of them would come up heads?

I think this question sounds deceptively simple, but isn't.

You would think that pretty much coin flips converge toward halfsies the more often you flip them, right? 423/670 is 63%, which is 13% more than the 50% one would intuitively expect.

But I've read that to find statistical significance, one has to find the chances that this event could occur *randomly*. So what are the odds that I could get 423-or-more flips to come up heads out 670 *at random*? That number seems like it would be quite small (which is what I want--- a small chance this is random; therefore the outcome has significance).

The 50-50 intuition sometimes is counter-intuitive. If you flip a coin four times, there are sixteen possible outcome configurations: HHHH, HHHT... TTTH, TTTT. How many are half-heads? You'd think 8, right? But there are only 6 possible configurations: HHTT, HTHT, HTTH, THHT, THTH, TTHH.

So that's why I want to be careful about this. I think I'm a little in over my head and so I'd like some help from an expert! Thank you so much in advance.

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# Probability question regarding 670 coin flips

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