I you were to flip a coin twice and it came out 'Heads' each time, would that be a coincidence?
What if the coin came up Heads ten times in a row? Is that still coincidence?
What about a hundred, a thousand? Still coincidence, or would you begin to get a little suspicious that something is not 'normal'?
I operate within the realm of coincidence vs. not. I do not have mathematical equations to govern what is and what is not a coincidence, so I do my best to arrive at the best conclusion I can come up with.
I recently had a chance to talk with my mother on this topic and she provided a different answer. To remind everyone, I answered that I would be suspicious after 18 heads, because 19/20 is represented in percentages as 95% which rounds up to 100% depending on your degree of precision.
My mother, interestingly, answered that she would become suspicious after 9 heads. This also rounds up to 100%, just with one less degree of precision than what I use.
Ideally, of course, I would want around 198 iterations to be done, which would be considered a decent sample size for this question. If we get heads 198 times, then we have a probability of 99.5%
This shows the importance of large sample sizes for gaining accurate readings. To get readings to the tenth of a percent, we would need a sample size of about 1,998 or about 2,000. This is a number that I keep in mind when reading many statistical papers and it might be one you would like to keep in mind, too.