"Exceptions" to a Correlation



In the course of explaining to people that "exceptions," meaning examples running counter to the trend, do not disprove claims that there's a correlation between two variables, I came up with the idea of using a link to this correlation simulator, which generates a scatter diagram for each run for the parameters entered, in order to help in explaining this.


I accompany the link with these instructions:

To get a good idea of the percentage of examples which will be "exceptions" to a correlation, check out this correlation simulator. For a positive correlation, the "exceptions" are the dots in the upper left and lower right quadrants. As the correlation coefficient is set to higher values, the number of "exceptions" will tend to decrease. But, as is easily seen, even at high values there are more "exceptions" than you may think.

But it occurred to me that there might be a formula for the proportion of exceptions, and I posted a question on Stack Exchange, a forum for questions in mathematics, statistics and science etc.

Sure enough, within 18 minutes someone posted a formula. It would have taken me much longer to derive it.

Anyway, the formula is No. of expected "exceptions" = arccosine (r) / pi, where r = Pearson's r.

Now, here's my question. Clearly, the "exceptions" discussed above are not really exceptions, and are in fact entailed by any correlation coefficients other than +-1. So what is the proper term for these data points, which lie in the upper left and lower right quadrants of the scatter diagram when the correlation is positive?

If there's no established term, what are your suggestions for how to refer to these data points?