Statistical checks:
check hypothesized distribution
•Probability of no zeroes (to show x ¹ 0) for v values of x in range of size r
•Range limits (e.g., x £ 22)
–same number of samples as neighbors (uniform)
–more samples than neighbors (clipped)
Statistical test over hypothesized distribution (are the hypothesized distributions meaningful?)
Much of the tool can be viewed as tests of hypothesized distributions.
x  0: say range is from -r/2 to r/2 (approximately); assumes uniform distribution.

[The hypothesized distribution is always:  the uniform distribution.  Don’t say that early in the slide, only mention uniform distribution when discussing range limit test.]

Recall that this is over multiple tests in a test suite, not a single test.

There is a test like this for every invariant.

This indicates the value of reporting the invariant, it is not a statistical test of the probability that it is really true over all possible executions.

This solves much of the problem, but some such undesirable invariants remain.