Unfortunately, in dicy cases, magnitude scale does need to be specified. One can cherry pick magnitude scales, and it has been done before with misleading results.

A test to see whether a pattern is depends on two things, in my mind. One is how many patterns were surveyed - the more scrutinized, the greater the significance required. Once one goes to a predictive mode rather than surveying the past, and is considering only a single hypothesis, however, 95% significance is the general benchmark required before further consideration.

The other factor is fairly obvious - if extremely unlikely events are predicted, fewer successes are necessary before a pattern can be guessed to be significant.

Probability in simple cases can be judged by the binomial theorem, here's a site with an explanation and the calculation: http://faculty.vassar.edu/lowry/binomialX.html