How would one give a one sentence definition of "alpha error" as if asked over dinner? Seems like the definition above is hinting at "critical region" with the phrase "acceptable to investigator". However, "relationship observed between 2 variables" is difficult to fit into any decent definition of alpha error, because if I'm not mistaken, alpha doesn't have anything to do with the data, just the characteristics of the test. They do a little better with p-value . . .
p value. The lowest level of significance at which a given null hypothesis can be rejected; that is, the probability of observing a result as extreme or more extreme than that observed if the null hypothesis is true. See also statistical significance.