On a Method of Determining Whether a Sample of Size n Supposed to Have Been Drawn from a Parent Population Having a Known Probability Integral has Probably Been Drawn at Random

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Abstract
The P[lambda]n test appeals first to the principle of independent probabilities, to ascertain the probability of more improbable individual occurrences, and then starting from this probability measures the probability of all sets of occurrences, not necessarily greater in each individual variate but more improbable as a whole set. It seems to involve fewer approximations and assumptions than the [chi]2 test, especially for small samples. Because a set of occurrences is found on hypothesis H1 not to be very improbable by test A, it does not follow that H 1 may be safely regarded as applying to the occurrences. A more stringent test B may show H 1 to be very improbable, or either or both tests, A and B, may show another hypothesis H 2 to be far more probable. A very high P[lambda]n or P[chi]2 should rouse our suspicion as well as a very low one.

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