One does not always need large sample sizes to trigger concern, chrisian. This is a classic Bernoulli Trial case and the likelihood of your reality can be easily calculated.
According to basic probability and statistics, a Bernoulli Trial is defined as a true or false event (you either did or did not succeed on the combine) with a consistent probability of success over each trial, and the trials are independent.
For your case we have a sample of 13 combines and a probability of success = .91;
Statistical question: What is the probability that chrisian would fail 6 or more times?
Probability he fails greater than or equal to 6 times:
13
S U M (13 choose k) * (.09)^k * (.91)^(13-k)
k = 6
I've calculated this sum for you, and the probability that you will fail 6 or more times under these conditions is approximately .00052, which is far better than the standard level of statistical significance. You were right to express concern.
Now, this result makes me believe that at least one of the assumptions was wrong:
(1) The probability of a success is .91
(2) The trials were independent
(3) The probability did not change over time.
I can't see their code, so any of the three could be possible.
According to basic probability and statistics, a Bernoulli Trial is defined as a true or false event (you either did or did not succeed on the combine) with a consistent probability of success over each trial, and the trials are independent.
For your case we have a sample of 13 combines and a probability of success = .91;
Statistical question: What is the probability that chrisian would fail 6 or more times?
Probability he fails greater than or equal to 6 times:
13
S U M (13 choose k) * (.09)^k * (.91)^(13-k)
k = 6
I've calculated this sum for you, and the probability that you will fail 6 or more times under these conditions is approximately .00052, which is far better than the standard level of statistical significance. You were right to express concern.
Now, this result makes me believe that at least one of the assumptions was wrong:
(1) The probability of a success is .91
(2) The trials were independent
(3) The probability did not change over time.
I can't see their code, so any of the three could be possible.
Comment