1 X 2 Chi Square? With controlled expected values?

Good Morning,

I’m wondering if you could possibly help me with a little problem.

I have some data:
1. Number and date of disease outbreak each year
2. Date a warning system for this disease occurred each year based on environmental factors.

I would like to get a p value comparing the total amount of outbreaks with warning vs those without.
I do not have enough data to do a complete contingency table I believe, I tried before and my results did not look right.

I would like to assess the probability for each year that the disease would be predicted by the system say 50% of the time, 60%, 70% etc.


No Warning Warning TOTAL
Outbreaks (Observed) 70 34 104
EXPECTED FREQUENCY 52(50%) 52(50%) 104(Total)

I have been trying different standard Chi Square statistics, but they don’t seem to be working. My p-values get smaller as I increase the expected frequency with a warning. This should not be the case, the probability should be reduced as I impose a higher expected warning compared to what was actually alerted.

If anybody could give me a bit of advice here I would be very grateful, even the name of an analysis which would meet the requirements of what I’m trying to do?

Thank you for your time.



Not a robit
For historic data (e.g., 2014) calculate the proportion of time the system accurately predicted outbreak. Next slap a 95% confidence interval on it and see if the interval excludes 50%, 60%, or 70%?
Is it okay to just use binomial probabilities?

(n k) p^k*q^n-q

but, use my observed values to determine the probability of success and failure, p and q and use my desired 50, 60, 70, 80, 90 and 100% as observed to see what the probability of achieving these rates is at each observed probability?

I'm sorry if that doesn't make sense.

I am just concerned, the binomial probability seems like such a basic, standard method, is it criticized? Is there a flaw? A more advanced method that should be used?