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.



Less is more. Stay pure. Stay poor.
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?