Forecasting rain from weather conditions Please bear with me - I have a very limited knowledge in statistics.
Here is my case (simplified):
A weather pattern is derived from 1 year of data. We are monitoring:


*

*sky conditions (sunny/overcast) 

*wind direction (E/W/N/S) 
Goal: We are trying to predict probability of "rain within 1hr".
Observations:


*

*if sky="overcast" AND wind="East": 18 out of 20 times it rains within 1hr. - p=0.9

*if sky="overcast" AND wind="South": 15 out of 20 times it rains within 1hr. - p=0.75


My problem is that there is only 20 occurrences on each pattern that gives me very low confidence (approx. +-22% at 95% confidence lvl) - apparently the predominant wind in the area is N/W :( 
Question:
Can I re-formulate my statement/pattern like this: 
if sky="overcast" AND (wind="East" OR wind="South") 33 out of 40 times it rains within 1hr. e.g. p=0.83?
If this is the case now that I have 40 occurrences would that give me better confidence interval, say approx. 15% at 95% cl?
Thank you in advance
 A: What you are doing is getting an estimate of the probability of rain under various different sets of conditions.  To talk about confidence intervals for the estimates you need some probability model for the proportion of time when the condition occurs rain within an hour would occur.  Knowledge of meteorology might lead to a stochatic model that could be useful to fit and use for prediction.
Without something like that I do not see how a statistical confidence interval is possible.  Assuming that each time the condition occurs the outcome is an independent Bernoulli trial with a "true' probability p that rain will result is a simplistic way to deal with it.  But it probably is not realistic.  The collection of instances that you have probably do not constitute a random sample thus invalidating the assumption of iid Bernoulli trials.
I see the value of your results as being good exploratory analysis from which models can be formulated and future experiments can be designed to do confirmatory analysis of the hypotheses formed from the exploratory analysis.  In the confirmatory phase predictions of rain based on a model could come to fruition.
