I am using a model to calculate observed frequencies, which some times gives non-integer values. I can round these frequencies but that seems like artificially distorting the information I have. For Example:
Example Data Yes No Male 11 19 Female 16 17
Assume my model just divides everything by 3, so model data becomes:
Yes No Male 3.67 6.33 Female 5.33 5.67
This data has to be used as "observed frequencies". Doing a chi-square test gives p value of 0.58. However, if I round this data to integers, chi-square test will give a p value of 0.8, which is very much different. My question is: is chi-square test theoretically valid on non-integer observed frequencies?
Edit: Please note that data and model specified in the question are not real, just to make you understand the problem I am facing. Real data is of this type.
Male Female Source1 10.8 18.2 Source2 16 17
The real data is the prediction of males and females according to the job roles and City from Bureau of Labor Statistics.
I have no control over the data coming from source1, which (surprisingly) contains decimal point numbers. All I can do is round the data from source1.