# Correlation between proportion variable and categorical variable

I am interested in testing for the correlation between influenza activity and different periods (different decades). The variable influenza activity is a combination of two variables: ILI proportion (ILI case/total population) $$\times$$ lab positivity (positive sample/total samples). So, it is the multiplication of two proportions. Variable period is categorical (period A, period B and Period C). Also, influenza activity is not normally distributed and, even though its factors are proportionate in nature, they don't add up to one. I am wondering which correlation test is most appropriate given the nature of these data: Spearman rho? Kendall tau? Quasi-poisson regression? OLS regression?

I'm quite the beginner at stats so I'd appreciate your input.

If you want to test a correlation you could construct a linear regression that codes for the categorical variable. You do this by splitting the categorical variable into binary predictors. Your model may look something like this $$\widehat{Influenza Activity}=\beta_0+\beta_1ILIPropotion*labPositivity+\beta_2PeriodA+\beta_3PeriodB+\epsilon$$ where the predictor Period A is 1 if the sample is from period A and 0 if not. Likewise for Period B. If it is period C. Another option is to run a one way ANOVA test which compares if there is a statistical difference in the dependent variable across different groups. This would tell you if Influenza Activity was different based on different periods. Hope this helps!