For a county s, let p(s) denote the probability that a single dog tests heartworm positive. For notation, n(s) is the number of tests in county s and k(s) is the number of positive tests at county s. For example, if county s has 3 positive tests out of 100 during 2011 and eight positive tests out of 200 during 2012, then k(s) = 11, n(s) = 300, and p^(s)=11/300 (a hat over a quantity indicates it is an estimate). Figure 1 displays county-by-county values of p^(s). This figure indicates that heartworm is most problematic in the Lower Mississippi Valley. The role of factors in explaining the prevalence rates will be discussed in Section "Factor quantification". No factors are involved in the calculation of p^(s).