## 2 Materials and Methods
### Data Management and Analysis  
During cell counting and bacterial counting, for each bulk-tank milk sample, the results of the two sub-samples from each sample were averaged and, then, the two means were again averaged for the final result regarding each bulk-tank milk.  
The data were entered into Microsoft Excel and analysed using SPSS v. 21 (IBM Analytics, Armonk, NY, USA). A basic descriptive analysis was performed. Exact binomial confidence intervals (CI) were obtained. For all statistical analyses and according to the standards employed for analyses of SCC, these were transformed to somatic cell scores (SCS) by using the equation \(\text{SCS}=\text{log}_{2}(\text{SCC}/100)+3\)[22; 23]. TBC were transformed to \(\text{log}_{10}\), and the transformed data were used in the analyses. At the end, for presentation of the results, the transformed findings were back-transformed into \(100\times 2^{\text{(SCS}-3)}\) and \(10^{\text{log}}\) data.  
Initially, SCC and TBC were compared between farms in accordance with the breed of the animals therein, by using an analysis of variance.  
Then, the outcomes for \"increased SCC in bulk-tank milk\" (i.e., with SCC over \(0.75\times 10^{6}\) cells mL\({}^{-1}\)) and \"increased TBC in bulk-tank milk\" (i.e., with TBC over \(1500\times 10^{3}\) cfu mL\({}^{-1}\)) were studied. The following variables were assessed for the potential association with SCC or TBC in the bulk-tank milk of the farms: breed, management system applied in the farm, application of machine-miking in the farm, month of lactation period at sampling, number of animals in the farms, average per animal yearly milk production in the farm and application of teat disinfection at milking. For each of these variables, categories were created. Exact binomial confidence intervals were obtained. Initially, the importance of predictors was assessed using cross-tabulation with Pearson's chi-square test univariable analysis without random effects. Subsequently, multivariable models were created using mixed-effects logistic regression with farms as the random effect, as defined by \(\hat{\text{Y}}=\text{b}_{0}+\text{b}_{1}\text{X}_{1}+\text{b}_{2}\text{X}_{2}+ \ldots+\text{b}_{1}\text{X}_{1}\) (\(\hat{\text{Y}}\): dependent variable, \(\text{X}\): independent variables) and initially offering to the model all variables, which achieved a significance of \(p<0.2\) in the univariable analysis. The variables were removed from the initial model by backwards  
Figure 1: Locations of 444 small ruminant farms around Greece that were visited for bulk-tank milk sampling.  
elimination. The \(p\) value of removal of a variable was assessed by the likelihood ratio test, and for those with a \(p\) value of \(>\)0.2, the variable with the largest probability was removed. This process was repeated until no variable could be removed with a \(p\) value of \(>\)0.2. The variables required for the final multivariable model on each occasion are shown in Table S2.  
Separate analyses were performed for sheep flocks and goat herds. Initially, the analyses for the outcomes \"increased SCC in bulk-tank milk\" and \"increased TBC in bulk-tank milk\" were performed by taking into account all breeds, independent of the number of farms with each breed. Then, the analyses were repeated by taking into account only farms with the six most frequently recorded sheep breeds and the four most frequently recorded goat breeds.  
For the evaluation of the zootechnical characteristics, [PERSON]'s chi-square test or analysis of variance was used as appropriate.  
In all analyses, statistical significance was defined at \(p<0.05\).