## 2 Materials and Methods
### Operational Sampling
#### 2.2.2 Summarizing Worker Proximity to Hazards  
We defined worker safety in terms of worker position relative to circular geofences surrounding each of the three hazards. Conceptually, the area inside each geofence was assumed to represent a work area with higher risk of fatal or non-fatal traumatic injury due to the potential for being struck by the hazard. While work inside these areas is necessary on partially mechanized operations, the presence of ground workers within geofenced areas require increased situational awareness and caution on the part of both ground workers and operators to avoid accidents. Areas beyond geofence borders encompass safe work areas, where the risk of injury from striking hazards is generally lower. Thus, at any given time, a worker was positioned either inside or outside the hazard geofences of 0-3 hazards and was classified as either safe or unsafe relative to each. Similarly, at any time, a given hazard such as the skyline carriage might have as many as three rigging crew workers in close proximity.  
Using the statistical programming environment, R, we created geofences centered at each hazard's coordinates, as recorded by the associated Atlas PT (or Garmin, in the case of the snag). The carriage geofence was assigned a radius of 30 m, approximating one tree length, to encompass the risk of being struck by both the carriage itself, swinging choker cables, or logs being yarded by the carriage. The loader geofence also had a radius of 30 m (one tree length). The snag's geofence radius of 60 m represented two tree lengths, which is the standard recommended safe working distance from danger trees published by OSHA [6] (1910.266(h)(1)(vi)).  
For each one second time stamp in the operational data, we calculated the distance of all ground crew from each of the three hazards. For the purposes of spatial analysis, and in order to summarize 6-7 entities moving dynamically in time and space, we grouped proximities in 5 m increments from 0-350 m. We then summed the frequency at which workers occupied each proximity zone at each of the three timber sales, as well as the proportion of time spent in safe and unsafe zones, internal and external to the geofence associated with each hazard. To simplify analysis, ground workers were analyzed as a group rather than individually. Rigging crew workers in the region regularly alternate roles, switching among, for example, hooking and chasing, and thus summarizing across all work tasks allowed workers to retain the same Atlas PT units without stopping to switch. Also, for the purposes of analysis, the locations of the workers and hazards reported by Atlas PT GNSS positioning were considered observed coordinates with an expected degree of error comparable to the error evaluated previously in the controlled experiment.  
We used the Marascuillo Procedure for comparing multiple proportions to test the null hypotheses that the proportion of observed worker presence in unsafe areas did not differ by (1) timber sale or (2) hazard type. The Marascuillo Procedure compares the test statistic (see Equation (3)) to a critical value (Equation (4)) calculated for each pair of proportions in a way that accounts for degrees of freedom when comparing multiple proportions simultaneously.  
\[value=|p_{i}-p_{j}| \tag{3}\]  
\[critical\ range=r_{ij}=\sqrt{X_{1-\alpha,\ k-1}^{2}}\sqrt{\frac{p_{i}(1-p_{i})} {n_{i}}+\frac{p_{j}(1-p_{j})}{n_{j}}}, \tag{4}\]  
where \(X_{1-\alpha,k-1}^{2}\) is the chi-square distribution with a confidence interval of 1 - \(\alpha\) (\(\alpha\) is the significance level) and degrees of freedom equal to \(1-k\), (\(k\) equals the number of populations). \(p_{i}\) represents the proportion for sample \(i\), \(p_{j}\) represents the proportion for sample \(j\), and \(n\) represents the sample size. If the value from Equation (3) is greater than the critical range, then the two compared proportions are significantly different.