# Use of Real-Time GNSS-RF Data to Characterize the Swing Movements of Forestry Equipment
## Materials and Methods
The resulting data from the field observation data sheets and the data received from the Garmin GNSS-RF receivers were entered into a spreadsheet and imported into the statistical analysis environment \"R\". The data were then processed, analyzed, and interpreted following the flow diagram represented in Figure 2.  
A chi-squared ANOVA test was performed to determine the significance of each individual parameter on the proportion of correct classifications. The parameters tested included transmission interval, swing angle, transponder location, cycle element, and the interaction of transmission interval and swing angle. Additionally, a binomial logistic regression was used to determine the influence of the predictor variables on cycle element classification of the GNSS data when compared to the field observations. A regression based two-one sided \(t\)-test (TOST) equivalence test was performed to analyze whether the predicted angles of the model derived from GNSS-RF data were statistically similar to the observed angle measures. To further analyze the relationship between observed and predicted angle measures derived from the GNSS-RF data, a linear regression based adapted two-one sided \(t\)-test (TOST) was performed with bootstrapping in order to determine whether the null hypothesis of dissimilarity could be rejected for the observed angle measures and predicted values. Unlike traditional hypothesis testing where a failure to reject null results in a conclusion of indifference, an equivalence test starts with the assumption of dissimilarity, meaning that a rejection of null indicates similarity. This analysis process then shifts the burden of proof onto the model's ability to derive accurate predictions. Equivalence testing was originally derived from bioequivalence testing used in the development of pharmaceutical drugs, and has been successfully adapted and utilized in tree physiology and biometrics research [27; 28]. While TOST tests for population-wide agreement, the regression based adaptation discussed by [PERSON] et al. also addressed point to point agreement between observed and predicted values [28]. This adapted analysis is able to test how well the distributions of the observed angles match the distribution of the predicted angles. Additionally, the ability to use bootstrap resampling makes this statistical approach favorable. Resampling was not done to provide an estimate of the distribution of the predicted values. The data retrieved from the GNSS-RF data packets and subsequent derivations provided us with the predicted value distribution. Rather, the bootstrap resampling is included to provide an estimate of the sampling distribution within the range of predicted angle measures; providing a larger sample size than could feasibly be obtained in fieldwork alone. The ability to increase sample size can strengthen the evidence for similarity in equivalence-based tests [28]. All statistical analysis was performed in R [29]. The equiv.boot function in the \"equivalence\" package was used to evaluate equivalence tests [30]. A total of 12 equivalence tests were conducted using 95% confidence intervals. These represented all combinations of the three transmission intervals (3), GNSS-RF transponder locations (2), and cycle elements (2). The equiv.boot function analyzes whether the slope and intercept of the regression of predicted angles fall within the desired region of equivalence, determining similarity or dissimilarity to observed angles. The region of equivalence for the regression was tested at \(\pm\)10% for both the slope and the intercept and 10,000 bootstrap replications were performed [28]. Equivalence testing shifts the burden of proof to difference. Figure 2: Flow diagram showing the progression of analysis of the spatial and observed data.