# Evaluation of Tooth Movement Accuracy with the F22 Aligner System: A Retrospective Study
## 2 Materials and Methods
### Statistical Analysis  
All the data obtained were synthesized and expressed as means and standard deviation (SD) for each movement analyzed and for each tooth type (incisors, canines, premolars and molars), per arch (maximla and mandible) and for both (total). The following data are reported considering the absolute values of the movements prescribed (\(|\text{T1}|\)) and those achieved (\(|\text{T2}|\)). The average values of imprecision (\(|\text{T1}-\text{T2}|\)) and accuracy \(|\text{T2}/\text{T1}|\times 100\) were also subjected to descriptive analysis.  
After verifying the normal distribution of the data obtained through the Anderson-Darling test for each single angular movement, the accuracy of each individual movement  
Figure 4: Summary of intra-arch linear measurements in the pre-treatment (**A**), reference (**B**) and post-treatment model (**C**). Ic: inter-canine width; lp1: inter-first-premolar width; lp2: inter-second-premolar width; Im: inter-molar width.  
was investigated by comparing the various tooth types in the two arches using the Kruskal-Wallis test. Any relationship between accuracy (dependent variable) and independent variables was investigated using chi-squared automatic interaction detection (CHAID) regression trees [35], as a function of recursive partitions (splits) of the data. The independent variables investigated were the amount of prescribed movement (T1) not expressed as an absolute value, tooth type (incisors, canines, premolars and molars for both arches), presence or absence of grip points and age and sex of the subjects examined.  
As regards linear intra-arch distances, the mean initial (T0), prescribed (T1) and achieved (T2) measurements were reported as means and SD. ANOVA was carried out to verify the presence or absence of statistically significant differences between the linear measurements (T0, T1 and T2). Significantly different measurements were directly compared (T0 - T1; T0 - T2; T1 - T2) via the Siegel-Tukey test.  
After 4 weeks, intra-arch linear distance measurements were re-performed on 50% of the total sample to verify the repeatability of linear measurements. The method error was calculated via the Dahlberg test, and the systematic error using Student's dependent \(t\)-test. Dahlberg values were in the range between 0.071 mm and 0.294 mm, with an average value of 0.205 mm. The average \(p\) value was 0.43, and in no case was there a statistically significant difference between the various measurements, evidencing the good repeatability of the same.  
All statistical analyses were performed with a significance level set at 0.05 (\(p\leq 0.05\) considered significant).  
On the basis of a sample of 120 cases, it is possible to affirm that the probability of rejecting the hypothesis of equality between averages of inclination between the study sample and the control sample is greater than \(\pi\) = (1 - \(\beta\)) = 0.9999, when the averages between them actually differ by 1. The probability of rejecting the hypothesis of equality when instead the averages are equal is 1% (\(\alpha\) = 0.01) [36].